ECOS3010: Assignment 1 (Total: 50 marks) Due 11:59 pm, Friday, September
16, 2022
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 file, no exceptions. Untyped work will not be marked and will
receive a mark of zero. You can draw a graph by hand, scan it, and include it as a figure in
the PDF. Please don’t forget to include your name and student number.
3. Carefully explain your work.
Question 1-5. Answer True, False or Uncertain. Briefly explain your answer. (each
question 4 marks)
1. The lack of double coincidence of wants precludes people from using credit for trans-
actions.
2. Consider stationary allocations in the OLG model of money. Individuals consume
the same amount of good when young and when old.
3. The optimal monetary policy in the OLG model of money is to have deflation.
4. In the Lucas price surprise model, a higher growth rate of money supply leads to a
lower level of output under nonrandom monetary policy.
5. The Lucas critique indicates that the government can use a random monetary policy
to stimulate output.
6. (10 marks) Consider the standard OLG model with money. Individuals are endowed
with y units of a perishable consumption good when young and nothing when old. There
are N individuals in every generation. Each generation has identical preferences where
u (c1,t, c2,t+1) = c
1/2
1,t + c
1/2
2,t+1. There exists one asset in the economy – money. The money
supply grows at a constant rate z, whereMt = zMt?1 and z > 1. The new money created is
used to finance government purchases of g goods per young individual in every period. The
initial old are endowed with M0 units of money. In the following, we focus on stationary
allocations.
(a) Find an individual’s budget constraints when young and when old. Combine them
to form the individual’s lifetime budget constraint. (2 marks)
(b) Solve for the optimal consumption allocation (c?1, c?2) chosen by the individual in a
stationary monetary equilibrium. How do (c?1, c?2) depend on z? (2 marks)
(c) Find the government budget constraint. Express government purchases g as a func-
tion of z and other parameters in the model. (2 marks)
Now instead of being endowed with y units of the consumption good, individuals can
supply labour ?1,t only when young. That is, the young supply labour ?1,t and consume c1,t,
but the old can only consume c2,t+1. One unit of labour supply produces one unit of the
consumption good. Each generation has identical preferences where
u (c1,t, c2,t+1, ?1,t) = c
1/2
1,t + c
1/2
2,t+1 ? ?1,t.
(d) Find an individual’s budget constraints when young and when old. Combine them
to form the individual’s lifetime budget constraint. (1 mark)
1
(e) Solve for the optimal consumption and labour supply (c?1, c?2, ??1) chosen by the indi-
vidual in a stationary monetary equilibrium. (2 marks)
(f) How do (c?1, c?2) depend on z? How does ??1 depend on z? Briefly explain the intuition
for your answer. (1 mark)
7. (10 marks) 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 fiat 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.
(a) Use the government budget constraint to find α 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. (2 marks)
(c) What is the inflation rate pt+1/pt? What is the real rate of return on fiat money?
(2 marks)
(d) Graph the stationary monetary equilibrium. Carefully label the axes and the optimal
allocation. (1 mark)
(e) Write down the resource constraint faced by a planner. (1 marks)
(f) Compare the individual’s lifetime budget constraint with the resource constraint.
Demonstrate that the monetary equilibrium satisfies the golden rule allocation regardless
of the rate of inflation. Explain why inflation does not induce individuals to reduce their
real balances of money in this case. (2 marks)
8. (10 marks) Figure 7.1 and Figure 7.2 in Chapter 7 show the correlation between in-
flation and unemployment in the US in different periods of time. Using the OECD database
(https://data.oecd.org/), find quarterly data on the inflation rate (CPI based) and the un-
employment rate for Australia. Plot the correlation between inflation and unemployment
for the following four decades: 1970-1979, 1980-1989, 1990-1999, 2000-2009. Please use the
unemployment rate as the x-axis and the inflation rate as the y-axis in your plots. Add a
trendline in each of your plot.
(a) In which decade(s) can we observe a positive correlation between inflation and un-
employment? In which decade(s) can we observe a negative correlation between inflation
and unemployment? (4 marks)
(b) Briefly provide one theory that can rationalize the negative correlation between
inflation and unemployment. (3 marks)
(c) Briefly provide one theory that can rationalize the positive correlation between in-
flation and unemployment. (3 marks)