d. Based on both the consumption-leisure optimality condition obtained in previous part (Based on both of the two first-order conditions, construct the consumption-leisure optimality condition) and on the budget constraint, qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relationship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes. in / affect the relationship (shift it outward, shift it inward, or impossible to deter mine). Briefly describe the economics of how you obtained your conclusions. 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:Au(c, 1) = Inc -1+¢where, as usual, c denotes consumption and n denotes the number of hours of laborthe consumer chooses to work. The constants A and are outside the control of theindividual, 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 realhourly 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 isAInc-n** +2[(1-1)wn- c],1+0where å denotes the Lagrange multiplier on the budget constraint.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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d. Based on both the consumption-leisure optimality condition obtained in previous part (Based on both of the two first-order conditions, construct the consumption-leisure optimality condition) and on the budget constraint, qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relationship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes. in / affect the relationship (shift it outward, shift it inward, or impossible to deter mine). Briefly describe the economics of how you obtained your conclusions.