ECON-4330 Advanced Macroeconomics I Professor Nurlan Turdaliev

Homework Assignment 2 Fall 2021

Due: Friday, October 29, 2021, 6pm

Problem 1

Consider a fiat money/barter system like that portrayed in this chapter. Suppose the number of

goods J is 100. Each search for a trading partner costs an individual 2 units of utility.

a. What is the probability that a given random encounter between individuals of separate islands

will result in a successful barter?

b. What are the average lifetime search costs for an individual who relies strictly on barter?

c. What are the average lifetime search costs for an individual who uses money to make ex-

changes?

Now let us consider exchange costs. Suppose it costs 4 units of utility to verify the quality of

goods accepted in exchange and 1 unit of utility to verify that money accepted in exchange

is not counterfeit.

d. What are the total exchange costs of someone utilizing barter?

e. What are the total exchange costs of someone utilizing money?

Problem 2

Consider a commodity money model economy like the one described in this chapter but with

the following features: There are 100 identical people in every generation. Each individual is

endowed with 10 units of the consumption good when young and nothing when old. To keep things

simple, let us assume that each young person wished to acquire money balances worth half of

his endowment, regardless of the rate of return. The initial old own a total of 100 units of gold.

Assume that individuals are indifferent between consuming 1 unit of gold and consuming 2 units

of the consumption good.

a. Suppose the initial old choose to sell their gold for consumption goods rather than consume

the gold. Write an equation that represents the equality of supply and demand for gold. Use

it to find the number of units of gold purchased by each individual, mgt , and the price of gold,

vgt .

b. At this price of gold, will the initial old actually choose to consume any of their gold?

c. Would the initial old choose to consume any of their gold if the total initial stock of gold were

800? In this case, what would be the price of gold and the stock of gold after the initial old

consumed some of their gold? Compare your answer in this part with your answer in part a.

Does the quantity theory of money hold?

d. Suppose it is learned that a gold discovery will increase the stock of gold from 100 units to

200 units in period t∗. Assume the government uses the newly discovered gold to buy bread

that will not be given back to its citizens. Find the price of gold at t∗ − 1 and at t∗. Also

find the rate of return of gold acquired at t∗ − 1.

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Problem 3

Suppose n = 1. Suppose the endowment grows, i.e. ωt = (yt, 0) where yt = Ayt−1, and A > 1 is a

constant. Also, ω1 = (y, 0). There is a constant amount of fiat money M . Suppose the preferences

of generations 1, 2, ..., are

u(c1, c2) =

√

c1 +

√

c2,

and those of the IO are

uIO(c2) = c2.

a. Write down equations that represent the budget constraints in the first and second period

of a typical individual from generation t. Combine these constraints into a lfetime budet

constraint of this individual.

b. Restrict attention to a stationary solution in which each generation would consume the same

fraction of its endowment when young. Write down the conditions that represents the clearing

of the money market in an arbitrary period t. Use condition to find the real rate of return of

fiat money in a monetary equilibrium. Explain the path over time of the value of fiat money.

c. Find the Golden Rule allocation for this economy.

d. Find the optimal (c∗1t, c∗2,t+1). Compare it with the Golden Rule allocation found above.

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