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Practice exam - past exam 2018
Macroeconomics (University of Melbourne)
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Practice Exam for Macroeconomics1
1. (10 marks) Is each of the following statements true or false? Write ‘T’ for true and ‘F’
for false on the scriptbook provided. No need to explain.
(1) The government’s intertemporal budget constraint (GIBC) requires the government to collect, over time, net taxes that are large enough, in present value, to
cover the present value of its spending as well as its initial debt.
(2) According to the life-cycle model, introducing a fully-funded social security system
does not affect national saving, national investment and real output, as social
security contribution pays the same rate of return as private saving.
(3) According to the life-cycle model, introducing a pay-as-you-go social security is
welfare-reducing as it reduces national saving and investment.
(4) According to the life-cycle model, regardless of the method of financing government expenditures, investment expenditures will always lead to higher steadystate welfare than consumption expenditures.
(5) According to the life-cycle model with constant money supply, money is neutral
both in the long run and in the short run.
(6) In recent decades, central banks have increased their focus on the interbank interest rate on overnight loans of bank reserves as the primary indicator of the stance
of monetary policy.
(7) High inflation tend to reduce welfare as inflation works like a tax on people’s
money holdings.
(8) According to the life-cycle model with money in the utility function, money and
capital are perfect substitutes in individuals’ saving portfolio.
(9) According to the two-country life-cycle model, cross-border investment serves to
equate returns to capital across countries.
(10) Financial intermediation can facilitate better risk sharing between borrowers and
suppliers of funds and lead to more efficient resource allocation.
2. (12 marks) Answer any TWO out of the following three short essay questions
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Instruction: This practice exam has the same format as the final exam. In terms of the degree of
difficulty, it is probably slightly more difficult than the final exam (in the sense that I deliberately give you
some less familiar questions to practice). After you have done a thorough review of all the study materials,
you should first work on this practice exam without referring to any study materials for two hours. Then
spend more time and try your best to work out every part of the questions, by referring to previous study
materials. Finally check your answer with my solution (to be posted by the end of week 12), give a good
think of your mistakes and what’s being tested in each question, and do the model questions a few more
times. It’s perfectly normal if you feel this practice exam is hard at your first try, as some of the setups are
new to you. After you have mastered these questions as well as the tutorial and exercise questions you have
been given, you will feel much better in the final exam.
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(a) (6 marks) Briefly explain under what circumstances a one-time deficit-financed
lump-sum subsidy to young individuals has no effects on the consumption and
welfare of the individuals who receive the subsidy and on capital formation and
output.
(b) (6 marks) Is it true that an increase in government consumption will always reduce national investment? In particular, does the method of financing government
consumption matter? Why or why not?
(c) (6 marks) Consider the two-country life-cycle model, how does the current account
balance and capital account balance of a low saving country change as the country
moves from autarky to free trade?
3. (12 marks) Consider a two-country life-cycle model. Suppose the two countries, country 1 and 2, only differ by propensity to consume. That is, the lifetime utility of a
generation-t individual is given by
0.3 0.7
u(cyt , cot+1 ) = cyt
cot+1
in country 1
0.6 0.4
u(cyt , cot+1 ) = cyt
cot+1
in country 2.
and
Capital is completely mobile between the two countries, but labour is completely immobile. Assume that capital depreciates at rate δ in both countries.
The two countries have the same population size: in every period N young individuals
are born in each country. Other elements of the model are standard, and the notations
are as follows:
· at+1 and a∗t+1 : the savings (capital holdings) for old age of a generation-t individual
in country 1 and 2, respectively
· wt : the worldwide real wage rate per worker in period t
· rt : the worldwide real interest rate in period t
· The production function of the representative firm in country 1: Yt = AKtβ Lt1−β ,
and that of the representative firm in country 2: Yt∗ = A(Kt∗ )β (L∗t )1−β .
(a) (7 marks) Derive the transition equation for the worldwide capital labour ratio,
proceeding in the following steps.
· Formulate the utility maximisation problem for a generation-t individual in
country 1, and find his optimal savings, at+1 . Similarly, find the optimal
savings of a generation-t individual in country 2, a∗t+1 . (If you know what the
solutions are for at+1 and a∗t+1 , then you can simply write them down without
using the first-order conditions to derive the solutions);
· Write down the conditions that characterise profit maximisation by firms;
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· Write down the market clearing conditions for the labour markets and the
world capital market;
· Combine all the equations to find the transition equation that describes how
the worldwide capital-labour ratio, kt , evolves over time.
(b) (5 marks) Let A = 4, β = 0.25, N = 100, and δ = 0.6, calculate the steady state
value for kt under free trade. Calculate the net foreign assets, and current account
balances of country 1 and country 2 in the steady state under free trade.
4. (15 marks) Consider a life-cycle model with fiscal policy. Suppose the government
imposes a proportional capital income tax, τ , on each old individual’s capital income
in every period t, and uses the tax revenues to finance a lump sum subsidy st to each
young individual in period t.
Assume that population size is constant, capital fully depreciates, and the utility function of an individual born in period t is given by ut = cot+1 . Other notations are as
follows:
· N : the number of young individuals born in every period
· at+1 : the savings (capital holdings) for old age of a generation-t individual
· wt : the real wage rate per worker in period t
· rt : the real interest rate in period t
· The collective production function of all firms in period t: Yt = Kt0.5 Lt0.5 .
Answer the following questions.
(a) (8 marks) Derive the transition equation for this economy, proceeding in the
following steps.
· Write down the budget constraints in young age and old age of an individual
born in period t, and find at+1 and cot+1 .
· Write down conditions that characterise firms’ profit maximisation;
· Write down the market clearing conditions for the labour and capital markets;
· Write down the government budget constraint in period t
· Combine all the equations above to find the transition equation that describes
how the capital-labour ratio, kt , evolves over time.
· Find the steady state values of the capital-labour ratio and old-age consumption, denoted as k̄, and c̄o respectively.
(b) (4 marks) Write down the resource constraint of the economy, and find the Golden
Rule level of the capital-labour ratio, denoted as kGR .
(c) (3 marks) Whether the introduction of this fiscal policy leads to higher or lower
welfare for individuals in the steady state, compared with the steady state with
no government activity (τ = 0 case)? Briefly explain your answer.
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5. (16 marks) Consider a life-cycle model with monetary policy. Suppose the government
prints money in every period such that money supply is expanded at a constant rate
z > 0, i.e.
Mt = (1 + z)Mt−1 , t ≥ 1,
where the initial money stock M0 is given, which is owned equally by the initial old
individuals. The newly printed money in every period t ≥ 1 is used to pay d units of
money (as interests) on each unit of money held by old individuals.
Other elements of the model are as follows: population grows at rate n (Nt+1 =
(1 + n)Nt ), capital full depreciates after production, and individuals only value secondperiod consumption (i.e., the individual’s utility is given by ut = cot+1 ). Other notations are given by:
· cot+1 : the consumption in old age of a generation-t individual
· at+1 : the capital holdings taken into old age by a generation-t individual
· mt+1 : the nominal money balances taken into old age by a generation-t individual
· Pt : the price level in period t
· wt : the real wage rate per worker in period t
· rt : the real interest rate in period t
.
· The collective production function of all firms in period t: Yt = AKtβ L1−β
t
Answer the following questions.
(a) (4 marks) Formulate the utility maximisation problem of a generation-t individual,
and show that the gross real rates of return on capital and money are the same.
(b) (3 marks) Use the money market clearing condition to find the gross real rate of
return on money in the steady state.
(c) (4 marks) Use the government budget constraint in period t + 1 to find the relationship between z and d.
(d) (3 marks) Using equations from above, find the steady state value of the capitallabour ratio, k̄, and the steady state value of old-age consumption, c̄o .
(e) (2 marks) How do output per worker and the welfare of individuals in the steady
state compare with their corresponding values that would be achieved if money
supply is fixed at M0 ? Briefly explain the intuition behind your result.
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