Econ 305 Final Exam
December 2002
D. Andolfatto
Name
Instructions. Please limit your answer to the space provided below each question. The exam is worth 85
marks.
1. [10 Marks]. The expenditure approach to measuring GDP implies Y ≡ C + I + G + X − M. Does this
identity imply that an increase in G must lead to an increase in Y ? Explain.
2. [10 Marks]. Despite the fact that real wages in Canada have been increasing steadily over the last 100
years, the amount of time that people devote to the market sector has shown no discernible trend. Is
this basic fact consistent with theory? Explain.
3. [15 Marks]. Consider the following (static) labour-leisure model. Individuals have preferences for
consumption (c) and leisure () that imply an MRS = λ(T − ). Individuals have an endowment of
time T that they may divide between work (n) and leisure; i.e., n + = T. The production of output
in this economy is given by y = zn, where z represents both labour productivity and the real wage.
There is a government that demands g units of output, which it consumes. The government acquires
this output by imposing an income tax τ , leaving individuals with disposable income (1 − τ )zn.
(a) Write down an individual’s budget constraint in terms of c and . What is the slope of this budget
line?
(b) Solve for the supply of labour as a function of (τ, z, λ). How does an increase in τ affect the supply
of labour? Explain.
(c) Is it true that real GDP in this model equals y = c + g ? If an increase in g requires an increase in
τ , then use this model to explain what happens to real GDP when the government embarks on
an ‘expansionary’ fiscal policy.
4. [15 Marks]. Consider an individual with preferences for time-dated consumption (c1 ,c2 ) that imply
MRS c /c
.
R.
an
= ( 2 1 )1 /2 This individual can borrow or lend freely at the (gross) real rate of interest
The individual has an exogenous earnings stream given by ( 1 2 ) = ( 0); i.e., think of this person as
approaching retirement.
y ,y
y,
(a) Solve for this person’s first-period consumption function. How does consumer demand respond
to an increase in the interest rate? Explain.
(b) Suppose that the government decides to supplement the income of retired people with a lump-sum
amount equal to
In order to finance this program, the government imposes a lump-sum tax
on the young and then saves this tax revenue at the market interest rate
In effect, this pension
program alters the individual’s after-tax income stream to (
) Solve for the individual’s
first-period consumption function as a function of (
)
s.
y − τ,s .
y,R,τ,s .
R.
τ
(c) Write down the government’s budget constraint. Insert this constraint into the consumption
function derived in part (b) above. What sort of effect does this pension plan have on the
behaviour of our consumer? Explain.
5. [15 Marks]. Consider a small open economy that is populated by a representative individual with
preferences for time-dated consumption given by ( 1 2 ) Let denote the real (gross) rate of interest.
Individuals are endowed with units of output in the current period. If units of output are invested
1 /2
units of output are produced in the future. The marginal product of
in domestic industry, then
1
− 1/2 .
(future) capital is given by 2
y
Ak
Ak
U c ,c . R
k
Capital depreciates fully after it is used in production.
(a) In equilibrium, the rate of return on capital and bonds must be equal. Use this condition to
solve for the demand for domestic capital investment kD . How does capital spending respond to
a decrease in the parameter A? Explain.
(b) Depict the equilibrium consumption allocation and investment level for this economy on a diagram
in (c2 − c1 ) space. Assume that initially, the current account position is equal to zero.
(c) Suppose that news arrives that causes our domestic agents to revise downward their forecast of
A. Using the result derived in part (a) and the diagram in part (b), depict the new consumption
allocation, investment level and current account position. Explain what is happening here.
6. [10 Marks]. According to the Malthusian growth model, a technological advance in production methods
leaves long-run living standards (real per capita income) unchanged. Even worse, a technological
advancement that reduces mortality rates is predicted to result in a decline in long-run living standards.
Using words only, explain the economic mechanism at work here. How does the evidence stack up
against the predictions of this model?
7. [10 Marks]. According to a version of the Quantity Theory of Money, the aggregate demand for nominal
money balances is proportional to the level of nominal GDP; i.e., MtD = ktPt Yt, where Pt is the pricelevel, Yt is the level of real GDP, and kt is a parameter. Assume that real GDP grows exogenously at
rate γ ; i.e., Yt = γYt−1 . Assume too that, owing to continued innovations in the economy’s payment
system, the parameter kt declines at rate θ; i.e., kt = θkt−1 (where θ < 1). If the monetary authority
has complete control over the money supply, how should it set monetary policy in order to achieve
price-level stability in this economy?