Kent State University
Macroeconomic Theory I
Practice
February 27, 2014
Consider a static economy with 2 consumption goods and labor. The government
needs to “consume” g = (g1 , g2 ) = (3, 4). That is, it needs to purchase 3 units of
good 1 and 4 units of good 2. In order to fund its expenditure, the government has
available linear taxes on consumption goods τ1 and τ2 .
The representative household solves (normalizing w = 1)
max α1 ln(c1 ) + α2 ln(c2 ) − l
(c1 ,c2 ,l)
s.t.
(1 + τ1 )p1 c1 + (1 + τ2 )p2 c2 = l
where ci is the consumption of the good i = 1, 2, and l is labor.
The representative firm solves
max p1 y1 + p2 y2 − l
(y1 ,y2 ,l)
s.t.
y1 y2
+
=l
θ1 θ2
where yi is the output of good i = 1, 2.
a. Set up the Ramsey problem for this economy.
b. Now suppose parameters for this economy are given by (α1 , α2 , θ1 , θ2 ) =
(0.3, 0.7, 12, 18). Solve the Ramsey problem for those particular values of parameters.
The rest of this question is about the implementation of the optimal allocation
that you just found.
c. Characterize the firm’s solution and the consumer’s solution.
d. How should taxes be set in this economy? In other words, find the consumption
taxes τ1 and τ2 that implement the optimal allocation.
e.Verify that the government’s budget constraint is satisfied.
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