# What effect did the introduction of the subsidy have on the optimal consumption path and on CA1?

Problem set assignment

Show all your work you must explain how you arrived at your answer.

Partial credit may be awarded if a substantial part of the answer is provided.

Question 1 (6 marks)

Suppose net investment income is N II = 100, the international asset position is
A = 3000, the international liability position is L = 4000, and the rate of return is 5
percent, r = 0.05.

(a) (3 marks) Economist John Green, a strong advocate of the dark matter hypothesis,
believes that A is not accurately recorded. Calculate the amount of dark matter and
the “true” international asset position, which we will denote T A, consistent with
Green’s view.

(b) (3 marks) Financial analyst Nadia Gonzalez does not believe in the dark matter hypothesis. Instead, she believes that A is accurately measured. In her view 5 percent is actually the rate of return on assets rA = 0.05, and the rate of return on the country’s international liabilities, rL, is different. Find the value of rL consistent with Gonzalez’s view.

Question 2 (14 marks)

In answering this question, assume that there are no valuation changes of assets, that the net international compensation to employees equals zero and that there are no net unilateral transfers.

Consider a three-period economy that at the beginning of period 1 has a net foreign asset position of 175. In each of the three periods 1, 2 and 3, GDP is 200. The interest rate on bonds held between any two consecutive periods is 6 percent; that is, r0 = r1 = r2 = r = 0.06.

(a) (4 marks) For this part of the question only, assume that in period 1, the economy runs a current account deficit of 5 percent of GDP. Find the trade balance in period 1(T B1), the current account balance in period 1 (CA1), and the country’s net foreign asset position at the beginning of period 2 (B1).

(b) (1 mark) State the transversality condition for this economy.

(c) (4 marks) For this part of the question only, assume that in period 1, the economy runs a current account deficit of 5 percent of GDP and that in period 2, the trade balance of the economy is zero, that is, T B2 = 0. Is the economy living beyond its means?

To answer this question find the economy’s current account balance in period 3 and the trade balance in period 3. Is this value for the trade balance feasible? [Hint: Keep in mind that the trade balance cannot exceed GDP.]

(d) (5 marks) Compute as a percentage of GDP the maximal current account deficit in
period 1 that is feasible for the economy.

Question 3 (30 marks)

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 · I0.750 and Q2 = 4 · I0.751 ,
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 = 0.3

(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.

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