General equilibrium

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

Pareto optimum

Pigou effect

Walrasian equilibrium

Schumpeterian innovators

Cobb-Douglas production function

Conspicuous consumption

Wicksellian natural rate of interest

Contract 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.”

Consider a price system involving four commodities, $q_1$, $q_2$, $q_3$, and $q_4$. If the goods are gross substitutes, it can be shown that the equilibrium will

(a) Satisfy the Hicks conditions of perfect stability, and

(b) Be dynamically stable.

Assume demand shifts from the first commodity to the second commodity. Again, assuming that the commodities are gross substitutes, it can then be demonstrated that:

(c) $P_1/P_2$ falls and $P_3/P_4$ remains unchanged;

(d) $P_2/P_3$ rises and $P_1/P_4$ falls;

(e) $P_3/P_1$ rises by a smaller proportion than $P_2/P_1$.

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

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

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

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

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.

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.

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.

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

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

(a) Is it possible to have a situation of general equilibrium without having all individual optimality conditions fulfilled? Explain.

(b) Is it possible to have all individual optimality conditions fulfilled without the state of the system as a whole being Pareto optimal? Explain.

Soviet planners do use open markets to permit relative prices to influence resource allocation. Briefly explain the role of prices in an economic system and the possible effects of restricting the role of prices.

(a) Is it possible to have a situation of general equilibrium without having all individual optimality conditions fulfilled? Explain.

(b) Is it possible to have all individual optimality conditions fulfilled without the state of the system as a whole also being Pareto Optimal? Explain.

(a) Is it possible to have a situation of general equilibrium without having all individual optimality condiions fulfilled? Explain.

(b) Is it possible to have all individual optimality conditions fulfilled without the state of the system as a whole being Pareto optimal. Explain telling what you mean by Pareto optimal.

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

(a) Illustrate verbally and diagrammatically the determination of:

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

2. The consumptive optimum and the volume of trade.

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

4. The individual’s wealth.

(b)

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

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

Is it possible to have a situation of general equilibrium without having all individual optimality conditions fulfilled? Explain. Is it possible to have all individual optimality conditions fulfilled without the state of the system as a whole being Pareto optimal?