Solution of EC904 Resit Exam
1. [20 marks] Answer both parts (a) and (b) of this question.
Dynamic efficiency in the OLG economy. Consider the two period OLG economy discussed
in the lectures with positive population growth
n >
0
and zero depreciation
δ
= 0
. Assume
that the household utility function is
log
c
y
t
+
β
log
c
o
t
,
where
c
y
t
, c
o
t
represent consumption
when young and old, respectively. Denote the wage as
w
t
and fix the labor supply as 1.
(a) Consider the simple partial equilibrium where wage and interest rate are fixed as
w
and
r
, respectively. In this simple setup, we can ignore capital
k
t
.
i. [5 marks] What is the decentralized consumption allocation for each generation,
given wage
w
? (Hint: solve for
c
y
t
, c
o
t
as functions of
w
. No need to go further to
discuss
k
)
Answer:
c
y
t
=
w
1+
β
, c
y
t
=
β
(1+
r
)
w
1+
β
.
ii. [5 marks] In this partial equilibrium, if the interest rate is low:
r < n
, is the decen-
tralized allocation dynamically inefficient, i.e., is it possible to obtain an consump-
tion allocation that is better than the decentralized allocation, for all generations? If
it is possible, give an example. If it is not possible, find the conditions such that the
decentralized allocation is dynamically inefficient. (Hint: try to find an alternative
consumption allocation
c
y
*
t
≥
c
y
t
, c
o
*
t
≥
c
o
t
for all
t
while
c
o
*
0
> c
o
0
for the first
generation
t
= 0
.)
Answer: Yes, it is dynamically inefficient.
A better allocation: Increase
c
o
0
by
(1 +
n
)
>
0
unit; decrease
c
y
0
by
, increase
c
o
1
by
(1 +
n
)
; decrease
c
y
1
by
,
increase
c
o
2
by
(1 +
n
)
; etc.
(b) [10 marks] If we consider the general equilibrium as in the lectures, where
w
t
and
r
t
are
determined by
k
t
, what is the condition for dynamical inefficiency at the steady state? If
the economy is dynamically inefficient, what government policies can be used to restore
the economy to efficiency? Give at least two examples and explain how these policies
change capital and consumption allocations and restore the efficiency.
Answer: The condition for dynamic inefficiency is
r < n
at the steady state. Government
policies including pension, government debt and money issuing can be implemented to
restore the efficiency. Pension: lumpsum tax on the young and lumpsum pension pay-
ment to the old, so that household savings and capital decrease and
r
increases above
n
;
Government debt: issue positive debt so that part of household savings become govern-
ment debt, and the rest of savings become capital, which is low enough and
r
is higher
than
n
; Money: issue money so that the part of household savings that are transformed
into capital becomes low enough and
r > n
.
2. [40 marks] Answer all parts (a) - (e) of this question.
Consider a standard Diamond-Mortensen-Pissarides model covered in the lecture. The econ-
omy is populated by a unit measure of infinitely lived firms and workers who discount the
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