ECON 7520 SEMESTER 1, 2023 Problem Set

• This is an open book assignment. No generative AI such as ChatGPT permitted.

• This is an individual assignment — group work is not permitted.

• You have until 10.00h AEST on April 6, 2023 to 1) download and 2) work on the assignment and to 3) upload your answers. You are required to upload your answers as a single, legible pdf ile to the relevant TurnitIn folder. E.g., you can handwrite your answers and then convert them to a pdf ile.

• Please keep your pdf ile reasonably small (say  5MB).

• You may email your pdf ile to [email protected] as proof of your time of submission if you experience technical dificulties with uploading it. You then still have to upload the same pdf ile to TurnitIn as soon as possible.

• File formats other than pdf are not permitted. You may not submit multiple iles.

• Where an extension has not been approved, the following penalties apply to late or non-submission: A penalty of 10% of the maximum possible mark of the problem set will be deducted per day for up to 7 calendar days, at which point any submis- sion will not receive any marks unless an extension has been approved. Each 24 hour block is recorded from the time the submission is due.

• By undertaking this assignment you will be deemed to have made the following declaration:“I certify that

– my submission is entirely my own original work, and no part of my answers has been copied from any other source or person except where due acknowl- edgement is made,

– no part of the work has been previously submitted for assessment in this or any other institution,

– I have neither given nor received any unauthorized assistance on this assess- ment item, and

– I am familiar with and understand the implications of UQ’s policies relating to academic integrity and student conduct.”

Instructions: Answer all questions.  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.

Total Questions: 3

Total Marks: 50

Question 1 (6 marks)

Suppose net investment income is NII  =  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 TA, consistent with Green’s view.

(b) (3 marks) Financial analyst Nadia Gonzalez does not believe in the dark matter hy- pothesis. 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 coun- try’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 deicit of 5 percent of GDP. Find the trade balance in period 1 (TB1), 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 deicit of 5 percent of GDP and that in period 2, the trade balance of the economy is zero, that is, TB2  = 0. Is the economy living beyond its means? To answer this question ind 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 deicit 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

lnC1 + lnC2 ,

where C1  and C2  denote consumption in periods 1 and 2, respectively.  Each period t  =  1, 2, the household receives proits  t  from the represenative irm it owns.  The production technologies in periods 1 and 2 are given by

Q1 = 3.5 · I0(0) .75

and

Q2 = 4 · I

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 irm invests in period t — 1 to be able to produce goods in period t.  The household and the irm have access to inancial markets where they can borrow or lend. The irm inances 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 B0(h) = — 10.

(a) (1 mark) Compute the initial net foreign asset position of the economy. (b) (1 mark) Compute the irm’s output Q1 and proit 1 in period 1.

(c) (3 marks) Compute the irm’s optimal level of investment in period 1 and its proit 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. Speciically, for each unit of investment that the irm makes in period 1, the government promises to pay the irm a subsidy of s2  ∈ (0, 1+r1 ) units of the good in period 2. The government inances 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.