Problem 4 Consider the leisure demand/labor supply model studied in class, and let the consumer have a specific utility function U(N,Y) = N2/3y1/3 As in lecture, let the price of consumption be normalized to 1, and let w denote the wage. (a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch to illustrate this situation. (b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything special about this particular example? (c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch that decomposes this into an income effect and a substitution effect. (d) Sketch the labor supply function. (e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes an income tax of a. Let T(a) denote the total tax revenue raised as a function of a. What is dT/da? Explain.

Problem 4 Consider the leisure demand/labor supply model studied in class, and let the consumer have a specific utility function U(N,Y) = N2/3y1/3 As in lecture, let the price of consumption be normalized to 1, and let w denote the wage. (a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch to illustrate this situation. (b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything special about this particular example? (c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch that decomposes this into an income effect and a substitution effect. (d) Sketch the labor supply function. (e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes an income tax of a. Let T(a) denote the total tax revenue raised as a function of a. What is dT/da? Explain.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.12P

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