Suppose That the Consumer Side of the Market for Good

Essay

Suppose that the consumer side of the market for good x can be modeled using a representative consumer with (initially - until part (d)) non-quasilinear preferences, and suppose the industry that produces x is perfectly competitive with identical firms.
a.Illustrate a demand and supply graph with the market clearing price and quantity.
b.Would a social planner who takes the distribution of income as given and seeks to maximize social surplus choose the same output quantity as the market clearing quantity in (a)?
c.Does your answer to (b) change if the social planner initially redistributes income in a lump-sum way and then maximizes social surplus?
d.Next, suppose tastes are quasilinear in the good x and identical for all individuals.But there are two different types of consumers (represented in equal proportion in the population) - rich type 1 consumers and poor type 2 consumers.At their current income levels, type 2 consumers consume only the good x (at quantity x′ ) and no "other goods".For what type of lump-sum redistribution will we no longer be able to represent the consumer side as if it arose from choices by a representative consumer?
e.Continuing with (d), suppose further that utility for an individual is given by the utility level associated with her consumption of x plus the dollar value of all other goods she consumes.Let type 2's utility level at her current consumption x′ be given by u′.If she were to then also consume $10 worth of other goods, her utility would be (u′ + 10).If a social planner could redistribute "$'s of other goods" from type 1 to type 2 in a lump-sum way, what shape would the utility possibility frontier have in the range where individuals get at least u′.f.Continuing with (e), draw the entire (first-best) utility possibility frontier (all the way to the horizontal and vertical axes) assuming that the utility possibility set has the feature you discovered in (e) and is convex.Indicate where on that utility possibility frontier we currently are in the absence of any redistribution.Which utility combination would be preferred to this by a Rawlsian social planner? Would a social planner who only cares about total utility object to the Rawlsian choice?
g.Now suppose that every dollar that is redistributed entails a penny of deadweight loss.How would your answer to (f) change? What would have to be true for the Rawlsian social planner to let go of his desire for full equality?