4. The consumption-leisure framework. In this question you will use the basic (one- period) consumption-leisure framework to consider some labor market issues. Suppose that the representative consumer has the following utility function over con- sumption and labor: A u(c, 1) = In c- 1+0 where, as usual, c denotes consumption and n denotes the number of hours of labor the consumer chooses to work. The constants A and o are outside the control of the individual, but each is strictly positive. (As usual, In(-) is the natural log function.) Suppose that the budget constraint (expressed in real, rather than in nominal, terms) the individual faces is c (1-t) w.n, where t is the labor tax rate, w is the real hourly wage rate, and n is the number of hours the individual works. Recall that n+ 1= 1 must always be true. The Lagrangian for this problem is A Inc-n* + a[(1-t)wn- c], 1+0 where A denotes the Lagrange multiplier on the budget constraint.

4. The consumption-leisure framework. In this question you will use the basic (one- period) consumption-leisure framework to consider some labor market issues. Suppose that the representative consumer has the following utility function over con- sumption and labor: A u(c, 1) = In c- 1+0 where, as usual, c denotes consumption and n denotes the number of hours of labor the consumer chooses to work. The constants A and o are outside the control of the individual, but each is strictly positive. (As usual, In(-) is the natural log function.) Suppose that the budget constraint (expressed in real, rather than in nominal, terms) the individual faces is c (1-t) w.n, where t is the labor tax rate, w is the real hourly wage rate, and n is the number of hours the individual works. Recall that n+ 1= 1 must always be true. The Lagrangian for this problem is A Inc-n* + a[(1-t)wn- c], 1+0 where A denotes the Lagrange multiplier on the budget constraint.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.11P

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