1
Collection of Practice Problems
Econ 204A
Henning Bohn
*
In previous years, students have often asked me about practice problems in addition to the problem
sets. Here is a collection. Some will be assigned for the weekly problem sets. I hope the others are
useful for practice.
Request
: Please tell me about errors or ambiguities. Many of the questions below are old exam
problems. As I am updating the course over the years, the notation, references, and sequencing has
changed, which means that some old problems may have lost educational value without me noticing
immediately. So if a problem seems obscure to you, please let me know. (Your incentive: your
problem set might shrink if you convince me that a problem is unclear.)
Part 1
:
1.1. Consider the twoperiod consumption model: Individuals have initial assets A, earn interest r on
assets, and earn wage income
(
w
1
,
w
2
)
. They maximize utility
U
=
u
(
c
1
)
+
β
u
(
c
2
)
.
a.
Assume
u
(
c
)
=
ln(
c
)
.
i. Solve for optimal consumption and period1 asset holdings as functions of wage income, the
interest rate, and the timediscount factor
β
. Discuss under what conditions a marginally
higher interest rate reduces consumption. [Discuss means: Interpret the solution. Conditions
may be exact, or necessary, or sufficient. Hint: Distinguish cases with
w
2
=
0
vs.
w
2
>
0
.]
ii. Show that the dependence of period1 consumption on
(
w
1
,
w
2
)
can be expressed in terms of
permanent income.
b.
Assume
u
(
c
)
=
1
1
−
γ
c
1
−
γ
where
γ
>
0,
γ
≠
1
.
Do the same as in (a). In the discussion, identify which results apply for all
γ
, and which ones
only for
γ
greater or less than one.
*
Provided online for use by UCSB students. (C) Copyright 2011 Henning Bohn
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1.2. Economists sometimes use the marginal propensity to consume (MPC) to express the effects of
income changes on consumption: MPC is defined as the ratio
Δ
c
t
/
Δ
w
t
of a change
Δ
c
t
in
consumption triggered by some change
Δ
w
t
in the current wage income that may or may not be
accompanied by changes in future wages. This question will ask you to compute the MPC for
several scenarios. (Hint: Use a spreadsheet for calculation.)
Assume the permanent income model with planning horizon of n periods. Assume
β
=1/(1+r) with
r=3% per year. Assume zero initial assets (A=0).
a.
Assume the time horizon is n=50 years (interpretation: roughly the life expectancy at age 30).
Determine the MPC from
i. a oneyear wage increase;
ii. an increase in wages that lasts 5 years;
iii. a wage increase that last for 35 years [intuition: until about retirement];
iv. a tax reduction for one year followed by a tax increase of the same size in the next year.
Discuss: How do the results compare? Do you find them surprising? Realistic? Why or why not?
b.
Determine the impact of a oneyear wage increase for consumers with alternative planning
horizons of, respectively: n=1 year; n=2 years; n=10 years; n=50 years; the limiting case of
n=infinity.
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 Fall '08
 Staff
 Economics, Steady State, Interest Rates, Capital accumulation

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