Consider the problem a society faces if it wants to both maximize efficiency while also insuring that the overall distribution of “happiness” in the society satisfies some notion of “equity”.

A: Suppose that everyone in the economy has tastes over x and a composite good y , with all tastes quasilinear in x.

(a) Does the market demand curve (for x) in such an economy depend on how income is distributed among individuals (assuming no one ends up at a corner solution)?

(b) Suppose you are asked for advice by a government that has the dual objective of maximizing efficiency as well as insuring some notion of “equity”. In particular, the government considers two possible proposals: Under proposal A, the government redistributes income from wealthier individuals to poorer individuals before allowing the market for x to operate. Under proposal B, on the other hand, the government allows the market for x to operate immediately and then redistributes money from wealthy to poorer individuals after equilibrium has been reached in the market. Which would you recommend?

(c) Suppose next that the government has been replaced by an omniscient social planner who does not rely on market processes but who shares the previous government’s dual objective. Would this planner choose a different output level for x than is chosen under proposal A or proposal B in part (b)?

(d) True or False: As long as money can be easily transferred between individuals, there is no tension in this economy between achieving many different notions of “equity” and achieving efficiency in the market for x.

(e) To add some additional realism to the exercise, suppose that the government has to use dis-tortionary taxes in order to redistribute income between individuals. Is it still the case that there is no tradeoff between efficiency and different notions of equity?

B: Suppose there are two types of consumers: Consumer type 1 has utility function u¹(x, y) = 50x^1/2+y, and consumer type 2 has utility function u² (x, y) = 10x^3/4 + y . Suppose further that consumer type 1 has income of 800 and consumer type 2 has income of 1,200.

(a) Calculate the demand functions for x for each consumer type assuming the price of x is p and the price of y is 1.

(b) Calculate the aggregate demand function when there are 32,000 of each consumer type.

(c) Suppose that the market for x is a perfectly competitive market with identical firms that attain zero long run profit when p = 2.5. Determine the long run equilibrium output level in this industry.

(d) How much x does each consumer type consume?

(e) Suppose the government decides to redistribute income in such a way that, after the redistribution, all consumers have equal income — i.e. all consumers now have income of 1,000. Will the equilibrium in the x market change? Will the consumption of x by any consumer change?

(f) Suppose instead of a competitive market, a social planner determined how much x and how much y every consumer consumes. Assume that the social planner is concerned about both the absolute welfare of each consumer as well as the distribution of welfare across consumers — with more equal distribution more desirable. Will the planner produce the same amount of x as the competitive market?

(g) True or False: The social planner can achieve his desired outcome by allowing a competitive market in x to operate and then simply transferring y across individuals to achieve the desired distribution of happiness in society.

(h) Would anything in your analysis change if the market supply function were upward sloping?

(i) Economists sometimes refer to economies in which all individuals have quasilinear tastes as “transferable utility economies” — which means that in economies like this, the government can transfer happiness from one person to another. Can you see why this is the case if we were using the utility functions as accurate measurements of happiness?