ECMBO6

MGEB06 – LEC 01 & LEC 02
Macroeconomic Theory and Policy: A Mathematical Approach
Assignment 1
Due: On or before Friday, October 4, 11:30am
Rooms: LEC01 IC 284 (Professor Parkinson’s office) LEC02 IC 286 (Professor Au’s office)
(Note: Assignments submitted after Friday, October 4, 11:30am WILL NOT BE accepted under ANY circumstance.)

Instructions:
You can submit an individual or group assignment.
If you submit a group assignment, there must be no more than FIVE students in your group and you just have to submit ONE copy.
YOUR GROUP MAY CONSIST OF STUDENTS ENROLLED IN EITHER SECTION.
A title page MUST be attached with your assignment; it MUST include your name(s), student number(s), and your lecture section(s).
Staple your assignment (Paper clips are not accepted).
A PENALTY OF 10% OF THE TOTAL MARKS WILL BE IMPOSED IF YOU DO NOT HAVE A TITLE PAGE AND THE REQUIRED INFORMATION or STAPLE YOUR ASSIGNEMNT.
Label your graph(s); otherwise, marks will be subtracted.
No credit will be given if you do not show your work.
Your answer should be structured in a way such that those that know little about economics will have no difficulty understanding your argument/answer.
Total marks: 100 points.

Question 1 (20 points) – Chapter 3
A closed economy can be described by the long-run classical model:
Y = 2KαL1–α
C = 8200 + 0.8(Y – T) – 600r
I(r) = 9550 – 400r
Note: r represents the real interest rate and is measured in percentage points (for example, if we find r = 10, then r is interpreted as being equal to 10%). Keep your answer to at least 4 decimal points.

Assume that there are two factors of production, capital (K) and labour (L), and that they are both fully employed. For this economy the supply of capital and labour are 10000 and 50625 respectively. In addition, labour’s share of output is equal to three quarters. Initially, the government collects one-eighth of the economy’s output as (income) taxes, and the size of the budget deficit is 400.

a) Compute the long-run equilibrium levels of consumption, investment and real interest rate. Also, find the long-run equilibrium real wage for labour and real rental price of capital. (5 points)

Suppose a law that requires the government to run a balanced budget is passed. In order to comply with the newly passed law, the government adjusts the (income) taxes collected.
b) Find the new long-run equilibrium levels of consumption, investment, real interest rate, real wage for labour and real rental price of capital. (5 points)
c) Explain your findings in parts (a) and (b) by using THREE diagrams (the loanable funds market diagram, the labour market diagram, and the rental market for capital diagram). (5 points)

Now, return to the initial long-run equilibrium as shown in part (a). Suppose instead, the government wants to encourage households to spend more by adjusting government spending, with the aim of increasing the (overall) level of private sector consumption by 3042.
d) Find the level of government spending that could achieve this goal. What is the new equilibrium level of investment? What happens to the government budget surplus/deficit? Explain. (5 points)

Question 2 (30 points) – Chapters 3 & 7
Initially, the economy is in its steady state. The economy experiences a technological breakthrough such that the level of total factor productivity increases by 5%. At the same time, the country has experienced an increase in the size of the capital stock.

a) In the context of the long-run classical model, what happens to the long-run equilibrium levels of investment and real interest rate? What happens to the real rental price of capital? Explain and support your answer with TWO diagrams: one for the market for loanable funds and one for the rental market for capital (only the first two diagrams will be graded). (15 points)
b) According to the Solow Model, what happens to the steady-state capital-labour ratio? In the new steady state what happens to the growth rate of output per worker? Explain and support your answer with ONE appropriate diagram. Be sure to explain what happens to the variables of interest during transition to steady state. (15 points)

Question 3 (30 points) – Chapter 7
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by:
Y = 2K1/4L3/4

Note: Keep your answer to 4 decimal points if needed. Be sure to show your work.

In this economy, workers consume 77.5% of income and save the rest. The labour force is growing at 1% per year while the annual rate of capital depreciation is 1.5%.
a) Solve for the steady state levels of the capital-labour ratio, output per worker, and consumption per worker? (5 points)
b) Is the steady-state level of consumption per worker maximized? If not, find the saving rate that will maximize the steady-state level of consumption per worker? (5 points)

Now suppose the economy is in its steady state as described in part (a). Suppose 500 residents of this economy have eaten contaminated cronut burgers and suffered from food poisoning. Unfortunately, half of those who got food poisoning died as a result of this food poisoning.
c) Suppose all who were killed were in the labour force. Solve for the new steady state levels of the capital-labour ratio, output per worker, and consumption per worker. Explain your answer with the aid of ONE appropriate diagram. Be sure to explain what happens to the variables (listed in part (a)) during transition to steady state. (10 points)
d) How, if at all, would you change the answer in part (c) if all those who were killed were not in the labour force? (5 points)

Return to part (a). Suppose the economy experiences a technological breakthrough such that the level of total factor of productivity increases by 50%. In addition, with the technological breakthrough, the rate of capital depreciation increases by 1.25 percentage points.
e) Solve for the new steady state levels of the capital-labour ratio, output per worker, and consumption per worker. (5 points)

Question 4 (20 points) – Chapters 2, 3 & 7
Answer the following questions. Each sub-part of the question is not related to the other part. Be sure to provide a written explanation in order to receive full credit.

a) “It is impossible for an economy to experience a rise in GDP and fall in GDP per capita at the same time.” True/False, explain. (5 points)
b) Many countries, including Canada, are facing the problem of an aging population. Two economists, 1 and 2, debate the effects of aging population on the economy. Economist 1 argues that aging population would cause severe problems to the economy because it would lower aggregate output and the growth rate of aggregate output. Economist 2 disagrees with economist 2, he says that aging population does not necessary have adverse impacts on the economy as long as the factors of production become more efficient. Explain, in words only, under what circumstance the claims made by both economists could be correct. Be sure to state the assumptions made in your answer explicitly. (15 points)