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(a) Derive the first-order conditions and show the solution is a c(w, T), n(w, T). pair of functions

(a) Derive the first-order conditions and show the solution is a c(w, T), n(w, T). pair of functions

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.2P
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4. Laffer Curve In the 1980s, President Reagan based his tax and spending policies on supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let 7 denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wnT where 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 the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute toward leisure and away from consumption. Hence as 7 rises, wn falls and tax revenue falls for high enough tax rates. Let U, V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A representative household solves max [U(c) + V (1 – n) {cn} subject to wn(1 – 7) 2 c. (a) Derive the first-order conditions and show the solution is a pair of functions c(w, 7), n(w, T).
Transcribed Image Text:4. Laffer Curve In the 1980s, President Reagan based his tax and spending policies on supply side economics. The idea behind supply side economics is the marginal tax rate is so high it discourages work. Cutting the tax rate would end up increasing tax revenue. We develop a simple model of this idea to determine the restrictions on the utility function required to generate a Laffer curve. Let 7 denote the tax rate, w the real wage rate, and n the labor supply. The tax revenue is T = wnT where 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 the restrictions on the utility function to generate the Laffer curve. As the tax rate T increases, workers substitute toward leisure and away from consumption. Hence as 7 rises, wn falls and tax revenue falls for high enough tax rates. Let U, V satisfy the standard assumptions. The model is static and households are endowed with one unit of time. A representative household solves max [U(c) + V (1 – n) {cn} subject to wn(1 – 7) 2 c. (a) Derive the first-order conditions and show the solution is a pair of functions c(w, 7), n(w, T).
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