4. Laffer CurveIn the 1980s, President Reagan based his tax and spending policies on supply sideeconomics. The idea behind supply side economics is the marginal tax rate is so highit discourages work. Cutting the tax rate would end up increasing tax revenue. Wedevelop a simple model of this idea to determine the restrictions on the utility functionrequired to generate a Laffer curve. Let 7 denote the tax rate, w the real wage rate,and n the labor supply. The tax revenue isT = wntwhere wn is labor income, which is the tax base. For convenience, assume w is constant.There is no reason for this assumption to be true, but we impose it to focus on therestrictions on the utility function to generate the Laffer curve. As the tax rate Tincreases, workers substitute toward leisure and away from consumption. Hence as Trises, wn falls and tax revenue falls for high enough tax rates.Let U, V satisfy the standard assumptions. The model is static and households areendowed with one unit of time. A representative household solvesmax [U(c) + V (1 – n){c,n}subject town(1 – 7) > c.(a) Derive the first-order conditions and show the solution is a pair of fumctionsc(w, 7), n(w, T).(b) Determine the impact of an increase in 7 on the labor supply decision. Show theanswer depends on the sign ofU"(c)c+ U'(c)(c) Suppose U"(c)c + U'(c) is monotone. This means for all positive consumption,U"(e)e+ U'(c) is either always increasing in c, constant, or decreasing. In whichof the three cases will the increase in the tax rate result in lower tax revenue? Tosimplify the problem, you can assumeU(c) =1-7 andV(1 – n) = 0(1– n)I realize the assumption on V violates the strictly concave of the utility function,but just go with it as a simplification.(d) Explain how the income and substitution effects impact your answer.(e) Drop the assumption w is constant. Assume now that output is produced asy = Anºwhere A > 0 is constant and0 < a < 1. Households receive labor income anddividend income D where all profits are distributed as dividend. The household'sbudget set iswn(1 – 7) +D > cIn equilibrium c = y.i. Solve the household's problem.ii. Assume there is a firm that manages the production process, hiring labor andpaying out profits as dividends. Write out the firm's problem.iii. Now vary the tax parameter 7 and determine what happens to equilibriumlabor, consumption and tax revenue as T varies.iv. Write out the equilibrium conditions. Assume the tax revenue disappearsand doesn't impact the goods market or provide any additional utility tohouseholds.v. In the first part of the question, you were told to treat w as fixed and deter-mine the impact of changes in 7 on the labor supply and tax revenue. In thesecond part of the question, you incorporated the impact of a change in thetax rate on wage rate. Explain why a prediction of the impact of an increasein the marginal tax rate based on the assumption the wage rate is constantis an example of the Lucas Critique - that some variables are held constantwhich actually functions of underlying parameters.

Labor income is the earnings earned by people through their employment or labor. It consists of…

and V(1 n) 0(1 n) I realize the assumption on V violates the strictly concave of the utility function, but just go with it as a simplification. (d) Explain how the income and substitution effects impact your answer. (e) Drop the assumption w is constant. Assume now that output is produced as y = Ana where A0 is constant and 0 < a < 1. Households receive labor income and dividend income D where all profits are distributed as dividend. The household's budget set is In equilibrium c=y. wn(1-T)+D≥C i. Solve the household's problem. ii. Assume there is a firm that manages the production process, hiring labor and paying out profits as dividends. Write out the firm's problem. iii. Now vary the tax parameter 7 and determine what happens to equilibrium labor, consumption and tax revenue as 7 varies. iv. Write out the equilibrium conditions. Assume the tax revenue disappears and doesn't impact the goods market or provide any additional utility to households. v. In the first part of the question, you were told to treat was fixed and deter- mine the impact of changes in 7 on the labor supply and tax revenue. In the second part of the question, you incorporated the impact of a change in the tax rate on wage rate. Explain why a prediction of the impact of an increase in the marginal tax rate based on the assumption the wage rate is constant is an example of the Lucas Critique that some variables are held constant allu functions of underlying parameters.

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC