Consider a two-period model of a small open economy with a single, perishable good.
Let preferences of the representative household be described by the utility function
ln C1 + ln C2,
where C1 and C2 denote consumption in periods 1 and 2, respectively. Each period
t = 1, 2, the household receives profits Πt from the represenative firm it owns. The
production technologies in periods 1 and 2 are given by
Q1 = 3.5 · I0.75
0
and
Q2 = 4 · I0.75
1 ,
where Q1 and Q2 denote output in periods 1 and 2, respectively, I0 = 39.0625 is exoge-
nously given and represents the investment from “period 0” and I1 denotes the investment
in period 1. Observe that the firm invests in period t − 1 to be able to produce goods in
period t. The household and the firm have access to financial markets where they can
borrow or lend. The firm finances its investments by issuing debt (both in “period 0” and
in period 1), as in the lecture. Assume that there exists free international capital mobility
and that the world interest rate, r∗, is 5% each period (i.e., r0 = r1 = r∗ = 0.05, where
rt is the interest rate on assets held between periods t and t + 1). Finally, assume that the
household’s initial net asset position is Bh
0 = −10.
(a) (1 mark) Compute the initial net foreign asset position of the economy.
(b) (1 mark) Compute the firm’s output Q1 and profit Π1 in period 1.
(c) (3 marks) Compute the firm’s optimal level of investment in period 1 and its profit in
period 2.
(d) (5 marks) Derive the optimal levels of consumption in periods 1 and 2.
(e) (3.5 marks) Find the country’s net foreign asset position at the end of period 1 and, for
each of the periods 1 and 2, the country’s savings, trade balance and current account
balance.
Now suppose that the government at the beginning of period 1 publicly announces an
investment subsidy. Specifically, for each unit of investment that the firm makes in period
1, the government promises to pay the firm a subsidy of s2 ∈ (0, 1 + r1) units of the good
in period 2. The government finances the subsidy by charging the household a lump-sum
tax T2 in period 2. The government neither has other expenditures nor other revenues. In
particular, T1 = 0.
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ECON 7520 SEMESTER 1, 2023
(f) (1 mark) Write down the government’s budget constraint in period 2.
(g) (4 marks) Write down a formula for the firm’s profit in period 2. Derive the optimal
investment condition and calculate the optimal investment as a function of s2. Using
a MPK-MCK-graph, illustrate in a figure how the optimal investment and the firm’s
period-2 profit Π2 change after the subsidy is introduced.
(h) (1.5 marks) Write down the household’s period 1 and period 2 budget constraints.
Derive the household’s intertemporal budget constraint.
(i) (2 marks) Derive the economy’s resource constraint. Compare it to resource con-
straint that holds without the subsidy. Provide intuition for your comparison.
(j) (6 marks) Assume that s2 = 0.1. Derive the household’s optimal consumption path
and the current account balances CA1 and CA2 in periods 1 and 2, respectively.
What effect did the introduction of the subsidy have on the optimal consumption path
and on CA1? Provide a detailed explanation of the effect on C1, C2 and CA1 of
introducing the subsidy and intuition for your results. Is the household better off
after the subsidy was introduced?
(k) (2 marks) Explain in words how your answer to (j) would change if the government
were to announce the subsidy only at the beginning of period 2