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.
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.
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.8P
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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 T
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)
{c,n}
subject to
wn(1 – 7) > c.
(a) Derive the first-order conditions and show the solution is a pair of fumctions
c(w, 7), n(w, T).
(b) Determine the impact of an increase in 7 on the labor supply decision. Show the
answer depends on the sign of
U"(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 which
of the three cases will the increase in the tax rate result in lower tax revenue? To
simplify the problem, you can assume
U(c) =
1-7
Transcribed Image Text: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 = Anº
where A > 0 is constant and0 < a < 1. Households receive labor income and
dividend income D where all profits are distributed as dividend. The household's
budget set is
wn(1 – 7) +D > c
In equilibrium c = y.
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 T 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 w as 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
which actually functions of underlying parameters.
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