Homework 3
Jonathan Heathcote
Due in Class on Tuesday February 28th
In class we outlined two versions of the stochastic growth model: a planner’s
problem, and an ArrowDebreu competitive equilibrium. We were working to
wards showing that allocations in the two setups would be identical.
1. (a) Complete the proof that the sets of equations that characterize (i)
the solution to the planner’s problem, and (ii) the competitive equi
librium are identical, and thus that one can solve for equilibrium
allocations by solving the planner’s problem.
(b) Now consider the following twist on the economy we described in
class. Income (from both labor and capital) is taxed at rate
τ
t
,
where
0
<τ
t
<
1
.
There is no allowance for depreciation: thus
the typical consumer’s budget constraint (in the sequence of markets
formulation, without statecontingent claims) is
c
t
+
k
t
+1
=(1
−
τ
t
)(
r
t
k
t
+
w
t
n
t
)+(1
−
δ
)
k
t
Revenues are used for nonvalued government purchases
G
.Con
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