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 7rises, 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){cn}subject town(1 – 7) 2 c.(a) Derive the first-order conditions and show the solution is a pair of functionsc(w, 7), n(w, T).

The link between tax rates and government revenue is depicted in economics by the Laffer Curve. At…

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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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.9P

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Question

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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