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ECOS3010: Assignment 2

ECOS3010: Assignment 2 (Total: 50 marks) Due 11:59 pm, Friday May 29
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 don’t forget to include your name and student number.
3. Carefully explain your work.
Question 1-3. Answer True, False or Uncertain. Brie‡y explain your answer. (each
question 4 marks)
1. In an international economy of perfectly substitutable currencies, an increase in the
stock of one country’s money reduces real value of all monies.
2. The negative correlation between in‡ation 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. (8 marks) Consider an economy of three-period-lived people in overlapping generations. 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 = nNt1.
There are no assets other than loans. 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. Write the budget constraints for
the young, the middle-aged, and the old. Be sure to de…ne any notation you introduce.
5. (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 = nNt1. 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 > n2.
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 individual’s preference is given by
u (c1; c2; c3) = c1c2c3:
(a) Find the rate of return on …at money. (1 mark)
(b) Describe and explain how an individual …nances his consumption in the secondperiod and third-period of life. (3 marks)
(c) Write down the budget constraints faced by an individual when young, middle-aged
and old. (3 marks)
(d) Solve for the optimal stationary allocation of (c 1; c 2; c 3) for all future generations.
(3 marks)
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6. (10 marks) Find the exchange rate data on Swiss Francs against U.S. dollar from 2007
to 2013. Can you identify how the U.S. monetary policy QE1 (QE refers to quantitative
easing) and QE2 implemented by the Federal Reserve a¤ect the relative value of the Francs
and the U.S. dollar? Suppose that the demand for the Swiss Francs and the demand for
the U.S. dollar stay stable throughout the sample period. Can you explain your …ndings
using the theory that we develop in our lectures?
7. (10 marks) The Tobin e¤ect predicts that higher in‡ation is associated with more
capital stock. Find relevant Australian data and check if we observe the Tobin e¤ect from
Australian data.
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