Consider again, as in exercise 15.5, the problem faced by a society that wants to both maximize efficiency and achieve some notion of “equity”.

A: Suppose again that everyone has tastes over x and a composite good y, but now suppose that tastes are homothetic.

(a) Does the market demand curve (for x) depend on how income is distributed among individuals?

(b) Would your answer to (a) be different if you thought that everyone had identical (homothetic) tastes?

(c) Suppose you are again asked for the same advice as in exercise 15.5A(b). What is your answer now?

(d) Repeat part A(c) from exercise 15.5 for this economy.

(e) Recall that we defined a situation as “efficient” if there is no way to change the situation and make someone better off without making someone else worse off. In general (i.e. not just within the context of the example in this exercise), is it possible to have two efficient outcomes where some individuals prefer the first outcome while others prefer the second?

(f) True or False: If the government redistributes income between individuals prior to the market for x operating, the outcome is efficient so long as income can be redistributed without cost.

(g) True or False: In the quasilinear example of exercise 15.5, all efficient outcomes (excluding those that involve corner solutions) will involve the same level of production of x, but in the example of the current exercise this is no longer the case.

(h) True or False: Assuming redistribution takes place before the market opens, a tradeoff between efficiency and equity only emerges in this economy if redistributing money between individuals involves the use of distortionary taxes.

(i) Does your conclusion in (h) hold more generally for non-homothetic tastes as well?

B: Suppose again, as in exercise 15.5, that there are two types of individuals in the economy. Type 1 has utility function u¹(x, y) = x^αy ^(1−α) and type 2 has utility function u²(x, y)=x^βy^(1−β) (with both α and β falling between 0 and 1). Suppose further that type 1 individuals have income I and type 2 individuals have income I′ .

(a) What is each type’s demand function for x assuming price p for x and a price of 1 for y .

(b) What is the market demand function for x if there are an equal number N of each type in the economy.

(c) Suppose α = β and money can be transferred across individuals without cost. Will the equilibrium output level in the x market be affected by income redistribution policies? Will individual consumption levels of x be affected by such policies?

(d) Next, suppose α /= β. Will the equilibrium output level in the x market be affected by income redistribution policies?

(e) Suppose again that you are asked for your advice on the two alternative policies described in exercise 15.5A(b) (assuming again that the government has the dual objective of maximizing efficiency and achieving some notion of “equity”.) What is your advice now assuming that individuals cannot trade goods with one another after they have purchased x?

(f) Assume again that the government is replaced by an omniscient social planner who shares the previous government’s dual objective. Will his decision on how much x to produce mirror the outcome of either of the two policies you considered in part (e)?