Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Define a weakly concave on the Cobb-Douglas Function
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Laffer curve
In the 1980s, president Reagan based his tax and spending policies on supply side eonomics. 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 T denote the tax rate, w is 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 convinience 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 towards leisure and away from consumption. Hence as T rises, wn falls and tax revenues 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…
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