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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 file to the relevant TurnitIn folder. E.g., you can handwrite

your answers and then convert them to a pdf file.

Please keep your pdf file reasonably small (say ≤ 5MB).

You may email your pdf file to c.mueller@uq.edu.au as proof of your time

of submission if you experience technical difficulties with uploading it. You then

still have to upload the same pdf file to TurnitIn as soon as possible.

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

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

1

ECON 7520 SEMESTER 1, 2023

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.

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 deficit 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 deficit 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 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.]

2

ECON 7520 SEMESTER 1, 2023

(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

lnC1 + lnC2,

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 · I

0.75

0

and

Q2 = 4 · I

0.75

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.

3

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.

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