Consumer theory

Trace the development of the demand concept from Adam Smith to the present, touching on the contributions of J.S. Mill, Cournot, Fleeming Jenkin, Walras, Böhm-Bawerk, and the statistical economists.

Answer (a) or (b), but not both.

(a) The final degree of utility curves of A and B for corn (X) and beef (Y) are as follows, the small letters x and y representing the quantities of X and Y consumed by the person indicated by the subscript.

For person A: $f_a(x_a)=-\frac{3}{2}{x}_a+\frac{19}{2}$ for corn (X); ${\varphi }_a(y_a)=-\frac{1}{2}{y}_a+6$ for beef (Y).

For person B: $f_b(x_b)=-\frac{3}{8}{x}_b+5$ for corn (X); ${\varphi }_b(y_b)=-y_b+7$ for beef (Y).

The total market supply of corn is $x=x_a+x_b=14$ and the total market supply of beef is $y=y_a+y_b=8$.

Without performing any numerical computations, explain how to deduce the combined demand curves of A and B for corn in terms of beef and for beef in terms of corn.

(b) Is there an equilibrium price and output when a commodity is produced by two competing monopolists? Discuss this problem touching on the solutions of Cournot, Edgeworth, Amoroso, and Wicksell.

(Answer both parts)

A. Defined or very briefly describe:

(1) Inelastic demand

(2) Elastic demand

(3) Incremental (or marginal) revenue

(4) Perfect competition (in terms of demand elasticity)

(5) Pure profit

(6) Productivity (incremental or marginal of a particular agency or factor)

B. Is export dumping evidence of domestic monopoly? Explain. Under what conditions does export dumping lead to a lower domestic price in the exporting country?

The theory of marginal utility: its origin, principal forms or interpretations, your own view of its meaning and use in price theory, and the critical appraisal of its validity. Consider especially the relations between the use of the principle as an explanatory concept and as a premise for the discussion of social policy.

Trace the development of the theory of consumer choice. Include in your answer an explanation of (a) the meaning attached by Smith to “effectual demand”, (b) the role assigned by Ricardo to demand in determining prices; (c) Jevons “the final degree of utility determines price”; (d) the contribution of Edgeworth, Fisher, and Pareto.

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

The U.S. Steel Corporation produces about one-third of the total ingot steel production in the United States (and a similar proportion of mill shapes and other forms of steel sold to steel-using industries). If the price elasticity of demand for steel is -0.5, what is the minimum absolute value of the elasticity of demand facing the U.S. Steel Corporation? What is the maximum absolute value? What can you conclude, without further information, about the monopoly power of the U.S. Steel Corporation? What further information, if any, would be relevant, and why?

A consumer buys in perfectly competitive markets, spending all of his income. Over a period of time his income changes and prices change, but it is our hypothesis that his tastes do not change.

Assuming no price-income situation was every exactly repeated, what possible behavior on his part, if any, could contradict our hypothesis? Why?

If the hypothesis is not contradicted, and if we then assume it to be correct, can we also assume that his indifference curves are everywhere convex to the origin? What possible behavior on his part, if any, could contradict the assumption of convexity to the origin? Why?

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.

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.

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.

Explain, and discuss the validity, purpose, and usefulness of any three of the following Marshallian concepts:

(a) quasi-rent;

(b) consumers’ surplus;

(c) unit elasticity;

(d) maximum satisfaction;

(e) representative concern.

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.

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.

Answer the following questions, true, false or uncertain and briefly defend your answer.

An increase in the demand for the product of a monopoly results in a rise in the price of the product.

In the theory of the household demand for perishable goods, for a given money income there is a fall in real income if the price of some good rises. The pure substitution effect is the effect on quantity demanded of a price change for constant real income. In the case of durables households own stocks of durables. Hence a rise in the price of durables causes the value of the stock of consumer owned durables to appreciate. Hence a price rise of perishable reduces the demand for perishables if money income is given and the income elasticity is positive while a price rise of durables increases the demand because it implies a rise in consumer wealth if the wealth elasticity of demand is positive.

What are appropriate budget constraints for the demand for durables?

Is the last statement beginning with “HENCE …” correct?

Would it make a difference if the durable good had a fixed life or if it lasted forever?

What are the counterparts of constant real income in the demand for durables?

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.

II. Fill in the blanks in the following questions.

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 Hick’s sense. Let all three curves go through the point $(p_o,x_o)$

If X is a superior good, then for a price lower than $p_0$, the quantity demanded will be larger for_____ than for _____. (Insert A, B, C, in correct spaces.)

If X is an inferior good, then for a price lower than $p_0$, the quantity demanded will be larger for _____ than for _____.

Suppose p_0 = \5$,$X_0 = \$20$, the corresponding money income \1,000$,andtheincomeelasticityofdemandforXis2.Supposethatataprice$\$4$, the quantity demanded on curve A is 25. 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 _____.

Blank is indifferent whether he wagers \1$ateven-moneythatacoinheregardsasfairwillcomeupheads.Heiseagertowager$\$1$ against \3$(i.e.,hepays$\$1$ if he loses, receives \3$ifhewins)thatheadswillcomeuptwiceintwosuccessivethrowsofthiscoin.(Heregardsthethrowsasindependentandsothechancesoftwosuccessiveheadsasoneinfour.)Lettheutilityofhisincomeifheloses$\$1$ be 100; if he wins \1, 101. Then the utility to him of his present income can be taken to be _____ (insert a number); the utility to his present income plus \$3$ _____ (insert the most accurate statement the evidence permits).

V. When someone offers a cigarette to pipe-puffing Surgeon General Luther Terry, he always grabs it. “Every one I accept I tear up,” he says. “That way there’s one less cigarette.” (Time, February 7, 1964).

Analyze the economics of the Surgeon General’s policy. In doing so, assume of course, that a substantial class of people with similar beliefs behave the same way, so the effect is at least potentially appreciable. Would it contribute to his objective of reducing smoking? If so, through what channels?

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.

III. A consumer in a three commodity market buys the following quantities at the following prices:

Situation A: Price of X = 1, Price of Y = 1, Price of Z = 1; Quantity of X = 1, Quantity of Y = 2, Quantity of Z = 5. Situation B: Price of X = 1, Price of Y = 1, Price of Z = 2; Quantity of X = 7, Quantity of Y = 0, Quantity of Z = 0. Situation C: Price of X = 3, Price of Y = 2, Price of Z = 1; Quantity of X = 0, Quantity of Y = 7, Quantity of Z = 0.

Prove that this behavior is consistent with his having constant tastes and an ordinal utility index.

Answer the following True, False, or Uncertain. Explain your answer briefly.

If two individuals engage in barter, or direct exchange of goods, then always either: a) One individual benefits by the transaction while the other one is hurt; or b) Both are neither benefited nor hurt.

In a perfect market economy, each consumer participates equally in determining what is produced.

If an increase in the demand for X results in an increase i n the price of X, the demand for X is upward sloping.

If the demand for X has unitary elasticity (η = -1), changes in the price of X will not affect the total expenditures on all other goods.

If one good is inferior, at least one other good purchased by the consumer has to be income-elastic (ηxI> 1).

If the marginal revenue is decreasing with an increase in the quantity X, the demand for X is inelastic.

The substitution effect of a decrease in price, as defined by Slutsky, is positive for a normal good and negative for an inferior good.

If the market for beef is in a stable equilibrium, changes in the supply of beef will have little or no effect on its price.

It is possible for a consumer to buy a fixed positive) quantity of X every month, whatever the price of X may be. (i.e., his demand for X has zero elasticity for all prices).

The demand for agricultural products is inelastic; hence plentiful harvests result in lower incomes for farmers, in a free market economy.

In view of (10), each individual farmer can improve his own position by destroying a part of his production in good years.

A linear and downward-sloping demand curve is always elastic at high prices and inelastic at low prices.

If the Laspeyres quantity index between two periods is 1.10 and the Paasche index is 0.90, the consumers’ taste must have changed,

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

A consumer with a utility function is in equilibrium if the marginal utility of each good is proportional to its price.

If all prices increase by 10%, but money income remains the same, the quantity of each good purchased will decrease.

The demand of a consumer for X cannot be infinitely elastic at every quantity of X, because of the budget constraint.

In an economy where the king distributes all the goods and services as free gifts to the consumers, all the prices are zero. Hence there is no place for price theory in that country.

The demand for X is of unitary elasticity, and 200 similar firms sell X. A reduction of 1% in the price PX charged by one firm will result in doubling that firm’s sales, if other firms sell the same quantity at any price.

Because of transportation costs, prices will differ in different geographical locations, whether or not there exists free competition in the market.

Two consumers, A and B, have equal and stable tastes and incomes. In December, each spent his entire monthly income on x units of X and y units of Y, when the prices in the market were $2.00 for X and $5 for Y. Consumer A accepted an offer of his employer to be paid in kind, by receiving the same quantities y and y every month directly. (He could still exchange any quantity of X and Y at the market, for the current market prices). B’s money income remained the same.

The following prices prevailed in the market during the next few months:

Month / $perunitofX/$ per unit of Y 1 / 2.00 / 5.00 2 / 2.20 / 5.50 3 / 2.00 / 5.50 4 / 2.00 / 4.50 5 / 1.80 / 4.50 6 / 2.20 / 4.50

1) Compare consumer A’s position in each of these months with his position in December (was he better-off, worse-off, or indifferent?)

2) Compare the positions of A and B in each month.

NOTE: Use budget lines (and, if necessary, indifference curves) for your analysis. Do not attempt to answer more questions than you were asked. Be brief and clear.

The current charge for telephone service in city C is $6.40 per month, allowing the consumer 80 free local calls every month, Each additional call costs five cents. Installation is free, and no long-distance calls are available.

NOTE: In the following, assume that each consumer behaves rationally, has constant money income and tastes, with convex indifference curves and no saturation in the relevant range.

Use separate diagrams for each sub-problem. Be precise.

Use a diagram with money-income Y and phone calls X on the axes, to show a consumer’s budget constraint. Be careful to show all the combinations of X and Y available to him, including the case where no service is installed.

(This portion is crucial for the rest of the problem).

Use indifference curves between Y and X to analyze the consumer’s decision whether to have a telephone installed or not.

Consumer A chooses to have a telephone, and he uses 120 calls every month. Show his equilibrium position geometrically. What is the average price (in cents) of a phone call for him? What is his marginal rate of substitution between money and phone calls?

If the current rates are replaced by a flat rate of 7 cents a call for any number of calls,

(a) Show consumer A’s new budget line, compared with the current position.

(b) Would he now use more or less than 120 calls per month?

(c) Would he be better-off, indifferent, or worse-off relative to the current position?

Consumer A claims that he would prefer to pay a flat rate of 84 per call rather than the current rates. Could he be rational? (demonstrate your answer geometrically).

Consumer B uses only the 80 “free” calls every month, given the current rates. Compare (as in (4)) his consumption and welfare positions with the alternative of being charged a flat rate of 8¢ per call for any number of calls. Could he be indifferent with respect to the two alternative rates?

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

The price elasticity of demand for a good will be higher, the higher is the income elasticity of demand for that good.

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

If a particular producer of grapefruit produces 10 percent of the total supply of grapefruit, the elasticity of demand facing that producer must be at least -10.

If the cross-elasticity of demand for X with respect to the price of Y is .5, the cross elasticity of demand for Y with respect to the price of X will also be .5.

The demand curve for a commodity which includes the “income effect” is necessarily more elastic than the demand curve for the same commodity which includes only the substitution effect.

Food and “all other commodities” cannot be complements.

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”.

Using indifference curves, derive the supply curve of labor as A function of real wages. Distinguish between the “income effect” and the substitution effect. State what, if any, will be the circumstances under which a rise in real wages will lead to a reduction in the quantity of labor offers.

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.

Comment briefly on the following statement:

“When equilibrium prices in competitive markets are disturbed, they tend to be re-established. Thus the first effect of an increased supply of eggs is to lower the price. At this lower price, consumption is increased, and the increase in demand tends to drive the price back up again.”

Increased costs cause manufacturers to reduce the size of 5 cent chocolate bars from 2-1/2 ounces to 2 ounces. Because the bars are smaller, people eat more of them and consumption rises from 10, 000 bars a week to 11,000.

Can these events be shown on an ordinary supply and demand diagram? If so, show them. If not, explain why.

Can the elasticity of demand for chocolate be computed? If so, compute it. If not, explain.

The following table gives hypothetical prices of pork and beef per pound in two years, and quantities consumed in a certain town.

Price per pound (1959, 1960) and Pounds consumed (1959, 1960): Pork: 40 cents, 50 cents; 1000, 800 Beef: 60 cents, 60 cents; 1000, 1200

Compute the elasticity of demand for pork and the cross-elasticity of demand for beef in terms of the price of pork.

Compute the Laspeyres price index for the price of meat from 1959 to 1960 (assuming that pork and beef are the only kinds of meat).

Draw an indifference map for pork and beef for a typical consumer and illustrate the changes shown in the table on his indifference map. Derive two points on his demand curve for pork.

Assume that the consumer’s money income is increased by an amount equal to his original income times the Laspeyres price index computed in (b). Demonstrate that he has been overcompensated for the price rise. Under what condition if any would this increase in income fail to overcompensate him?

Show each of the following events on an indifference map:

The change in the consumption of margarine following an increase in income (axes: butter and margarine. Assume that the income elasticity of demand is positive for butter and negative for margarine.)

The change in the consumption of bread following a rise in its price. (axes: bread and all other commodities.) Identify the income and substitution effects of the price change.

Do part (b) over using Friedman’s “Marshallian demand curve” concept and explain the difference between the diagrams for (b) and (c).

If the consumer’s utility function is separable, then his marginal utility must be declining for all goods.

In a two good world, consumer indifference curves must be everywhere convex to the origin. Otherwise there is no solution to the consumer’s problem of maximizing his satisfaction subject to his budget constraint.

The following figures represent the prices and quantities of two commodities, A and B, consumed by three individuals having the incomes stated in two different periods of time.

First Period | $P_a$ | $Q_a$ | $P_b$ | $Q_b$ | Income Arthur: $1, 20, $2, 10, $40 John: $2, 20, $1, 10, $50 Paul: $2, 20, $1, 10, $50

Second Period | $P_a$ | $Q_a$ | $P_b$ | $Q_b$ | Income Arthur: $2, 10, $1, 20, $40 John: $1, 10, $2, 20, $50 Paul: $2.50, 10, $1.25, 20, $50

Assuming that each individual spends his whole income on the two commodities, and assuming also that there is no change in tastes between the two periods, indicate for each individual what the above information reveals as to whether the bundle of goods consumed in Period I represents a lower or a higher level of satisfaction that the bundle consumed in Period II. Explain your conclusions fully. (It is recommended that a diagram be used in answering this question.)

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.

A substitute for a product is invented. What, if anything, can you say about the effect of this invention on (a) the position; (b) the elasticity of the demand curve for the initial product? (To fix ideas, one example is the effect of the invention of electric shavers on the demand for safety razors; another, and perhaps more widely quoted example, is the effect of the introduction of financial intermediaries on the demand for money.)

Comment briefly on each of the following passages (explanation, justification, disproof, qualification, as may be appropriate).

“It is not the case that an increased demand for mutton must in the long run necessarily operate to lower the price of wool. An increased demand for mutton will stimulate sheep farming, but it will also stimulate the substitution of crossbred [mutton type] for merino [wool type] breeds; and the resultant of these two opposite tendencies is logically indeterminate.”

“When Consols are at 93½ , and business in in a tranquil state, it matters not how many buyers of these securities there are at 93, or sellers at 94. They are really off the market. Those only are operative who may be made to buy or sell by a rise or a fall of an eighth. The question is, whether the price shall remain at 93½, or rise to 93 5/8, or fall to 93 3/8. This is determined by a very few persons and by the sale or purchase of very small amounts.”

“The degree of monopoly control by a seller equals the degree by which price exceeds marginal revenue.”

“The degree of monopoly control by an employer as employer equals the degree by which the value of the marginal product of labor exceeds the marginal supply price of labor.”

“Where it is the case that people would not give as large a total sum for a larger quantity of an article than for a smaller, this would be expressed geometrically by saying that the demand curve would cut negatively a rectangular hyperbola.” [negatively means cut from above]

“The fact that supplying labor with better or more instruments results in an increase in output has sometimes led to the conclusion that capital is productive, a phrase which must be used with care. The strictly accurate statement is that labor applied in some ways is more productive than labor applied in other ways. Tools and machinery, buildings and materials, are themselves made by labor, and represent an intermediate stage in the application of labor. Capital as such is not an independent factor in production, and there is no separate productiveness of capital.”

a. If elasticity of demand is unity, and original rate of sales is 1,000 per month, what will happen to the rate of sales if price falls 50 per cent?

b. If elasticity of demand is two, and original rate of sales is 1,000 per month, what will happen to the rate of sales if price falls 25 per cent?

c. “Since elasticity of demand measures variations in quantity demanded divided by variations in price, the elasticity of the demand for anything will be seven times as large for seven similar demanders taken together as it is for one.” Comment.

If a commodity has a negative income elasticity, the function relating price and quantity consumed may have a positive slope.

If two goods are substitutes in consumption, a fall in the price of one will always result in a fall in the price of the other.

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

If the “true cost of living” for a consumer is interpreted to mean the cost of staying on a given indifference surface, then upper and lower limits for the change in a consumer’s true cost of living between period 0 and period 1 are given respectively by the Laspeyres and Paasche indexes using the consumer’s own purchases as weights.

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.

If a worker’s utility function in the two dimensions, (1) leisure and (2) all other goods and services, is homogeneous of first degree, then his supply curve of labor will be backward sloping.

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) 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.

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?

Indicate briefly the meaning of each of the following phrases, identify the economist (or economists) associated with each, and state some of his major contributions to economics:

Engel’s Law

Say’s Law

Iron Law of Wages

Schumpeterian innovators

Conspicuous consumption

Contract curve

Elasticity of demand

(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.

(40 minutes)

The long run demand function for a commodity is

q = 100 – p. The price has been $30 for several years; it now drops to $20. Half the consumers react to the new price immediately; the other half (due to habit, etc.) do not adapt until a year later. Calculate the elasticity of demand at a price of $20 (1) the first year, and (2) the second year after the price reduction.

A consumer assures you that his indifference curves intersect each other. You have an unlimited number of observations on his purchases at various incomes and prices. What tests can you make of the alleged intersections?

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.

(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.

The accompanying graph gives a set of consumption indifference curves for two commodities or services each of which for some range of quantities and in combination with some amounts of the other is capable of being either a “good” or a “bad” (a “product” or a “factor”) like books and bookshelves, or cutting the grass and playing the piano (either of which may be “labor” or “play”). Of the curves drawn, $I_1$ corresponds to the lowest level of utility. Answer this question on this paper, wherever relevant filling in the blanks.

What is the interpretation to be placed on point B?

Mark of $I_1$ into four sectors according as

(1) _____both X and Y are “goods”

(2) _____X is a “good” and Y is a “bad”

(3) _____X is a “bad” and Y is a “good”

(4) _____X and Y are both “bads”

Use letters to designate the dividing points between the sectors and enter the description of each sector in the proper place above.

Budget lines AC and A´C´ are the usual type which supposes that the consumer must pay for both products and has a fixed sum to spend on both.

(1) The consumer’s optimum position for A´C´ is _____.

(2) The consumer’s optimum position for AC is _____.

On budget lines EF and GH, one of the commodities is something the consumer must pay for (it is a “product” and has a positive price), the other is something he gets paid to accept (it is a “factor” and has a negative price). In addition for both lines, the consumer has a fixed sum derived from some other source to spend.

(1) For EF _____ is the product; _____ is the factor.

(2) For GH _____ is the product; _____ is the factor.

For OK also one commodity is a product and one is a factor but there is no additional source of expenditures and hence no way from the line itself to know which is which. However, it does make a difference to the optimum position which is which.

(1) If X is a factor and Y a product, then the optimum point is _____.

(2) If Y is a factor and X a product, then the optimum point is _____.

(3) Can you suggest a simple graphical way of distinguishing the two cases?

Define briefly the following terms:

Marginal revenue

Fixed cost

Income elasticity

Profit

Production function

Diminishing returns

Inferior good

Luxury

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.

(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.

If a demand curve is defined as the relationship between price and quantity of X, the real income and the prices and quantities of other goods held constant, it will have an elasticity of -1.

If all commodities had positive income elasticities, there would be no merit in the present distinction between substitution and income effects.

The elasticity of demand for X with respect to the price of Y never equals the elasticity of demand of Y with respect to the price of X.

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

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

“The price paid for water is no indication of its true value in use because the water makes the production of additional wealth possible. Thus a farmer may pay his irrigation district $8.00 for water per acre of land, but the value of the crops grown might be in the neighborhood of $100 per acre.”

The fact that a consumer, in equilibrium, is not consuming all of the possible commodities, implies that he gets increasing marginal utilities from the commodities that he does consume.

A tax on American citizens who go abroad will reduce tourist expenditures and hence improve the U.S. balance of payments only if the demand for foreign trips is elastic.

Assume that a comprehensive system of point rationing is superimposed on a money price system. Each consumer is given an equal number of points although money incomes are very unequal. Point prices exist for every commodity for which a money price exists, and a consumer must pay over both points and money to purchase a commodity. To simplify the analysis, assume throughout (1) that the points are dated, (that is, can be used only during a specific period), (2) that fixed and known quantities of various commodities are available each period.

(a) Indicate (on an indifference diagram or in any other manner) how to determine the quantity of each good that an individual would purchase, given money prices, point prices, his money income, and his point income (i) if it is illegal to transfer points from one person to another and consumers conform to this requirement, and (ii) if points may legally be bought and sold for money. In this case, take as given to the individual consumer also the price of points in terms of money.

(b) If the only thing the government fixed were the number of points each individual receives, and it were to allow the money prices, point prices, and price of points in terms of money to be determined on the market, there would not be a unique set of values of these variables that would establish equilibrium, because the number of variables would be greater than the number of conditions. Explain this statement. Suppose the government tries to remove the indeterminacy by assigning values to some variables on the basis of criteria other than clearing the market. How many variables could the government so set and still have a determinate equilibrium? Does it matter which variables the government sets?

(c) It has been argues that every consumer will gain if non-transferable points, case (a) (i), were made freely transferable into money, case (a) (ii). Do you think this correct? Discuss.

(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?

1. Comment briefly on the following two sentences, taken from newspaper stories:

a. “Demand went up and therefore price went up.”

b. “Price went up and therefore demand declined.”

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. Descriptive data:

a. Population: a community consists of three classes—rich, middle-class, and poor. The numbers and family incomes are:

Rich: 1,000 families, $10,000 income per family.

Middle-class: 10,000 families, $3,000 income per family.

Poor: 1,000 families, $1,000 income per family.

b. Commodities: There are two commodities: housing and food, considered as single composite commodities.

c. Demand curves: All individuals in the community have the following demand curves:

$h=I/(2p_h)$

$f=I/(2p_f)$

where

$h$ = number of housing units per time unit.

$p_h$ = price per housing unit.

$f$ = number of food units per time unit.

$p_f$ = price per food unit.

$I$ = income of the family per time unit.

d. Supplies available.

There are available 205,000 housing units, and 205,000 food units. These amounts are available regardless of price and cannot be increased in the period considered.

Questions:

Determine:

a. The aggregate demand curve for the entire community for (1) housing, (2) food.

b. The prices that will prevail, assuming a free market.

c. The quantity of food and housing consumed by a family of each class.

d. The elasticity of the market demand curve for each product at a quantity of 205,000 units.

2. Appraise the following quotation from A. C. Pigou: “Since elasticity measures variations 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.”

3. “As Sir R. Giffen has pointed out, rise in the price of bread makes so large a drain on the resources of the poorer laboring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive farinaceous foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it.” Marshall, p. 132.

a. Give your own verbal explanation of how such a positively sloping demand schedule can arise.

b. Draw an indifference curve diagram that will display this phenomenon.

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

2. Discuss critically the following quotation from Stigler:

“The principle of an increasing $S_{yx}$ [the marginal rate of substitution of y for x] corresponds to the older theory of diminishing marginal utility of a commodity as its quantity increases. More precisely: if $S_{yx}$ is increasing, then the marginal utilities of y and x must be decreasing; if the marginal utilities of y and x are decreasing, then $S_{yx}$ is probably, but not necessarily, increasing.”

3. Assume that the demand curve for complete flashlights of a standardized type is known; that the case and bulb are produced separately from the batteries; that the cost of putting the batteries in the case can be neglected; that the number and type of batteries put in each flashlight is fixed and unchangeable; that the supply curves of (1) case and bulb assembly and (2) batteries are known; and that the markets for complete flashlights, case and bulb assemblies, and batteries are reasonably competitive.

a. Indicate how to derive the demand curve for batteries alone. Under what assumptions is this demand curve valid; and for what kinds of problems is it relevant?

b. Suppose the supply curve of case and bulb assembly shifts to the right (i.e., supply increases). What effect will this have on the price of batteries?

c. Under what conditions would you expect the derived demand curve for batteries to be extremely inelastic?

4. Statistical demand curves for fluid milk are derived by two different procedures.

(1) Data for a particular year for the 48 states of the United States are used to obtain a correlation equation expressing (a) the price of fluid milk in a state as a function of (b) per capita consumption of fluid milk in that state and (c) per capita income in that state.

(2) Data for a period of years for the United States are used to obtain a correlation equation expressing (a) the price of milk in the United States as a function of (b) the per capita consumption of fluid milk in the United States and (c) the per capita income in the United States.

Under what conditions, if any, would you expect the results to be identical? If the results are not identical, discuss the relative advantages and disadvantages of each. Indicate the conditions under which you would expect (1) to give a better estimate of “the” demand curve for milk and, the conditions under which you would expect (2) to give a better estimate. How, if at all, could one determine which set of conditions prevails.

Answer the following True, False, or Uncertain and explain your answer briefly. Your score depends on your explanation.

In a free market economy, all consumers participate equally in determining what will be produced.

A free market economy gives ample incentives to conserve natural resources provided that it is clear who owns each unit of the resources.

The cross-elasticity of demand between substitutes is positive.

If two linear demand curves each intersect the price axis, (q =0) the one that has the higher intercept is more elastic at this quantity.

An increase in the price of beef will increase the demand for pork and decrease the demand for beef.

If the market for eggs is in equilibrium an increase in supply will cause only a small change in price.

The elasticity of demand for oranges is greater in absolute value than the elasticity of demand for fruit.

Show by means of an indifference map (axes: oranges and grapefruit) the effect on the consumption of oranges of an increase in their price, the price of grapefruit remaining unchanged. Distinguish the income and the substitution effects. State whether you have used the Hicks or the Slutsky method.

How would your map have differed if the axes had been bread and meat? If they had been bread and butter?

Increased costs cause manufacturers to reduce the size of 5 cent chocolate bars from 2-1/2 ounces to 2 ounces. Because the bars are smaller, people eat more of them and consumption rises from 10,000 bars a week to 11,000.

Can these events be shown on an ordinary supply and demand diagram? If so, show them. If not, explain why.

Can the elasticity of demand for chocolate be computed? If so, compute it. If not, explain.

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.

Translate into the apparatus of indifference curves and budget lines the following phenomena:

The individual likes good music more, the more he hears.

The individual has monopsonistic power with respect to one commodity.

(a) The consumption of the two commodities (however spaced) is poisonous.

(b) The consumption of either commodity alone is poisonous.

The individual cannot afford one of the commodities.

(a) One of the commodities yields increasing marginal utility.

(b) Both do.

(a) Appraise: “Recent studies of domestic consumption in low-cost municipalities demonstrate that the demand for electric current is highly elastic, expanding rapidly as the cost declines. The national average consumption of the United States was 604 kilowatt-hours in 1933. The average charge to consumers on October 1, 1934, for the whole country is reported as 5.4 cents per kilowatt-hour. In Seattle where the average cost is 2.58 cents, the average consumption is 1,098 kilowatt-hours. In Tacoma, the charge is 1.726 cents and the consumption 1,550. In 26 cities of Ontario, the average charge is 1.45 cents and the consumption 1,780. Finally, in Winnipeg, where the average net charge is only 8 mills per kilowatt-hour the average per capita consumption exceeds 4,000 kilowatt-hours.” (Report of the National Resources Board, December 1, 1934, Government Printing Office, 1934, p. 39.)

(b) Will a specific tax (a tax of a specified number of dollars per physical unit) on a commodity raise its price more or less than an equivalent ad valoremtax (a tax of a specified percentage of the price)? Assume that the commodity is produced and sold under competitive conditions.

(a) Figure 1 gives the locus of points of tangency between indifference curves and budget lines parallel to ab (and cd). ABCDEFGH is therefore and “expansion path” or curve showing the quantity of X and Y and individual would buy at different incomes and constant relative prices. Fill in the following table with as precise statements as are deducible from Fig. 1 by observation without measurement:

Segment | Income elasticity of (X, Y) | Good is Superior (S), Inferior (I), or Uncertain (U) (X, Y) AB BC CD DE EF FG GH

(b) ABCDEF in Figure 2 is the locus of points of tangency between indifference curves and budget lines representing different money prices for X but the same money price of Y and money income (i.e. budget lines like ab and ac rotating about a). Fill in the following table with as precise statements as are deducible from Fig. 2 by observation without measurement.

Segment | Income elasticity of (X, Y) | Good is Superior (S), Inferior (I), or Uncertain (U) (X, Y) AB BC CD DE EF

The accompanying diagram showing a set of indifference curves between income and work is part of a diagram given by Boulding in Economic Analysis in his discussion of the effects of various types of direct taxation, and reproduced by Schwartz and Moore in the March 1951 American Economic Review. The latter write, “Given O Q2Q5 as a rate of pay, the equilibrium position is P1 where the rate of pay is equal to the MRS between leisure and income. Let us assume that we are to collect a tax from this individual equal to OL. One method of collecting the tax would be to levy a poll tax, leaving the rate of pay unaltered, as LP5. Another direct tax would be a proportional income tax represented by OSP2 which would have the effect of lowering (flattening) the rate of ‘take-home’ pay. To extract the same amount of revenue as the poll tax does, this rate of pay must be tangent to an indifference curve at an intersection with LP5. Thus P2Q2 = OL. Since the rate of ‘take-home’ pay is flatter, P2 must lie below and to the left of P5; i.e. less effort is expended and the worker enjoys a smaller net income. More important, his welfare is diminished because he must be on a lower indifference curve…Given the premises of the conventional indifference curve pattern, this must necessarily be true.”

(a):

(1) Why do the indifference curves in the diagram slope positively?

(2) How can you justify their being drawn concave upwards?

(3) The statement that OQ2Q5 is “a rate of pay” is of course wrong. OQ2Q5 is a line. Reword the statement so it is accurate.

(4) What do the authors mean by MRS?

(b) If we suppose the diagram to stand for a “representative” individual, or one of a society of identical individuals all to be taxed alike, the last sentence in the quotation is false: the authors' welfare conclusion does not follow from their premises and arguments. Point out the fallacy in the proof.

(c) Under what conditions is the authors' welfare conclusion valid? Can you give a proof of your statement?

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.

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.

Treat charitable contributions as a commodity entering the utility functions or indifference curves systems of the contributor. Assume, as is largely true, that contributions can be deducted from income in arriving at taxable income. Assume a proportional tax rate equal to t.

What would be the effect of an increase in the tax rate for any one person alone on his contributions? How does your analysis compare with the traditional analysis for commodities?

Is he more likely to increase or decrease his contributions?

Suppose now the tax rate increased for everyone. Would your answers to a. and b. be significantly different?

The concept of marginal utility is subject to the objection that it implies a numerical measurement of total utility. How can we overcome this difficulty? Translate into terms which do not involve the cardinal measurement of utility:

(a) The law of diminishing marginal utility.

(b) The Pareto optimality condition that the ratio of the marginal utilities of two goods must equal for all individuals in a free-exchange economy.

Sketch the indifference curve mappings implied by each of the following. Show the preference directions in each case:

(a) “I like to spend hours at the beach. I’d like it even more if I remembered to bring my suntan oil.”

(b) “I don’t care whether I eat steak or lobsters.”

(c) “I’d pay anything not to take this test.”

In a situation with two commodities, X and Y, and starting with an individual’s interior (non-corner) endowment, derive his demand curve for commodity X. Is the demand curve derived one with real income constant in the Hicksian or Slutsky sense? First, however, explain the Hicksian versus Slutsky demand curves.

What is an income-compensated demand curve? Carefully derive one graphically. How does it differ from an ordinary demand curve? For a normal good, which of the two curves is more elastic? Why? What might be an empirical use of an income-compensated demand curve?

“Since 1900 real income has increased tremendously, yet the average number of children per family has decreased.” Consider the following possible explanations, and graphically illustrate in terms of market opportunities and indifference curves between the number of children (x) and all other goods (y). Children are inferior goods; since we are richer we want fewer of them. (b) Children are not inferior goods; however, it has become more expensive to bear and raise children. (c) Children are not inferior goods, nor have they become relatively more expensive. What has happened is that tastes have changed.

Explain the following accurate statement: The gain from search activity is related to the dispersion of prices charged by different sellers. The gain is also related to the fraction of the individual’s income spent of the good and its income elasticity. Give a real world example of a good whereby the buyer searches a little and another good whereby the buyer searches a lot. Explain why.

(a) Explain the meaning of the statement: “In the theory of demand, a demand function, such as $Q_a=F(P_a,P_b,I)$, is linearly homogenous of degree zero.”

(b) Demand curves are relatively more elastic in the long run than in the short-run. Explain.

(c) Explain the concepts of cardinal and ordinal utility. Discuss how the shortcoming of cardinal utility are resolved in ordinal utility, e.g., diminishing marginal utility.

What does it mean if an indifference curve between goods X and Y (a) becomes parallel to the X axis, (b) is positively sloped and has higher indifference curves to its right, (c) is positively sloped and has higher indifference curves to its left, (d) is negatively sloped and has higher indifference curves to its left?

Assume that the cost of a unit of search is the same for all goods and all have the same price variability in the absence of search.

(a) Show that if the cost of search is proportional to income, the rich will search more and thus pay less for goods with income elasticities greater than unity and search less and pay more for goods with income elasticities less than unity.

(b) On the basis of these results, do you expect the poor to pay more for good? Are there policy implications in your findings which may increase the welfare of the poor?

What are the four essential properties of indifference curves between two goods? Explain the justification for each property.

What is the meaning of the expression “The optimum of the consumer”?

Characterize (graphically) a normal good, an inferior good, and an ultra-superior good. Give examples of each. For two goods X and Y, which of the above must they be if the Income Expansion Path (IEP) has a positive slope? What can you say if the (IEP) has a negative slope?

Demand curves tend to be more elastic in the long run than in the short run. Explain.

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?

What is an income-compensated demand curve? How does it differ from the ordinary demand curve? For a normal good (positive income elasticity), which of the two curves is the more elastic? Why?

In a situation with two commodities, $x_1$ and $x_2$, starting with an individual’s interior (non-corner) endowment, derive his demand curve for commodity $x_2$. Is the demand curve derived one with real income constant in the Hicksian or Slutsky sense? First explain the Hicksian vs Slutsky demand curves.

Give brief (a sentence or two) comments to the following:

(a) Demand curves tend to be more elastic in the long run than in the short run.

(b) Men (persons) do not differ significantly from roaches.

(c) Unemployment means that there are not enough jobs to go around.

(d) The tendency for mechanics to charge women higher prices for a given emergency repair than that charged men.

What are the four essential property of indifference curves between two goods? Explain the justification for each property.

(a) In a situation with two commodities X and Y, starting with an individual’s interior (non-corner) endowment derive his demand curve for commodity X. Is this an “excess-demand” curve or a “full-demand” curve?

(b) Explain Friedman’s concept of the “real-income-constant” demand curve. Is the demand curve just derived one with real-income-constant in his sense?

Explain Friedman’s concept of the “real-income-constant” demand curve. Is the demand curve just derived one with real-income-constant in his sense?

“Since 1900 real income has increased tremendously, yet the average number of children per family has decreased.” Consider the following possible explanations, and illustrate in terms of market opportunities and family indifference curves between the number of children (x) and all other goods (y). (a) Children are inferior goods; since we are richer we want fewer of them. (b) Children are not inferior goods; however, it has become more expensive to bear and raise children. (c) Children are not inferior goods, nor have they become relatively more expensive to raise. What has happened is that tastes have changed.

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?

Give brief answers to each of the following:

(a) “Since a monopolist is the only supplier of a well-defined product, there is no limit to the price it may charge.” Is this statement true or false?

(b) Explain why a monopolist will never set a price (and produce the corresponding output) at which the demand is price-inelastic.

(c) “The ultimate monopoly product would be one whose cross elasticity of demand, with respect to any and all other products, was zero.” Comment.

(d) “The reason movie theaters charge youngsters and oldsters less than the rest of us is because theater owners want to help these two low-income groups.”

Give brief answers to each of the following:

(a) “Since a monopolist is the only supplier of a well- defined product, there is no limit to the price it may charge.” Is this statement true or false?

(b) Explain why a monopolist will never set a price (and produce the corresponding output) at which the demand is price-inelastic.

(c) “The ultimate monopoly product would be one whose cross elasticity of demand, with respect to any and all other products, was zero.” Comment.

(d) “The reason movie theaters charge youngsters and oldsters less than the rest of us is because theater owners want to help these two low-income groups.”

Do the following comments reflect sound economic reasoning? Explain why or why not. (a) “I paid $200.00 for this economics course. Therefore, I am going to attend the lectures even if they are useless and boring.” (b) “Since we own rather than rent, housing does not cost us anything.” (c) I own 100 shares of stock that I can’t afford to sell until the price goes up enough for me to get back at least my original investment.” (d) “It costs to produce private education, whereas public schooling is free.”