Question

This Problem is from "Advanced Microeconomic Theory – Geoffrey Jehle, Philip Reny"

5.26 Suppose that in a single-consumer economy, the consumer is endowed with none of the consumption

good, y, and 24 hours of time, h, so that e = (24, 0). Suppose as well that preferences are defined

over R2

+ and represented by u(h, y) = hy, and production possibilities are Y = {(−h, y) | 0 ≤ h ≤ b

and 0 ≤ y ≤

√

h}, where b is some large positive number. Let py and ph be prices of the consumption

good and leisure, respectively.

(a) Find relative prices py/ph that clear the consumption and leisure markets simultaneously.

(b) Calculate the equilibrium consumption and production plans and sketch your results in R2

+.

(c) How many hours a day does the consumer work?

Answer 1