ECOS3010: Assignment 1

ECOS3010: Assignment 1 (Total: 50 marks) Due 11:59 pm, Friday April 24
1. Homework must be turned in on the day it is due. Work not submitted on or before
the due date is subject to a penalty of 5% per calendar day late. If work is submitted more
than 10 days after the due date, or is submitted after the return date, the mark will be
zero. Each assignment is worth 10% of total weight.
2. TYPE your work (including all mathematical equations). Homework is
submitted as a typed .pdf …le, no exceptions. Untyped work will be returned to the student
and incur a late submission penalty. You can draw a graph by hand, scan it, and include it
as a …gure in the PDF. Please don’t forget to include your name and student number.
3. Carefully explain your work.
4. Please submit your assignment via Turnitin on Canvas before the due time. No hard
copy is needed.
Question 1-5. Answer True, False or Uncertain. Brie‡y explain your answer. (each
question 4 marks)
1. A permanent increase in money supply cannot a¤ect any variable in the OLG model
of money.
2. In the OLG model of money, …at money does not pay interest, so money’s rate of
return is 1.
3. Suppose that the government …nances its expenditure through seigniorage revenue.
There exists an upper limit on the amount of the seigniorage revenue that can be generated.
4. The original Phillips curve …nds that there is a negative correlation between in‡ation
and output growth.
5. The Lucas critique indicates that the government can use a random monetary policy
to stimulate output.
6. Consider the OLG model that we develop in class. There are N people in every
generation. Each individual is endowed with y units of goods when young and nothing
when old. Suppose that monetary authority prints …at money at the rate z but now does
not distribute the newly printed money as a lump-sum transfer to the old. Instead, the
government distributes the newly printed money by giving each old individual  new dollars
for each dollar acquired when young. (20 marks)
(a) Use the government budget constraint to …nd  as a function of z. (2 marks)
(b) Write down the individual’s budget constraints when young and old. Combine them
to form the individual’s lifetime budget constraint. (3 marks)
(c) What is the in‡ation rate pt+1=pt? What is the real rate of return on …at money?
(4 marks)
(d) Graph the stationary monetary equilibrium. Carefully label the axes and the optimal
allocation. (4 marks)
(e) Write down the resource constraint faced by a planner. (2 marks)
(f) Compare the individual’s lifetime budget constraint with the resource constraint.
Demonstrate that the monetary equilibrium satis…es the golden rule allocation regardless
of the rate of in‡ation. Explain why in‡ation does not induce individuals to reduce their
real balances of money in this case. (5 marks)
7. (10 marks) Figure 1 and Figure 2 in Chapter 5 of the textbook show the correlation
between in‡ation and unemployment in the U.S. in di¤erent periods of time. Find data on
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in‡ation and unemployment in Australia. Annual frequency data is …ne, but you can use
quarterly frequency if you prefer. In your answer, please indicate the source of your data.
(a) Can you …nd an episode where there is a positive correlation between in‡ation and
unemployment? If so, plot the data. Use a theory that we develop in class to justify the
positive correlation.
(b) Can you also …nd an episode where there is a negative correlation between in‡ation
and unemployment? If so, plot the data. Use a theory that we develop in class to justify
the negative correlation.
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