ECOS3010代写、代写Java/C++编程

日期：2022-10-15 02:45

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)