ECOS3010: Assignment 2
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 not be marked and will
receive a mark of zero. You can draw a graph by hand, scan it, and include it as a ?gure in
the PDF. Please donít forget to include your name and student number.
3. Carefully explain your work.
Question 1-5. Answer True, False or Uncertain. Brieáy explain your answer. (each
question 4 marks)
1. In an international economy of perfectly substitutable currencies, an increase in the
stock of one countryís money reduces real value of all monies.
2. The negative correlation between ináation and the real interest rate can be explained
by the Fisher e§ect.
3. The rate of return equality holds in the model of illiquidity.
4. The rate of return equality is inconsistent with the observations found in the Equity
Premium Puzzle.
5. Cooperative stabilization can help countries have a ?xed exchange rate regime and
avoid high ináation.
6. (10 marks) Consider an economy of three-period-lived people in overlapping gener
ations. Each individual is endowed with y goods when young and old and nothing when
middle-aged. The population of each generation born in period t is Nt , where Nt = nNt 1.
There are no assets other than loans.
(a) Explain how private debt can be used to provide for consumption when middle-aged.
Point out who lends to whom and write the condition for the equality of supply and demand
for loans in period t. (5 marks)
(b) Write the budget constraints for the young, the middle-aged, and the old. Be sure
to de?ne any notation you introduce. (5 marks)
7. (10 marks) Consider the model of illiquidity where individuals live for three periods.
Each individual is endowed with y units of the consumption good when young and with
nothing in the other two periods of life. Let Nt be the number of individuals in the generation
born at t with Nt = nNt
t
1. There are two types of assets in the economy. (No inside money
or private IOUs are available.) One asset is ?at money, with a ?xed supply M. The other
asset is capital. A unit of capital can be created from a unit of the consumption good in any
period t and capital can be created in any amount. Two periods after it is created, a unit
of capital produces X units of the consumption good and then disintegrates. Let X > n
2
.
Assume that the stock of money is distributed equally to the initial middle-aged and
each initial old can produce Xk0 units of the consumption good in the ?rst period. Now
suppose that an individualís preference is given by
U(c1; c2; c3) = c1c2c3:
1(a) Find the rate of return on ?at money. (2 marks)
(b) Describe and explain how an individual ?nances his consumption in the second
period and third-period of life. (2 marks)
(c) Write down the budget constraints faced by an individual when young, middle-aged
and old. (2 marks)
(d) Solve for the optimal stationary allocation of (c1 ; c2 ; c3 ) for all future generations.
(4 marks)
8. (10 marks) Consider the OLG model with capital. Each individual is endowed
with y units of the consumption good when young and with nothing when old. Let N be
the number of individuals in each generation. Suppose there is one asset available in the
economy ? capital. A unit of capital can be created from a unit of the consumption good
in any period t and capital can be created in any amount. One period after it is created, a
unit of capital produces X units of the consumption good and then disintegrates. Assume
that each initial old can produce Xk0 units of the consumption good in the ?rst period.
Now suppose that an individualís preference is given by
U(c1; c2) = (c1)
1
2 (c2)
1
2 :
We focus on stationary allocations.
(a) Write down the budget constraints faced by an individual when young and old.
Combine the budget constraints to and the lifetime budget constraint for an individual. (1
mark)
(b) Solve for the optimal allocation of (c1 ; c2 ) for all future generations. What is the
optimal k ? (2 marks)
Now suppose an additional asset is available in the economy ??at money. Money supply
grows at a constant rate z, Mt = zMt
t
1. The government imposes a legal restriction such
that individuals must carry a real money balance of at least q units of the consumption
good from the young to old. That is, the amount of money held by a young individual
should be at least worth q units of the consumption good. Assume that q is a small number
and exogenously given.
(c) Describe how an individual ?nances his second-period consumption if X > 1=z.
What if X
1=z? (2 marks)
(d) From now on, letís assume X > 1=z. Write down the budget constraints faced by
an individual when young and old. (1 mark)
(e) Solve for the optimal allocation of (c1 ; c2 ) for all future generations. What is the
optimal k ? (2 marks)
(f) How does z a§ect the choices of (k ; c1 ; c2 )? Does the Tobin e§ect exist? (1 mark)
(g) Explain how the choices of (k ; c1 ; c2 ) would change if q is very big? (Hint: you can
think about the extreme case that q is approaching y.) (1 mark)