University of Miami Neoclassical Growth Model and Fiscal Policy Questions

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2. (20 points) Neoclassical Growth Model: Consider the two main equations for the
Neoclassical Growth Model with exogenous labor:
2/4
akt+1
??/?? af
+ (1-5)
Bau/act+1
f(kt, Zin) = t + (kt+1 – (1 – )kt)
where Zt is exogenous labor-augmenting technological progress. In the steady state, Ž
and ñ grow at rates of 7z and Yn such that (dž /dt) /Z = y; and (dñ/dt)/n
= n.
—
=
Assume that both the production and utility functions take the CES form:
1/7
f(kt, Zin)
7

Okty + (1 – 0)(Zen)
(act
1/2
u(ct, ?)
=
act + (1 – a)TP
where 0 0 determines the elasticity of substitution between consumption and
leisure. Finally, households are assumed to have a unitary time endowment.
(a) Derive the steady state expressions for capital and output in terms of only exoge-
nous variables.
=
=
For parts (b)-(d): If you are unable to obtain an answer to part (a), you may
assume that the steady state expressions for capital and output take the form of
k=0xZñ and f(k, Zn) = of Zn, where ok and of are exogenous parameters.
(b) Use your solutions from part (a) to mathematically show that this model economy
exhibits the following long-run properties:
i. The output-labor ratio grows at a rate equal to growth in technical progress.
ii. The capital-output ratio is constant.
(c) Compute the steady state expression for consumption.
(d) Suppose that a = 1 so leisure is not valued by households. Compute the long-run
rate of growth in utility from consumption.
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3. (22 points) Fiscal Policy: Consider the infinite-period general equilibrium framework
government. The representative household chooses a path of consumption and
over an infinite horizon, {Ct+s, le+s}=0, to maximize the objective function:
3/4
V = ??*u(ct+s, le+s)
s=0
subject to the following real period-t budget constraint:
Ct + at = (1 + rt)at-1 + wint(1 – 77″) – tt
where at is real wealth, rt is the real interest rate, wt is the real wage rate, né = 1 – 14 is
labor supply, Tt” is a proportional tax rate on wage income, and tt is a lump-sum tax.
The representative firm chooses capital and labor input to maximize profits. (You may
assume that the firm here is identical to the firm in question 1.)
The government faces the following real period-t budget constraint:
9t + bt = bt-1(1+rt) + Tt
where T4 = t4 + tu wint is the government’s total tax revenue from households.
(a) Write down expressions for real private savings, government savings, and national
savings.
For parts (b)-(d): Suppose that the government makes two tax temporary changes
in period t: (i) the tax rate on wage income is decreased (17″ 1); and (ii) the lump-sum
tax is increased (t+1) as needed so that total tax revenue remains constant in period t.
Furthermore, assume that the substitution effect dominates the income effect for
household labor supply decisions.
(b) Explain how this policy change will affect each of the three definitions of savings
from part (a) (if at all), holding constant wt and rt. Make reference to both household
optimality conditions in your answer.
(c) Explain whether or not Ricardian Equivalence holds for this policy change.
(d) Use supply-and-demand diagram of the Labor Market and the Financial Market to
show how the policy would affect equilibrium prices and quantities in each market.
(e) Use a supply-and-demand diagram for the Goods Market to show a possible equilib-
rium outcome on GDP; and P4 as a result of this policy change.
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macroeconomics

Fiscal policy

neoclassical growth model

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