Producer theory

A producer of cement has a monopoly of the market in the area adjoining his plant, but is an insignificant factor in the rest of the country, where there are many competing producers. He can sell any desired portion of his output in the competitive market at the price there prevailing. Given the price prevailing in the competitive market, the demand schedule in his own monopolized market, his own average cost schedule, and any additional information which may be necessary for the solution of the problem, find the price he should charge in his own market, and the quantities he should sell in each market, to maximize his net revenue.

Discuss the significant of variability of the proportions of the factors of production and of variability of the supplies of the productive factors for a marginal productivity theory of distribution.

(Answer either A or B)

A. State briefly the doctrine of market price and natural price of the early classical economists; contrast this with Marshall’s analysis of long-run and short on price, and give your own view of the correct classification of viewpoints with respect to time.

B. State and critically discuss the classical doctrine of productive and unproductive labor, and in view of the issues raised formulate a correct definition of production in economics.

Indicate whether each of the following statements is True, False, or Uncertain and justify your answer briefly.

Production of a commodity occurs under conditions of fixed proportions. The supply curve for A shifts to the right. It is to the advantage of the owners of A that expenditure on A shall have represented a small part of total costs.

A firm will not carry on production at a given level of output, if one factor exhibits increasing average returns at that output level.

When a firm is in equilibrium, the ratio of the price of a factor to the marginal physical product of the factor determines the marginal cost of production.

If the demand for output is perfectly elastic, a decline in the price of factor A will always increase the demand for factor B unless A and B are perfect substitutes (only two factors employed).

If the demand for output is less than perfectly elastic, a decline in the price of A may either increase or decrease the demand for factor B.

If a monopsonist is not a monopolist, it is possible to construct the monopsonist’s demand curve for a factor.

If all the factors used by a firm are paid the value of their marginal products, the sum of the payments will equal the total receipts of the firm.

If all factors are paid the value of their marginal products, it would not be possible to increase total real output of the economy by any change in the allocation of factors.

Briefly discuss the familiar diagram of a family of short-run cost curves for a firm, with an “envelope” as a long-run curve. State the main “cases” for price-equilibrium under monopoly and under “perfect competition.” Explain why the point of tangency with both curves descending may be such an equilibrium-supply, and particularly why it locates the minimum cost for the corresponding output.

Define briefly the following terms and indicate their use in economic theory:

Backward bending supply curve

Giffen effect

Composite demand

Elasticity of substitution

Exhaustion of product

Marginal value product

Sunk costs

Rent

Firm

Present value

Rate of time preference

Describe the cost curves for an individual firm, explaining the relation between short-run and long-run curves, average and marginal cost curve. Explain the equilibrium of the firm for various market conditions of competition.

b. Describe the demand curves on the part of the individual firm for factors of production under various market conditions of competition.

c. Demonstrate that (a) and (b) are fundamentally translations of one another.

It is sometimes alleged that unionized firms are not injured by competition with non-union firms in the same industry because the presence of the union wage scale and working conditions enables the firm to obtain better quality labor, to have better labor morale and labor relations, etc.

Analytically, are these arguments well-founded? Discuss.

What data would you need on union and non-union firms to confirm or reject these arguments as an empirical proposition? In particular, would you use comparative output per man-hour, unit labor costs, or what? Why one and not another?

Indicate whether each of the following statements is true (T), false (F), or uncertain (U). Give a brief explanation of your answer.

If the income elasticity of demand for a product is greater than unity, the relative price of that product will rise as real per capita incomes increase, i.e., will rise relative to products with income elasticity less than unity.

When a firm is producing in a region of rising marginal cost, that firm is in equilibrium because average costs are increasing also.

The market price of steel and iron scrap fluctuates more than the price of finished steel primarily because the scrap market is competitive while the finished steel market is in the hands of monopolists.

If automobile firms overproduce and competition forces down the price of new cars, this harms a car owner who has purchased his car on credit since his mortgaged car has suffered a decline in price.

It is frequently stated that the more disagreeable or dirty a job is the more it will be necessary to pay workers, but this is contradicted by the fact that college professors earn more than foundry workers.

Lowering the support price of wheat in the United States at present would aggravate rather than relieve the problem of surpluses, since farmers would simply produce proportionately more in order to maintain their incomes.

An increase in demand for a commodity increases its price, but an increase in price reduces demand. Increases in demand tend, therefore, to be self-compensating.

Increasing the minimum wage rate to one dollar per hour will have little or no effect outside the South, since most workers now being paid less than one dollar per hour are in the South.

In the absence of factors making for an increase in demand, and other things being equal, a new method will be introduced sooner in a competitive than in a monopolized industry.

Without collective bargaining, the workers’ market disadvantage would enable the owners of other productive agencies to appropriate income that would otherwise go to labor.

With collective bargaining, workers in general can appropriate income from the owners of other agents.

In equilibrium, it is enough to know the marginal factor cost of any one factor and its marginal physical product to know the marginal cost of the product, even though the product is produced by many factors.

The demand for a product at the market price is inelastic. It follows that the product must be produced under conditions of net internal diseconomies.

Under competition, the marginal efficiency of capital is equal to the marginal physical product of a particular kind of capital good times the price of the product.

To assert that the rate at which a consumer is willing to substitute x for y decreases as the quantity of x increases along an indifference curve is equivalent to saying that the indifference curve is concave toward the origin.

Discuss the role of “Euler’s theorem” in distribution theory, and give your own position on the issues.

Define (a) perfect competition, (b) oligopoly, (c) monopoly, (d) monopolistic competition, (e) cartel, (f) monopsony.

State the conditions of maximum return for the individual firm in a form in which they are applicable to all the preceding market conditions. Indicate the special form which these take for each of the preceding market conditions.

Define “length of run” and state is effect on these conditions.

Indicate whether each of the following statements is true (T), false (F), or uncertain (U). Explain briefly the basis for your answer.

_____. If the market elasticity of demand for peaches is -2, a peach producer whose output accounts for 1/20th of the total supply of peaches will be faced by a demand function of elasticity -40.

_____. If a constant amount of carpenters’ services is required per unit of housing constructed, and the elasticity of demand for housing is -1, the elasticity of demand for carpenters’ services used in housing must be less (in absolute value) than unity.

_____. If the production possibilities for wire can be represented by a Cobb-Douglas production function, and the wire industry is competitive, a rise of 10 per cent in the wages of wire-workers will lead to a reduction of 10 per cent in their employment.

_____. The elasticity of demand for a group of commodities with respect to the average price of the group can never be larger in absolute value than the largest of the individual price elasticities of the commodities which comprise the group.

_____. If total consumer expenditures are the same before and after a tax, then an excise tax on a consumer good of elastic demand will lead to an increase in consumer spending on other consumer goods, while an excise tax on a consumer good of inelastic demand will lead to a decline in consumer spending on other consumer goods.

_____. A tax of 10 per cent per year on the rental value (actual or imputed) of all land will in the long run lead to a lowering of the marginal productivity of labor in agriculture.

_____. A technological advance opening up widespread possibilities for new investment in the electronics industry at very high rates of return will tend to lower the real value of the existing stock of residential housing in the United States.

_____. A supply curve passing through the origin has an elasticity equal to unity.

_____. Given certainty, no firm would hold inventories.

_____. A negatively sloping supply curve of labor implies a positively sloping demand curve for leisure.

_____. It is impossible to derive a supply function for a monopolist.

_____. A legally enforced minimum wage for a particular occupation may increase employment in that occupation.

_____. Wage rates rise while interest rates remain the same. It follows that the ratio of capital to labor will increase.

_____. Engel’s laws are due to Friedrich Engels.

Derive a demand function for a factor of production. What does it depend on? What things are held constant in the derivation?

In the analysis of supply, an important role is played by a fourfold classification of economies or diseconomies of production: internal and external, each of these cross-classified as pecuniary and technical.

What does each of the four concepts mean and what role does it play in the analysis of supply?

For each of the four concepts, what would be its counterpart in the analysis of demand? If you can, illustrate by example each type of economy, each type of diseconomy.

Why is so much more importance attached to these concepts in the analysis of supply than in the analysis of demand?

Indicate whether each of the following statements is true (T), false (F), or uncertain (U). Explain briefly the basis for your answer.

A tax on a product whose supply is of zero elasticity will have no effect on resource allocation.

If factors of production are used in absolutely fixed proportion in the production of a particular product, the demand for each of the factors by the producers of the product will be completely inelastic with respect to price.

Since 1951 interest rates have risen by about 50 percent whereas real wages have risen only by approximately 24 percent. This implies that firms are and will be using more labor per unit of capital than they did in 1950.

An income tax has no resource misallocating effects.

A competitive firm will increase its demand for factor A as a result of a fall in the price of factor B.

“A monopolist has no supply curve.” Hence it is impossible to predict his response to a shift in the demand curve facing him.

Budget studies have yielded an income elasticity of demand for food of .5 for urban families and of . 35 for farm families. This implies that farm families have substantially different tastes or consumption habits.

Price stabilization at the mean of fluctuating prices would harm consumers.

Product A is one of the major inputs used in the production of product B. Price control is imposed on product A, but not on product B, at a level below the equilibrium price of A. This will result in a fall of the price of B.

A tax of 50% of the gross sale price of all new automobiles in the U. S. will in the short run tend to double the market value of used automobiles, and in the long run tend to double the gross market price of new automobiles as well.

We frequently speak of “the substitution of capital for labor”. What do you take this phrase to mean (a) for an individual firm; (b) for the economy as a whole? Does your interpretation allow for the fact that the major part of the cost of new capital equipment is labor cost?

Describe the cost and supply aspects of the long-run equilibrium conditions under competition for two joint-products, when the proportions in which the two products are produced are: (a) non-variable, (b) variable.

Answer whether the statement is true, false, or uncertain. In each case, write a few sentences explaining your answer. Your grade will depend heavily on your explanation.

The elasticity of a linear supply function that passes through the origin is always unity.

If a firm is producing in the region of rising marginal costs, the firm is realizing profits.

An effective price ceiling on cotton, i.e., one that holds its price below the free market level, will decrease the price of textiles.

Steel prices and output usually move together during business cycles. This means that the income effect of a rise in price is greater than the substitution effect.

Firms try to minimize unit costs; at the point where unit costs are at a minimum, they equal marginal costs; therefore, firms tend to operate where their unit and marginal costs are equal.

Marginal productivity theory does not apply if factors are always used in fixed proportion.

Since all firms in competitive industry have the same marginal costs, it is meaningless to speak of more or less efficient firms.

If a Paasche price index is higher than the Laspeyres' index, tastes must have changed.

The demand for a product at the market price is inelastic. It follows that the product must be produced under conditions of net internal diseconomies.

“Commodities with higher, income elasticities have higher demand (price) elasticities.” (Stigler, 1952 ed., p. 45)

If X and Y are substitutes, a decline in the price of X can increase the amount of Y demanded only if Y is an inferior good.

The elasticity of demand for a group of commodities with respect to the average price of the group can never be larger in absolute value than the largest of the individual price elasticities of the commodities which comprise the group.

A rational consumer is insatiable.

A. The demand function for a product is P = 115 — Q. The total cost of producing Q units in one plant is given by TC = 400 — 100Q^{2} + Q^{3}. Only one-plant firms are allowed.

(a) What is the long run competitive solution (price, quantity, and the number of firms in this industry)?

(b) What would be the approximate price charged and the quantity produced if there was only one one-plant firm and it maximized its profits. (Work only with round figures.) How much profit would it make?

B. Assume now that a firm may have more than one plant. What is the monopoly solution? How much profit will it make?

Answer each question “true”, “false”, or “uncertain”, and explain your answer briefly. Your grade will depend heavily on your explanation.

A competitive firm will increase output as the result of a fall in the price of one of its inputs.

In equilibrium, a competitive firm has all the business (sales) it wants. Hence advertising is incompatible with either competition or equilibrium.

Duopolists with different cost functions cannot achieve a monopoly price without transfer payment between the firms.

A multiplant firm will schedule its output so that the marginal costs are equal in all plants.

The price of haircuts in Chicago is approximately 40 percent higher than in New York; therefore, average earnings of barbers in Chicago are higher than in New York.

The supply curve of a monopolist is inelastic at the point of maximum monopoly profit.

If it takes one day to catch a beaver and two to catch a deer, one deer will exchange for two beavers.

Assume that the world demand elasticity for tin is -2 and that Bolivia produces 1/3 of the world’s tin. Therefore, the elasticity of demand for Bolivian tin is at least -6.0 (in absolute value).

A safety ordinance prohibiting the use of automobiles older than 10 years will increase the long run demand for new automobiles.

The own-price elasticity of demand for a commodity is no smaller in absolute value, than the marginal propensity to consume that commodity.

For a single consumer the sum of income elasticities of demand for all commodities is unity, while the sum of their price elasticities is zero.

It is a convention in economics to draw consumption indifference curves convex to the origin, but we have no way of knowing whether they really are.

Each firm in an industry is given a license to operate and no new firms are allowed to enter. The value of a license rises over time. Does this prove that firms operate subject to diseconomies of scale?

If the supply schedule of an industry is perfectly elastic then the production function for the industry is characterized by constant returns to scale.

No one would resort to the cultivation of inferior lands if he did not run into diminishing marginal returns on fertile land. Since inferior lands are in cultivation, diminishing returns must be present.

If there are empty seats on a train then marginal cost pricing requires that new passengers should ride free.

I. Indicate whether each of the following statements is true (T), false (F), or uncertain (U) and state briefly (on this paper) the reason for your answer.

The elasticity of a straight line demand curve varies from point to point.

In the long run, demand has no influence on the price of the product of a competitive industry that uses no specialized resources.

Marginal revenue is always greater than average revenue when average revenue is rising as quantity increases.

[4. and 5.] Assume that the government is going to purchase a predetermined quantity of rice for foreign relief and that it is considering making its purchases (a) directly from the growers of rice, or (b) through the regular dealer on the grain exchange. Assume also that there are no other governmental actions affecting rise growing or marketing.

The price to the domestic consumer of rice that remains will be higher in case (a) than in case (b).

The price received by the farmer for the rice that remains will be higher in case (a) than in case (b).

An “inferior” good is one such that a larger quantity is demanded at a high than at a low price.

If the quantity of Y increases and the quantity of X decreases in such a way as to keep total utility constant, then the rate of substitution of Y for X is independent of the quantity of X.

The income of the farmers raising corn increases when the price of corn rises. The rise in income is the “income effect of the rise in price.”

[9., 10., 11.] The Gimcrack Company is a monopoly, selling in two distinct markets. Transportation costs between the two markets can be neglected.

The company will always charge the same price for gimcracks in the two markets.

The company will sell such quantities in the two markets as will make the elasticities of demand the same in the two markets.

The company will sell such quantities in the two markets as will make marginal revenue the same in the two markets.

III. Find the mistakes (there are at least six) in the accompanying diagram showing long run and short run marginal and average cost curves for an individual firm, and explain the general principle corresponding to each particular mistake.

I. Indicate which alternatives, if any, are correct or fill in the indicated blanks. Where you think it required, briefly justify your answer.

Marginal revenue (a) cannot (b) may (c) must rise as output increases.

A monopolized product initially sells for $1. A tax is imposed on the product. A tax of t cents per unit will reduce marginal revenue at the pre-tax output (a) more, (b) less, (c) the same amount, (d) sometimes more sometimes less than a tax of t per cent.

In the preceding example, the imposition of a tax of t cents will lead the monopolist to reduce output (a) more, (b) less, (c) the same amount, (d) sometimes more sometimes less than a tax of t per cent.

A reduction in demand for a product is followed by a rise in quantity sold despite no change in conditions of supply. It follows that the product is being produced (a) in a competitive industry with increasing returns, (b) in a competitive industry with external diseconomies, (c) by a monopolist, (d) this result is impossible under any of the preceding conditions.

Assume that the government has been supporting the price of wheat by buying any wheat offered to it at its support price. Suppose it abandons the program. In the new position of long period equilibrium the total amount received by producers will rise (a) only if the market demand for wheat is inelastic in the range between the support and new price, (b) only if the market demand for wheat is elastic in this range, (c) whatever the demand elasticity, (d) under no circumstances.

An individual buys four commodities, W, X, Y, and Z, currently spending one-quarter of his income on each. The income elasticity of W and X are 2; of Y, 1. The income elasticity of Z is _________?

Consider three demand curves for commodity X: A, for given money income and other prices; B for given apparent real income in Slutsky's sense; C, for given real income in Hicks' sense. Let all three curves go through the point $(p_o,x_o)$. If X is a superior good, then for a price higher than $p_o$, the quantity demanded will be larger for ____ than for ____ than for ____ (Insert A, B, C, in correct spaces).

Suppose p_o = \2$,$x_o = 40$,thecorrespondingmoneyincomeis$200, and the income elasticity of demand for x is unity. Suppose that at a price of $2.50, the quantity demanded on Curve A is 20. Then the income compensation required to pass from A to B is $ _____ (be sure to indicate sign of change) and the quantity demanded on curve B is _____.

If long run average cost (LRAC) equals short run average cost (SRAC) at an output on the falling segment of the LRAC curve then short run marginal cost (SRMC) (a) exceeds, (b) equals, (c) is less than long run marginal cost (LRMC) at that output.

If LRAC is rising and less than SRAC, then SRMC is (a) rising, (b) falling, (c) greater than SRAC, (d) less than SRAC.

In a discussion of the World Series last fall, Jones offered to take either side of a bet with Smith involving a payment of $2 by one party if the Pirates won, of $1 if the Yankees did. It follows that Jones' estimate of the probability that the Yankees would win is _____ and that his utility function of income is (a) concave upward, (b) linear, (c) concave downward, (d) not concave upward, (e) not concave downward.

Alternatively, Jones refuses to take either side of the preceding bet but offered to take either side of a bet involving a payment of $200 by one party if the Pirates won or of $100 if the Yankees did. This behavior (a) contradicts or (b) is consistent with the expected utility hypothesis.

II. Translate the following quotations into economics and discuss:

"Costs are down partly because contractors expanded their equipment to get ready for the Federal Government's enlarged program. But it was cut back in 1959. … Some contractors needed work to pay for their expensive equipment, and they began making low bids, often at cost, to get the work. They complain bitterly about the price-chopping competition." (Time, Dec. 12, 1960)

"Most foods will be much more abundant and a bit cheaper in 1959 than they were this year [1958]. This optimistic forecast was made by the Agriculture Department which warned, however, that retail price cuts won't be as deep as the prospect of plenty would seem to indicate. Higher marketing and processing costs, officials explained, will partly offset the expected decline in food prices at the farm."

Mark the following True, False, or Uncertain. Explain your answers very briefly.

A monopolist can afford to pay wages below the market wage rates.

A rise in the price of gasoline will lead to a rise in the price of tires.

In a long run competitive equilibrium, the marginal firms produce where marginal costs equal average total costs.

If a firm is in long run equilibrium, it is also in short-run equilibrium, whether it is a competitive or a monopolistic firm.

If a production function is characterized by constant returns to scale, an increase in the use of one factor by 10% will increase output by less than 10%.

A rise in the price of any factor used by the firm (other things unchanged) will always lead to a decrease in production by the firm.

A firm producing the same product in many plants will determine the quantity produced in each plant so that average costs will be equal in all the plants.

If a firm has zero variable costs, then its best profit output is where the elasticity of demand for the product is unitary.

A firm will carry production to the point where the marginal productivities of all variable factors are equal.

In a competitive industry with external economies, the total short run supply curve of the industry shifts to the left when there is a permanent decrease in demand for the product.

A monopolist is faced with the following stable demand schedule for his patented machines:

Price per machine (thousand dollars) / Quantity per month / TR / MR / TC / MC 40 / 1 35 / 2 30 / 3 25 / 4 20 / 5 15 / 6 10 / 8 5 / 10

The Costs of production are $5000 per machine, and the fixed costs are $16000 per month.

1.) Compute total and marginal revenue and total and marginal costs in the table above.

2.) Find the equilibrium price, quantity and profits of this firm.

3.) A tax of $60,000 per month is imposed on the firm. Find the new price, quantity and profits.

4.) Instead, a tax of 60% of the market price is imposed on the machines. What will be the monopolist price, output, profits? The tax revenues?

5.) Alternatively, a tax of $24000 per machine is levied. What are the equilibrium price, quantity, profits and tax revenues? What will be the long-run equilibrium quantity?

6.) If no tax is imposed, but a maximum price of $10,000 is enforced, what will be the quantity sold? The Profits?

7.) State your preference among the 5 alternatives ((2) – (6)) above, and justify your choice briefly.

Derive the expression for the elasticity of demand facing a particular producer in terms of the elasticity of “total demand” in the market and of the elasticity of “other supply”.

True, False or Uncertain. In each case write a few sentences explaining your answer.

If the firms in the coal industry were to merge into one single firm, the demand curve for coal miners would become more elastic.

Marginal cost exceeds average cost wherever marginal cost is rising.

In the case in which factors combine in fixed proportions to produce a product X, the elasticity of demand in industry X for a factor will be greater, the larger is the fraction of the total costs of producing X which is spent on hiring the factor in question.

A firm having monopsony power in the market for its labor will hire workers up to the point where their wage is equal to their marginal value product (marginal physical product times marginal revenue), not to the value of their marginal physical product.

If, at a point in a homogeneous production function, the marginal product of A is rising, the marginal product of B will be negative. (Consider A and B as the only two factors.)

If, at a point in a homogeneous production function, the marginal product of B is negative, the marginal product of A will be rising. (Consider A and B as the only two factors.)

Discuss and comment on Marshall’s four rules of derived demand

Discuss the relationship between short run and long run cost curves. Is a shorter run marginal cost curve always more elastic than a longer run marginal cost curve going through the same point on the long run average cost curve

True, False, or Uncertain. In each case write a few sentences explaining your answer. Your grade will depend heavily on your explanation.

If the United States exports one tenth of its coal, the elasticity of supply of domestic coal being unity, the elasticity of supply of U.S. coal exports must be at least 10.

If the price of X rises while the price of X stays constant, the amount of Y demanded will always increase, so long as X and Y are substitutes. (Assume money income and other prices remain unchanged.)

The own-price elasticity of demand for a commodity must always equal or exceed, in absolute value, the cross elasticity of demand for that commodity with respect to the price of any other commodity.

The own-price elasticity of demand for a commodity must always equal or exceed, in absolute value, the marginal propensity to consume that commodity.

When the production function is such that factors of production combine with each other in fixed proportions to produce a product, the own price elasticity of demand for the use of any of the factors in the production of the product must be less than the price elasticity of demand for the product. (Assume that the production of the product in question is competitive.)

The income elasticity of demand for a commodity is the marginal propensity to consume that commodity divided by the average propensity to consume that commodity.

The elasticity of demand for labor in the production of automobiles will be lower in the case in which the quantities of other factors are given than in the case in which the prices of other factors are taken as given.

The elasticity of demand facing a monopolist will be lower than the elasticity of demand facing the same industry if it were competitive.

The welfare cost of a 5 percent tax on automobiles is the same as the welfare cost of a 5 percent subsidy on all goods and services other than automobiles.

The welfare cost per dollar of tax receipts of a 5 percent tax on automobiles is the same as the welfare cost per dollar of tax receipts of a 5 percent tax on all goods and services other than automobiles.

If, at a point in a production function which is homogeneous (of degree 1), the marginal product of factor B is negative, the marginal product of factor A will be rising (in the sense that the marginal product of A will be higher when the proportion of factor A to factor B is slightly increased). Assume that A and B are the only two factors.

The supply curve of labor can be backward bending only if leisure is an inferior good.

The demand for the services of a factor of production in a particular industry will be more elastic, the larger is the share of that factor in the total costs of the industry in question.

All short run average cost curves are tangent at (at least) one point to the long run average cost curve.

The GJS corporation, manufacturers of gadgets, have determined that for every 10 per cent increase in the capacity of a gadget factory, minimum short-run average total cost falls by 1 per cent throughout the relevant range of capacities.

What can you say about the production function for gadgets over the relevant range?

Suppose that the company hires two factors of production, labor and capital, and pays each its marginal product. Will anything be left over for the owners of the company who contribute no services? Explain.

Suppose that the company wants to build a plant to produce 10,000 gadget per week. What can you say about the size of the plant that will produce these most efficiently?

By means of appropriate diagrams and/or explanations, show the short-run effect of each of the following taxes on the output and profits of a monopolist.

An excise tax of 10 cents per unit of product.

An excise tax of 10 percent of the price of the product.

A corporate profit tax equal to 50 percent of net profits.

On the following questions, indicate whether True (T), False (F), or Uncertain (U), with brief explanation.

A firm produces output $x$ using inputs $a_1$ and $a_2$, which it purchases competitively at prices $p_1$ and $p_2$. Its total cost is given by

where $A$, $?$, $a_1$, $a_2$ are constants.

(a) The demand for the first factor is given by

(b) The production process of the firm exhibits constant returns to scale.

(c) The above cost function corresponds to a Cobb-Douglas production function.

In Ronald Coase’s celebrated article on the nature of social cost the first example concerns the externality imposed by a cattle ranch that is next to a corn farm. The cattle can wander into the corn farm and eat some of the corn. This increases cost to the corn farmer and imposes an externality on him. Construct a formal analysis of the following situation:

(i) Let there be two firms such that the output of each firm is an “input” in the production function of the other. Let the other inputs be of the same kind, say, labor and capital. Let the output prices be given and let the input prices be given. Derive the profit maximizing solution for the two firms.

(ii) Give a precise measure of the externality and show that the solution in (i) does not depend on who pays whom.

(iii) Under what conditions will the dollar amount of the externality be proportional to the output of the other firm?

Consider an economy with two, L and K, factors of production producing goods, X and Y, under conditions of constant returns to scale. Assume that X is relatively L-intensive at all factor prices.

(a) Analyze the effect of an increase in L on the production of X and Y on the assumption that the relative price of X and Y is constant. How would the increase in L affect the share of L in the economy’s income?

(b) Analyze the effect of an increase in the relative price of X on relative and absolute factor rewards, and on the share of L in the economy’s income. Would your answer be altered if both production functions were of Cobb-Douglas type?

(c) Analyze the effect of an increase in K on the relative price of X on the assumption that neither X nor Y is inferior in the community’s consumption.

Discuss the probable shape of the long-run cost curve for an industry operating under approximately perfect competition. How would it differ in the short run, i.e., in response to an unanticipated shift in the demand-curve for the product, assumed not to be permanent?

Indicate whether each of the following statements is true or false and explain briefly why.

1. An “inferior” good is one for which the marginal utility is negative.

2. The short-run marginal cost curves cross the long-run marginal cost curve from below (proceeding from left to right) at the quantities corresponding to the points of tangency of their respective average curves.

3. For a homogeneous production function of degree one, and, for given relative factor prices but varying output, both of the following are true:

a. The ratios of the quantities of the various inputs are constant at all levels of outputs.

b. The average productivities for each factor are constant at all levels of output.

4. Suppose you have the following budget data for two periods for a consistent consumer (i.e., a consumer who, in those situations where the same two commodity bundles are within his budget and he chooses one of them, will never choose the other one): prices of all goods in only the first period $p_{i1}$ for $i=1,2,\dots ,n$) and quantities purchased of all goods ($q_{i1}$ and $q_{i2}$ for $i=1,2,\dots ,n$).

Then it is true that implies that the consumer is “better off” in the first period than in the second.

5. Consider an individual’s demand functions for two goods, $x_k$ and $x_j$. Then the cross elasticity of demand for $x_k$ with respect to $p_{ik}$ is equal to the cross elasticity of demand for $x_j$ with respect to $p_k$ when only the substitution terms are considered.

6. “The more the merrier” is a denial of the law of diminishing marginal utility.

7. “The increment of product resulting from adding one more worker to a firm should not be attributed exclusively to labor because it results partly from the more intensive working of the other productive factors.”

8. A tax of 20 per cent on all wages and salaries will decrease the supply of labor by more than a tax of 20 per cent on overtime pay alone.

9. Carpenters would not receive a wage equal to the value of their marginal product if they were a “specific factor of production” in the industry using their services.

10. The demand function for labor on the part of a competitive industry can in some cases be more elastic in the neighborhood of a given point if the quantities of other factors are taken as given than if the prices of other factors are taken as given.

Sales of some firms are occurring at prices below average variable cost. Suppose there were no legal restrictions on merger. Under what conditions, if any, would the firms in the industry prefer merger as a means of reducing industry output?

Discuss the probable shapes for a particular plant of its short-run and its long-run average cost curves, and given these curves, explain the derivation of the corresponding marginal cost curves.

On what grounds can it be held that in any important industry, increase in output is in the static long-run likely to be subject to conditions of increasing cost? Give and discuss the arguments which have been presented in support of different views.

Suppose that a single monopolist takes charge of an industry which has hitherto been in the hands of a large number of independent producers and which makes extensive use of a specialized type of labor. Give an account of the factors which will determine the effect of the change on (a) the industry’s output, and (b) the volume of employment of labor by the industry.

I. (140 points) True, False, or Uncertain. Explain your answer in each case. Your score will depend heavily on your explanations.

If a firm is producing in the region of rising marginal costs, the firm is realizing profits.

The competitive firm attempts to equalize price, marginal cost and average cost.

The marginal cost of producing a commodity is equal to the price of any one factor divided by its marginal physical product, even though many factors are used in producing the commodity.

Almost all railroads are reported to have gross revenues from dining car service that are less than the direct expenses of providing the service. In their own interest the railroads should increase the price of dining car meals.

Because of the facts stated in number 19, the railroads should discontinue dining car service.

The elasticity of a linear supply function that passes through the origin is always unity.

III. (40 points)

Some prominent manufacturers such as Sunbeam, Eastman Kodak, and Bayer Aspirin, set minimum prices below which retailers may not resell their products. In most states an agreement to this effect between a manufacturer and some retailers is legally enforceable on all retailers.

(a) What is the probable effect of this practice on the net rate of return on factors of production used in retailing?

(b) What is the probable effect of this practice on the net profits of the manufacturers concerned?

Explain your answers fully.

Define the following terms precisely and indicate briefly the use made of each in economics:

Demand

Supply

Equilibrium

Indifference Curve

Marginal

Rate of Substitution

Marginal value product

Marginal efficiency of capital

Production function

Time preference

Profit

Rent

Run

Net advantages

Variable Costs

(a) “I wouldn’t take it if you paid me”. Draw the consumption indifference curves implied by this statement. (You may find it helpful to suppose first that there is some finite minimum price per unit at which the speaker would take “it”; then approach the limit implied by the quotation.)

(b) “I’ve reached the point of diminishing returns, so I better quit”. Analyze, indicating under what conditions and for what definition of diminishing returns this is a valid inference from the conditions for a maximum.

(a) Complaints are often heard about the “high” incomes of bootleggers in dry states, or gamblers where gambling is illegal, or smugglers, etc. Are high incomes in such cases evidence of the success or the failure of the laws? Explain your answer.

(b) A man buys a ticket in a lottery and wins. View this as a business transaction. How much, if any, of his prize is properly regarded as “profit”? Does your answer use the concept of “profit” implicit in the common statement “entrepreneurs seek to maximize profit”? Justify your answer and indicate the difference, if any, between the two concepts.

(a) Outline the theory of joint supply

(b) What factors determine the elasticity of the derived supply curve of one of a pair of jointly supplied items? Show the direction of influences and prove your statements graphically or otherwise.

Define the following terms precisely and indicate briefly the use made of each in economics:

Demand

Supply

Indifference Curve

Rate of Substitution

Marginal value product

Marginal efficiency of capital

Production function

Time preference

(a) Outline the theory of joint supply

(b) What factors determine the elasticity of the derived supply curve of one of a pair of jointly supplied items? Show the direction of influences and prove your statements graphically or otherwise.

Using diagrams, briefly discuss the long-run cost curve for a competitive industry. Indicate, with diagrams, the response to be expected from (a) an expansion of demand, (b) a decrease of demand, within periods too short for a significant change in the fixed investment.

Develop the major aspects of the theory of a competitive firm, and compare it with the theory of consumer behavior. What are the similarities and the differences between the two theories and the concepts used in each?

Analyze briefly each of the following propositions: Marginal productivity analysis…

proves that the existing distribution of income is ethically just;

provides a basis for understanding the demand for factors of production;

is a complete theory of the determination of the prices of production;

provides a basis for understanding the supply of factors of production;

does not apply in the case of fixed proportions.

(1 hour) Answer each question “true” or “false” and explain your answer very briefly.

It is a tautology that the average costs of all firms are equal in equilibrium in a competitive industry.

A cartel which allows its members to buy and sell output quotas will have a larger net profit for all firms combined than one which does not.

Since all firms in a competitive industry have the same marginal costs, it is meaningless to speak of more and less efficient firms.

A fall in the price of houses will increase the sales of doorbells; a fall in the price of doorbells will not increase the sales of houses; therefore Slutsky’s equation is wrong.

The average size of farm has risen in recent decades in the United States and Canada. This shows that the farm enterprise is typically subject to increasing returns to scale.

A specialized machine has a life of 5 years. Total returns to it in periods of less than 5 years are quasi-rents.

Assume that the world demand elasticity for tin is -2, and that Bolivia produces 1/3 of the world’s tin. Therefore, the elasticity of demand for Bolivia tin is at most -6. 0.

If factors of production are used in absolutely fixed proportion in the production of a particular product, the demand for each of the factors by the producers of the product will be completely inelastic with respect to price.

A supply curve is a curve displaying the quantities which will be supplied at all possible prices. It follows that there is no supply curve under monopoly.

If a firm is operating in the region of falling marginal costs, it must be making losses because marginal cost is then less than average cost.

III. (40 minutes)

It has often been suggested that the demand for a durable good could be increased if “something were done about the large number of used items on the market” The practical suggestions usually are (1) a government regulation forbidding the use of items older than some specified age, e.g. declaring all pre-1950 cars as “unsafe” and withholding license plates from them or (2) “the manufacturers should buy up the used items and destroy them or export them at a loss. Discuss the consequences of these two types of policies on (a) the demand for new durable equipment and (b) the profitability to the industry of the two policies.

IV. (40 minutes)

“The first impact of this policy (tight money) is the higher interest rate. Plainly the impact of this will be very different on a firm that has control over its prices and hence can pass along this higher cost as compared with the firm whose prices are given and which, accordingly, must bear the cost itself. The point need not be labored.

“The U.S. Steel Corporation justified its price increase of 2 weeks ago by the contention that its cost had risen. In doing so it not only conceded its ability to pass higher costs, including higher interest charges, to the consumer but based its policy on the need to do so. But no such opportunity is open to the farmer or to the smaller businessman. They cannot raise their prices, for they are market-determined. They shoulder themselves the costs of this policy.”

Analyze and evaluate this statement. Disregard the peculiar problems of monetary policy. Treat it as a question about the differential impact of a change in any factor price on a competitive firm or industry as against the impact on a monopolistic firm. Does a change in factor cost “hurt” less in one case than in the other? What do you understand by “passing the cost on to the consumer” and how does the distinction between a monopoly and a competitive industry affect this? Assume the same cost curves and the same shifts in both cases.

(60 points) Indicate whether you believe each of the following statements to be true, false, or uncertain. In each case write a few sentences explaining your answer. Your grade will depend heavily on your explanation.

If the rate of obsolescence is constant over time for each type of capital equipment, a rise in the rate of interest will shorten the optimal life of capital equipment.

If oranges are substitutes for apples, apples are complementary to cheese, and cheese is a substitute for butter, oranges and butter are complements.

If a certain commodity is rationed and subject to price control, and there is a black market price for it, the black market price is the equilibrium price of the commodity in the absence of price control.

Let ${\sum }_i{p}_{i1}{x}_{i1}$ and ${\sum }_i{p}_{i2}{x}_{i2}$ be the expenditure of a firm on factors of production per unit of output at two points in time. If ${\sum }_i{p}_{i1}{x}_{i2}>{\sum }_i{p}_{i1}{x}_{i1}$ and ${\sum }_i{p}_{i2}{x}_{i1}<{\sum }_i{p}_{i2}{x}_{i2}$, the production function of the firm has changed between the two points of time.

A company cannot have a monopoly if its shareholders receive only the normal rate of earnings on their stock in it.

If the production function of an Industry is subject to constant returns to scale, the industry supply curve will be horizontal.

If it were possible to travel backwards as well as forwards in time, everyone would be a millionaire.

The development of better fertilizer will increase the value of farm land.

Manufacturers frequently advertise that their products contain extra ingredients, and they generally succeed in selling “extra-ingredient” products (e.g. Bufferin) at higher prices than “similar” single-ingredient products (e.g. aspirin). This implies that consumers have a diminishing marginal rate of substitution between the ingredients.

The removal of a barrier to competition anywhere in the economy must make society better off.

Given:

a three-product world,

the cross-elasticity of demand of x with respect to the price of z is zero,

the own-price elasticity of demand for x is -1,

y and z are substitutes,

expenditures on X occupy half of consumers’ budgets, expenditures on Y one quarter of consumers’ budgets in the initial situation,

it follows that the own-price elasticity of demand for y is greater than 1.5 in absolute value. (For this question consider all price-elasticities defined to include the substitution effect only.)

The price-elasticity of demand on the part of a competitive industry for a factor of production will be greater, the smaller is the share of that factor of production in the total costs of the industry in question.

If production in industry X (assumed to be competitive) is governed by a Cobb-Douglas production function, then no wage set by the trade union in that industry will produce greater total labor income than any other wage.

A tax of a fixed amount per unit of output, placed upon the product of an industry with constant costs, will necessarily result in a smaller rise in price if that industry is organized (and behaves) as a monopoly than if the industry is competitive.

In an industry employing just two factors of production, the elasticity of demand on the part of that industry for either factor must be less in absolute value than the elasticity of substitution between the two factors in that industry.

(25 points)

Industry X is composed of 10 firms, and organized as a cartel. The pricing policy of the cartel is determined by the following rule: each firm will produce one-tenth of the output of the whole industry, and the price set for the final product will be just equal to the marginal cost of production in the firm with the highest marginal cost. Show how you would measure the welfare cost of this arrangement, as compared with a competitive equilibrium.

The firms now merge into a single monopoly firm, the previous 10 firms now becoming 10 divisions of the new company. All ten divisions continue to operate and have the same marginal cost functions as they did when operating separately. Show how you would measure the welfare costs of this new arrangement. Under what circumstances, if any, would these welfare costs be lower than those of case A?

The government now intervenes to break up the monopoly. The same 10 firms as existed in case A are reconstituted; collusion is somehow prevented; and merger is precluded by a requirement that no firm shall expand the total volume of its capital. Assume that the firms begin operating under this new arrangement with each of them having the amount of capital resulting from a long-run equilibrium under case B, and that the firms behave competitively. How would you measure the welfare costs of this arrangement? Under what circumstances, if any, would these welfare costs exceed those measured under case B?

Discuss the relationship of marginal cost to prices:

under short-run competitive equilibrium;

under long-run competitive equilibrium

when (1) the industry is subject to external diseconomies of large production; (2) the industry operates under conditions of constant cost.

In order that an industry shall operate at constant costs as its output is varied, what conditions must hold as to:

the definition of “industry”;

the supply curves, general and partial, of the factors used by that industry;

the mode of operation of the law of diminishing returns in that industry;

the presence or absence of internal diseconomies of large-scale firms in that industry;

the size of the changes in output?

Find the mistakes (there are at least six) in the accompanying diagram showing long and short run marginal and average cost curves, and explain the general principle corresponding to each particular mistake.

Define briefly the following terms:

Marginal revenue

Fixed cost

Income elasticity

Profit

Production function

Diminishing returns

Inferior good

Luxury

Discuss the following quotations:

(from a newspaper story) “The Sun Rose Bar and Grill…advertised ‘the largest glass of beer in the city for five cents’ and did a tremendous business in eight-ounce glasses of beer as soon as the public realized it was no April Fool proposition…

‘If enough of us do this’ said…one of the proprietors, ‘the brewers will have to cut prices!’”.

(from a newspaper story) “Domestic producers of oil contend that unrestricted imports hurt them not only because they swell the supply, but because a barrel of foreign crude costs about $1 less than a comparable barrel of U.S. crude.”

“All of this is to say, of course, that in practice what we have to reckon with is not a unique marginal cost for a given level of output, but a complex of marginal costs, each of which is pertinent to a particular period of time. As a longer period of time is considered, more of the ‘fixed factors’ become variable. Because of this greater flexibility in the production process, long-run marginal cost will generally be less than short-run marginal costs.” A. Bergson in A Survey of Contemporary Economics.

Indicate whether statement is true, false, or uncertain, and briefly give your reason.

A firm has a monopoly in its home market and also sells in a perfectly competitive world market; if its home-market price is 50% above the world market price, the elasticity of demand in the home market must be 3.

If a multiplant firm has to produce a given quantity of output, it will never pay it to produce in more than one of its plants if that plant has decreasing marginal costs.

The development of more rapid urban transport will inevitably raise the aggregate rental value of urban residential property.

If the number of acceptable applicants for admission to medical schools is less than the number that could be accepted, the medical profession cannot be raising its earnings by artificially restricting entry.

The rate of interest is determined by the marginal productivity of capital.

If a particular commodity is subject to a special tax not imposed on other commodities, removal of that tax will always increase economic welfare.

If the supply curve of a competitive industry has a positive slope, it means that the industry is subject to decreasing returns to scale.

If wage rates, on the average, increase at the same rate as average product per worker, this means that the marginal return on investment declines over time.

Entrepreneurs in a competitive industry may realize short term gains or profit as a result of an increase in the price of an input (due to a shift in the supply function for the input), even if the demand curve for the industry remains unchanged.

A. A drug manufacturer stated that the prices of drugs sold in England were priced at about one half the price of similar drugs in the United States. The reason given for the price difference was that per capita incomes were much lower in England than in the United States and the English could not afford to pay as much for the drugs.

Accept the factual statements as valid. Discuss the statement in terms of:

Demand functions for drugs in the two countries (income and price elasticities).

Whether the manufacturer could be maximizing his profits.

International trade restrictions on drugs in the two countries.

B. In a given competitive industry, both price and output increase between two time periods. Indicate why each of the following statements is consistent or inconsistent with the observed changes in price and output or is simply irrelevant:

The industry has a perfectly elastic supply curve.

The demand curve has shifted to the right.

The factor supply curves are upward sloping.

The industry is subject to diminishing returns.

Total revenue has increased because the price elasticity of demand is greater than unity.

Rents and quasi-rents have increased.

A. In the effect of union-produced wage increases on prices, one economist says,

“A competitive industry (with a horizontal long run supply curve] will eventually pass all of a wage increase on to consumers in higher product prices” but “a monopolized industry, if it maximizes profits both before and after the wage increase, will not pass on the full amount of the wage increase in prices.”

Assume that the monopolized industry, like the competitive, operates under long-run constant costs.

Explain precisely what “pass all of a wage increase on to consumers in higher prices” means.

Is the statement for the monopolized industry correct? If so, prove it. If not, state why not and indicate any additional conditions required to make it true.

B. This economist also says that the competitive industry “will regain its normal rate of profit”, whereas, in the monopolized industry, “the wage increase will lower monopoly profits”

What does the word “profit” mean in these statements? in the phrase “maximizes profits” of the preceding question?

Do the two statements imply a difference in results in the sense that the monopolized industry will not regain “its normal rate of profit”?

Indicate briefly what other meaning or meanings, if any, does the term “profit” have in economic theory.

(60 minutes) True-False. State very briefly the reason for your answer to each question.

The cross-elasticity of demand of left shoes with respect to the price of right shoes is zero.

A competitive firm buying electrical equipment was not injured by the collusion of the producers (General Electric case) even if the collusion raised prices above the competitive level.

If a consumer’s income rises in the same proportion as a Laspeyres index of his cost of living, his real income is rising.

Duopolists with different costs cannot achieve a monopoly price without transfer payments between the firms.

The marginal utility of income is not constant for a worker who increases his hours of work when the wage rate rises.

If two goods are substitutes in consumption, a 10 cent fall in the price of either good will lead to the same increase in the consumption of the other good.

A minimum wage law may increase the demand for labor by some firms.

A competitive firm will have a more elastic demand function for a factor of production than a monopsonist.

If a firm is operating in the region of falling marginal costs it must be making losses, since marginal cost is then less than average cost.

A multiplant firm will schedule its output so that marginal costs are equal in all plants.

(30 minutes) Capital formation may be defined as the use of current resources in such a way as to increase future income, and on this definition capital formation includes investments in equipment, human beings, and discovery of new knowledge. Discuss the problem of the meaning of the marginal product of capital, and whether capital as defined is subject to diminishing returns.

(20 minutes) Each firm in an industry is given a license to operate, and no new firms are allowed to enter. The value of a license rises over time — does this prove that firms operate subject to diseconomies of scale?

A flat sum tax on the firms in an industry will never have an effect upon output in the short-run.

The short-run price elasticity of the supply of beef can be negative.

The assumptions of competition, constant returns to scale, and equilibrium are inconsistent.

A competitive firm will increase its output as a result of a fall in the price of one of its inputs.

(20 points) Define briefly:

Indifference curve

Income effect of a change in price

Equilibrium price

Marshallian demand curve

Marginal rate of substitution

(40 points) Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and state briefly the reason for your answer.

A government subsidy of $100 per year to each grower of potatoes enacted after the end of a particular planting season and expected to be continued indefinitely will lower the price of potatoes (which it is assumed cannot be stored)

_____ a. for that season's crop.

_____ b. in the long run.

During period when general business is improving, both the price and output of steel rise. This means

_____ a. that the income effect of the rise in price is greater than the substitution effect.

_____ b. that the demand for steel is inelastic.

_____ c. that the demand for steel increases with income.

Removal of rent control would

_____ a. reduce the money wages of maids.

_____ b. reduce the price of trailers.

_____ If the removal of rent controls were to lead to a rise in rents, then the total amount paid in rents would decline if the demand for rental housing were elastic and rise if the demand for rental housing were inelastic.

_____ "Since elasticity measures variation in quantity (demanded or offered) divided by variations in a price, the elasticity of demand for anything will be seven times as large for seven similar demanders as it is for one." (A. C. Pigou)

_____ A rise in the price of coal will reduce the number of "Okies" trying to go to California.

(40 points) Assume that a system of point rationing is superimposed on a price system. Each consumer is given a specified total number of points, point prices are set on various commodities, and a consumer must pay over both points and money to purchase a commodity. For simplicity, assume that there are only two commodities in the system. Indicate (on an indifference diagram or in any other manner), how to determine the quantity of each of the two commodities an individual would purchase, given money prices, point prices, his money income, and his point income.

(a) If it is illegal to transfer points from one person to another and consumers conform to this requirement. In your explanation, distinguish among the various special cases that may arise.

(b) If points may legally be bought and sold for money. In this case, take as given also the price of points in terms of money.

(c) Suppose that a fixed total quantity of each of the two goods is available; that point prices are fixed by the government, money prices are freely determined so as to clear the market; and that in case (a) some consumers are left with points which they cannot spend because they do not have enough money. The legal prohibition against transferring points is now removed, the point prices and the total number of points issued are unchanged, and the price of points in terms of money is determined in the open market. What, if anything, can be said about the price of points in terms of money under these conditions?

Indicate briefly whether the following statements are correct or incorrect and why.

Economic theorists contend that, under competition, wages are always equal to the marginal product of labor. It seems to follow that if they are right, the simplest way to raise the productivity of labor, and hence to increase the total output of society, is to force employers to pay higher wages.

The value of the marginal product of a laborer employed at the same wage rate is higher if he is employed by a monopolistic firm than if he is employed by a competitive firm. It follows that the monopoly employs labor more efficiently.

A rise in wages will tend to lower the marginal productivity of capital.

The law of diminishing returns is contradicted by the fact that agricultural output of this country has increased tremendously despite a decrease in the proportion of the working population on farms.

Discuss the conditions that may give rise to long-run decreasing cost for an industry. What are the implications of the various conditions for the state of competition in this industry.

Suppose the wage differential between northern and southern laborers of the same grade were eliminated by raising the southern wage rates. Discuss the short- and long-run economic effects, including the effects on employment in the north and south.

A particular industry composed of numerous competing firms each producing a single product has been hiring labor by the hour and is in a position of long-run equilibrium. This industry (and no other) is required, because of a new law, to hire the labor by the year at a guaranteed annual wage equal to the hourly wage prevailing prior to the change times the number of hours in a normal working year. Discuss (1) the short-run effect of this change on (a) the average and marginal cost curve of a typical firm, (b) the output of that firm, (c) the number of man hours of labor employed by that firm; (2) the long-run effects on the number of firms in the industry and the output of the industry.

Part I

The income of farmers from the sale of their products depends on the prices at which the products sell. The general level of agricultural prices, in turn, depends primarily on the income of nonfarm population. But the income of the nonfarm population depends on the prices of nonfarm products which, in turn, depends partly on the income of farmers.

This kind of analysis is often criticized as circular reasoning and hence as incapable of leading to any useful conclusions. Is this criticism valid? Explain your answer.

Discuss the following quotation from Marshall:

"A useful history of the opposition to machinery is given in Industrial Democracy (by Sidney and Beatrice Webb)…It is combined with the advice (to trade unions) not generally to resist the introduction of machinery, but not to accept lower wages for working on the old methods in order to meet its competition. This is good advice for young men. But it cannot be followed by men who have reached their prime."

How would you expect prices in local, neighborhood, stores in large cities to compare with prices in the central shopping district (in Chicago, the "loop")? In your answer, distinguish among different products, and include an evaluation of the statement so often made by neighborhood stores that they can charge lower prices because they pay lower rents.

Part II

There are 100 each of A and B farms. The product schedules of one farm are

Number of laborers / Total Product (A Farm / B Farm): 1: 40 / 40 2: 90 / 80 3: 140 / 115 4: 185 / 145 5: 225 / 170 6: 260 / 190 7: 290 / 205 8: 315 / 215 9: 335 / 220

a) Determine wages, rents, and employment on both types of farms

(i) if there are 900 laborers and full competition

(ii) if with 900 laborers, the laborers on the A farms organize and succeed in setting a wage rate of 40,

(iii) if, with 900 laborers, the laborers on the A farms organize and succeed in raising the standard wage rate to 47.

b) State briefly the general economic principles illustrated by each part of the above problem.

Consider a hypothetical society in which there is no investment, either net or gross. All capital is completely permanent, not subject to change in form but capable of being used for different purposes. There is no lending or borrowing, no selling or buying of capital goods: whoever owns the capital goods is forced by the laws or conventions of society to hold them and is permitted only to rent them out (i.e., all capital is subject to the conventions that now govern human capital). Hence there is no market interest rate that matters, and all saving takes the form of hoarding of cash. The total amount of money in society is fixed in nominal units (say dollars). Wages are initially rigid (by law or otherwise) and the society is in a state of Keynesian unemployment equilibrium, unemployment keeping the real income down to a level at which dissaving equals saving, so total net saving is zero. Now wages are made flexible. Describe the process of adjustment to a new equilibrium position. Does this new position involve unemployment? What is the equilibrium condition on total net saving? What forces operate to bring about the satisfaction of this equilibrium condition?

2. Indicate which of the following statements are true (T) and which false (F):

[T] If a one per cent increase in price will cause more than a one per cent reduction in amount demanded, the demand for the commodity is elastic.

[F] Cost of production affects price only through its effect on the rate of production.

[F] If production of a commodity is completely monopolized, and if the monopolist takes full advantage of his position, no changes in the cost of production will have any effect upon price.

[F] A fixed tax (say, a license tax of $10,000) would operate to increase the price at which a monopolist would make the largest net return (or largest net earnings).

[blank] An individual firm will undertake to equalize marginal revenue and marginal cost.

[F] An excise tax is likely to increase the price of a competitively produced commodity by the full amount of the tax.

[T] If price exceeds the competitive producer’s average expense it will therefore be advantageous for him to increase his rate of production.

[T] A monopoly will never operate at a price at which the demand of its product is inelastic.

1. Define briefly the following terms:

a. Income elasticity of demand

b. Demand curve for the product of an individual firm

c. Supply curve

d. Marginal revenue

e. Cross elasticity of demand

f. Oligopoly

5. “In conversations with gold mining engineers a phrase glibly and frequently repeated is ‘sweetening the ore.’ By this phrase reference is made to the practice of diverting production in profitable periods to the poorer ores and perhaps restricting output in the richer fields. Under this practice the better ores are preserved for periods in which mining costs have risen so that over a long period of time output can be held more steady. Contributing also to a policy of sweetening the ores is the reluctance of producers to install capital equipment in a period in which the tendency is for mining expenses to increase with the general advance of wages and living costs. By the time the equipment is installed it might be expected that wages and price levels would be adjusted to the increased price of gold.”

Discuss the wisdom of the policy described in this quotation from the point of view of the individual producer. Assume that the individual producer seeks to maximize the present net capital value of his mining properties. Discuss separately (a) the alleged policy of “diverting production in profitable periods to the poorer ores and perhaps restricting output in the richer fields”; (b) the alleged policy of postponing the installation of capital equipment.

6. Assume a change in the laws so that less stringent conditions are imposed for bankruptcy and reorganization in a particular field (say the production of steel). As a consequence, a number of steel firms reorganize, wiping out a large part of their bonded debt. What would you expect to be the short- and long-run effects of these events on (a) the output and prices of the reorganized firms; (b) the amount of investment in the industry; (c) the rate of interest paid by the industry for new loans; (d) the output and prices of the industry? In each case, give the basis for your answer.

Answer each of the following “true,” “false,” or “uncertain” and explain your answer briefly. Your score will depend heavily on your explanation.

If two linear demand curves have the same slope at the same price, then at that price the one for which quantity is largest is least elastic.

An important difference between an indifference map and an isoquant map is that indifference curves never cross.

An important difference between the utility functions depicted by usual indifference maps and production functions is that distances in utility space can be ordered but not measured.

The following conditions are necessary and sufficient for the short-run maximization of monopoly profits: (a) Marginal revenue is equal to marginal cost; (b) price is greater than average variable cost.

An increase in fixed cost caused by an increase in the rate of interest on long run term debt will increase long-run marginal cost but not short-run marginal cost.

An effective legal minimum wage above the prevailing wage will increase the employment of a firm that is a monopsonist in the labor market.

The costs of owner-operated businesses are generally understated because the owners do not pay themselves wages. If they did, the accounting costs would be equal to the economic costs.

The way to produce a given output in the long run at lowest cost is to construct the plant whose short-run average costs are at a minimum at that output.

If a monopolist maximizes profit in the short-run and operates where total revenue is at a maximum, he has no variable costs.

A production function shows constant returns to scale if an increase of 10 per cent in the input of one factor will increase output by 10 per cent.

(a) Draw the short-run cost curves, demand curve, and marginal revenue curve of a monopolist who is suffering a short-run loss and is minimizing this loss. Indicate the amount of the loss on your diagram. (b) Show the same situation by means of short-run total cost and total revenue curves.

A farmer has two plots of land on which he grows corn, plot A and plot B. The following table shows the amount of corn he can produce on each plot with varying applications of fertilizer of a given quality.

Fertilizer Used (pounds) | Plot A (output in bushels) | Plot B (output in bushels) 0 | 10 | 8 1 | 14 | 13 2 | 16 | 17 3 | 17 | 20 4 | 18 | 21 5 | 17 | 20

If the price of fertilizer is $1.50 per pound and the price of corn is $1.00 per bushel, how much fertilizer will he use on each plot? (The figures are not intended to be realistic.) Under what circumstances would he use four pounds on each plot?

(a) Discuss the meaning of “profits” in connection with the theory of distribution. Outline briefly “a” theory of “profits.”

(b) A private enterprise economy is frequently described as motivated by the desire to maximize “profits.” Is the word “profits” in this statement used in the same sense as in the discussion under (a)? Explain any difference.

Indicate whether each of the following statements is TRUE, FALSE, or UNCERTAIN. In each case write a few sentences explaining your answer. Your grade will be determined by your explanation.

It is immediately obvious that if the firm has any significant degree of monopoly power, sales maximization would be better for the rest of the economy than profit maximization.

When a firm increases its price because its raw material costs have risen, the buyers accept the price increase more readily.

If A and B are produced in fixed proportions and consumed in fixed proportions, one of the two will be free.

Marshall asserts that the rents of different qualities of agricultural land will approach equality as the economy grows in population and wealth.

An industry whose output is increasing cannot be making negative profits.

The prohibition on environmental pollution by (say) a factory cannot increase national income.

A competitive industry is more likely to cartelize when the probability of expropriation increases.

Regulation of a competitive industry by the government will decrease the probability of cartelization.

In the social security systems of most countries, the age of retirement after which old age pensions are “payable” is lower for women than for men (usually 60 as compared with 65 years of age), even though on the average women live significantly longer than men. This is a clear case of discrimination against men, which should be protested by the Men’s Liberation Movement.

The U.S. personal income tax system allows married couples to “split” their aggregate income equally and pay tax on the results at the same rates as single people would. This is a clear case of discrimination in favor of heterosexuality that should be vigorously protested by the Gay Liberation front.

If the elasticity of supply is less than unity, and the elasticity of substitution in production greater than unity, a fall in the price of a factor must increase the demand for it.

Labor can be “Exploited” only if there is monopoly in the product market.

Assume there is an exhaustible resource that can be extracted at a constant marginal cost c. Assume there is a competitive industry that extracts this resource. Derive the behavior of the equilibrium price over time if the demand schedule for the product remains constant over time.

Under the same demand and cost conditions, derive the equilibrium price if the resource is controlled by a single firm.

In an anti-trust case against the Aluminum Company of America, Judge Learned Hand argued that the Aluminum Company could be regarded as having essentially a complete monopoly on aluminum despite the existence of a highly competitive market in secondary or reclaimed aluminum (made from scrap) accounting for about one-third of the total aluminum used for fabrication. He justified this conclusion on the grounds that all secondary aluminum derives ultimately from primary aluminum produced earlier and hence that the Aluminum Company through its control of the output of primary aluminum indirectly controlled the quantity of scrap available.

Evaluate the economic validity of this argument. To simplify your analysis assume that a single firm, say the Aluminum Company of America, has a complete monopoly of primary aluminum; that aluminum for fabrication comes from primary aluminum and secondary aluminum; and that primary and secondary aluminum are perfect substitutes. Indicate in detail how to determine the optimum price for the Aluminum Company to charge and the optimum output for it to produce if (a) the secondary aluminum is refined and sold by a large number of firms under competitive conditions; (b) it has a complete monopoly of secondary aluminum as well.

Hand's conclusion presumably is that the price of aluminum would be the same in cases (a) and (b). Is he correct? If not, would it be higher in case (b) than in case (a)? Lower?

Find the mistakes (there are at least six) in the accompanying diagram showing long and short run marginal and average cost curves, and explain the general principle corresponding to each particular mistake.

Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and state briefly the reason for your answer. It is to be understood that in each question the appropriate “other things” are to be held constant.

1. The imposition of a minimum wage for labor of type X higher than the preceding wage leads to an increase in the number of laborers of type X employed. It follows that labor of type X is hired under monopsonistic conditions.

2. Under both competition and monopoly in the product market, marginal value product of a factor to a firm is equal to marginal physical product of the firm times marginal revenue to the firm from the sale of the product.

3. Marginal productivity analysis shows that, in the absence of monopsony, a laborer gets as a wage his marginal value product. If this analysis is correct, it follows that unions can raise wages in the absence of monopsony only if they either make each worker more efficient, or increase demand for the product, or make the demand for the product more elastic.

4. The law of variable proportions (or diminishing returns) is contradicted by the fact that agricultural output of this country has increased tremendously despite a decrease in the proportion of the working population on farms.

5. The rate of interest is equal to the rate of time preference of consumers.

6. At present levels of operation, three quarters of the total cost of the XYZ railroad is overhead cost that does not vary with traffic, only one quarter is variable cost. It follows that marginal cost is much less than average cost.

7. The demand curve of an individual firm for a factor of production is identical with its marginal value productivity curve for the same factor of production.

8. The demand curve of a firm for a factor of production is a meaningless concept if the firm is a monopsonistic purchaser of that factor.

9. A declining long run supply curve is impossible in a competitive industry.

10. Marginal factor cost is equal to the price per unit of a factor whenever the product market is competitive.

11. According to the theory of joint demand, the absolute value of the elasticity of derived demand for a factor of production will be smaller the more inelastic the supply of that factor.

12. The fact that individuals do not choose occupations solely on the basis of their pecuniary attractiveness helps explain why the supply curve of labor for a particular occupation has an elasticity greater than zero.

13. If all types of services were used only in fixed proportions, a marginal-productivity theory would be neither necessary nor possible.

14. Our society is often described as a “profit” economy or “profit-maximizing” economy. The word “profit” is here used in the same sense as in the uncertainty theory of “profit.”

15. “Profit” as defined in the uncertainty theory of profit is the expected return to any factor assuming uncertainty over and above the guaranteed expected income it can obtain if it assumes no uncertainty.

16. If one income is higher than another before income tax it will also be higher after a progressive income tax, provided only that the marginal tax never exceeds 100%. It follows that if one accepts the theory that individuals act as if they sought to maximize their income, he must also accept the conclusion that such taxes do not alter individual's actions and hence are not shifted.

17 and 18. A minimum wage law is repealed. The wage rate of a class of workers hired under competitive conditions was equal to the minimum before repeal and falls after repeal. It follows that:

17. The total wage bill for this class of labor will rise, remain constant, or fall, according as the elasticity of demand for labor of this class is greater than, equal to, or less than unity in absolute value.

18. The quantity of labor of this class employed will fall, remain constant, or rise according as the elasticity of supply of labor of this class is positive, zero, or negative.

19. The great technological improvements in the past few decades in the production of synthetic fibers (rayon, nylon, etc.) and associated decline in their relative price has, among other effects, tended to raise the price of meat in general, especially of lamb and mutton.

20. At the same time, stringent rationing of meat consumption in Great Britain, by tending to offset this effect, has improved the competitive position of the synthetic fiber industry, and so enabled it to expand more than otherwise.

The price of nylon thread for use in making women's hosiery was recently lowered drastically when DuPont decided to make much larger quantities available. The resulting decline in the price of hosiery was viewed by at least some manufacturers and retailers as a misfortune and as portending smaller profits for themselves. Were they right? In the short run? In the long run? Justify your answers.

A subsidy of $X is paid per acre of land devoted to growing soy beans. Will this lead to a rise or to a decline in the yield per acre on land devoted to growing soy beans prior to the introduction of the subsidy? Justify your answer.

Answer each of the following as true, false or uncertain and justify your answer in the space provided.

Over time in the U.S. since 1929 output of the service industries rose at about the same rate as that of goods. Since the price of services rose at least as rapidly as that of goods, the income elasticity of demand for services would be greater than that for goods.

A weighted average of all price elasticities must add up to one.

Suppose the excise tax on bus travel was reduced and not on plane, train or other travel. This would reduce the use of buses if such travel was a sufficiently strong inferior good relative to other kinds of travel.

The ability of firms of very different sizes to survive in an industry means that the long run marginal cost curve is horizontal over the range of firm sizes that survive.

If an increase in the output of any firm lowered the marginal cost curves of other firms in the same industry (external economies) a competitive industry as a whole might show increasing returns; i.e., have a negatively inclined supply curve.

Short run marginal costs can never be below long run marginal costs.

Suppose that a competitive firm maximizes not income but its sales subject to the constraint that it does not make any losses. Then reduction in the demand for its product might not lead it to reduce output.

Goods X and Y are either substitutes, complements, or independent if an increase in the amount of X either reduces, raises or leaves unchanged the marginal utility of Y.

If the price of a good competitively produced was free to vary and yet did not change much between a seasonal low and a seasonal high in demand, this means that the industry’s long run marginal cost curve was very elastic.

An ad valorem tax, with a tax rate proportional to producer’s price, on a competitive industry that yielded the same revenue at the initial output as a specific tax, fixed amount per unit, would reduce output less than the specific tax.

What are the essential characteristics of exchange opportunities and production opportunities, on the social levels?

Which good will have a greater fall in its price as the crop is more fully harvested: one that will store more readily or one that is more perishable? Why?

Exchange consists of acts which allow the possibility of trading endowment elements with other members of society– exchange opportunities only arise in a social context. Production opportunities represent alternative combinations attainable by transformation or dealing with nature. In exchange, the quantity supplied of a commodity must equal quantity taken –i.e., algebraic sum of supply and demand must equal zero for every commodity. Exchange conserves the social totals of commodities. Production alters the social totals, i.e., less of some goods, more of others.

Assume a simple competitive economy with J individuals and 2 goods X and Y. Both production and exchange can take place. Every individual has identical tastes and opportunities (so that the single-individual solution will be a miniature representation of the social solution). Assume, further, that all endowments consist only of the numeraire commodity, Y.

(a) Illustrate verbally and diagrammatically the determination of:

1. The production optimum, the amount produced, the total cost.

2. The consumptive optimum and the volume of trade.

3. The price, the marginal cost, and the marginal value in use.

4. The individual’s wealth.

(b)

1. Assume that a technological change has made it possible to produce twice as much X for any given sacrifice of Y. If both X and Y are superior goods, modify the analysis above to show the effect on the price of X, the amount of X produced, and the amount of Y sacrificed.

2. Returning to the conditions of a above, suppose the various individuals’ endowments occur at differing points along the given productive opportunity locus. Would the optimum production and consumption points be different? Would any trade take place? Explain.

What are the essential characteristics of exchange opportunities and productive opportunities, on the individual and on the social levels?

It has been said that exchange makes possible new types ofproductive opportunities as well, through the institution of the firm. Analyze.

Assuming an ordinary-shaped long-run average-cost curve in advance of any “fixed-cost” commitment (a so-called “planning curve”), indicate the shape of the relevant average-cost after such a commitment:

(a) If the “fixed costs” were expended to purchase durable inputs that were perfectly unspecialized to the firm.

(b) If they were expended to purchase inputs that were perfectly specialized. Justify and explain. Do not consider Alchian “volume-effects”, or transition and costs (haste premiums).

Give very brief (one paragraph) answers to the following:

(a) Collusions have the natural tendency to break down.

(b) Cost minimization is the general criterion of economic behavior.

(c)Laissez faire capitalism encourages deceitful advertising, dishonesty, and faithlessness. Comment.

(d) Is a person who loses his job through no fault of his own also unemployed thereafter through no fault of his own? Explain.

An urban rapid-transit line runs crowded trains (200 passengers per car) at rush hours, but very empty trains (ten passengers per car) at off peak hours. A management consultant makes the following argument:

“The cost of running a car for one trip on this line is about $50 regardless of the number of passengers. So the per passenger cost is about 25¢ at rush hour but rises to $5 per passenger in off peak hours. Consequently, we had better discourage off-peak hour business.”

Explain the fallacy. “Commutation tickets” sold by some transit systems (reduced-price, multiple-ride tickets) are predominantly used in rush hours. Are such tickets a good idea?

The literature on the behavior of the firm poses it as a profit maximizer, a wealth maximizer, a growth maximizer, a sales maximizer, a sales maximizer subject to a prescribed profit rate. Which of these do you use (why?) and how do you manage to allow for these other assertions of firm behavior?

The Cobb-Douglas production function has the following form:

$q=f(x,y)=A{x}^{\alpha }{y}^{1-\alpha }$

Show that such a function is linearly homogeneous to degree one and state two other characteristics of such a production function. Also prove mathematically that with a production function such as a Cobb-Douglas that if factors are paid according to their marginal products the total product is “exhausted”.

Armen Alchian’s definition of costs differs from the standard textbook definition. What is the difference? Explain how his definition may be better. Why does he use capital values in his measurement of costs?

“The distinction between the long run and the short run is a fiction with no counterpart in the real world.” Evaluate this criticism, explaining why one might make the statements, but show how this fictional distinction might be defended.

Why is most productive activity carried out by firms rather than by individuals who contract mutually with one another?

Alchian’s definition of cost differs from the standard textbook definition. What is the difference? Explain how his definition may be better.

Explain how cost curves are “monetized” values of product curves.

Give very brief (one paragraph) answers to the following:

(a) Collusions have the natural tendency to break down.

(b) Cost minimization is the general criterion of economic behavior.

(c) Laissez faire capitalism encourages deceitful advertising, dishonesty, and faithlessness. Comment.

(d) Is a person who loses his job through no fault of his own also unemployed thereafter through no fault of his own? Explain.

What are the essential characteristics of exchange opportunities and productive opportunities, on the individual and on the social levels?

It has been said that exchange makes possible new types of productive opportunities as well, through the institution of the firm. Analyze.

Assuming an ordinary-shaped long-run average-cost curve in advance of any “fixed-cost” commitment (a so-called “planning curve”), indicate the shape of the relevant average-cost curve after such a commitment:

(a) If the “fixed costs” were expended to purchase durable inputs that were perfectly unspecialized to the firm.

(b) If they were expended to purchase inputs that were perfectly specialized. Justify and explain. Do not consider Alchian “volume-effects”, or transition costs (haste premiums).

Explain how cost curves are monetized values of product curves.

“The advent of the one man bus involved more capital equipment: an automatically operated coin box and door control device - to name two of the capital goods that replaced the conductor.”

(a) Is this a case of capital replacing labor? Where?

(b) Is this a case of labor replacing labor? Where?

Evaluate the following statement:

(a) Taiwanese labor is far less productive than American labor as evidenced by the fact it takes so much of it to get things done e.g., it may take three or four Taiwanese to do a job done by one American;

(b) American agricultural land is less fertile than Taiwan land as evidenced by the lower yield per acre in the U.S. Separately evaluate both statements.

Both monopolists and purely competitive firms are assumed to behave as if they seek to maximize profits, yet monopoly is held to result in an inefficient allocation of resources as compared to pure competition. Explain. Marginal costs serve as a guide as to how much of a good product, while average variable costs help indicate whether to produce at all. Explain.

You are given the following demand function for the firm:

$Q=20-p$. Its total cost function is $TC=Q^2+8Q+2$. Find

(a) profit-maximizing output

(b) equilibrium price

(c) elasticity of demand at the equilibrium price

(d) profits

Is this firm a price-taker or price-searcher? Why?

Suppose that Florida migrant farm workers are effectively unionized. What will be the impact of the unionization on (a) the price of Florida oranges, (b) the profits of Florida fruit growers in the short run and in the long run, (c) the mechanization of the fruit picking industry and (d) the employment of fruit pickers?

State the law of diminishing returns. Then explain why you agree or disagree with the following statements. (You may use a graph with your answer.)

(a) If the marginal product of labor is decreasing, the average product of labor is decreasing.

(b) If the marginal product of labor is increasing, the total product of labor is increasing at an increasing rate.

(c) When the marginal product and the average product are equal the average product is at a maximum.

Suppose that Florida migrant workers are effectively unionized. What will be the impact of the unionization on (a) the price of Florida oranges, (b) the profits of Florida fruit growers in the short run and in the long run, (c) the mechanization of the fruit picking industry and (d) the employment of fruit pickers? Explain each answer.