Question

Consider two identical countries, A and B, in our standard overlapping generations model. In each country, the population of every generation is 200, and each young person wants money balances worth 40 goods. Assume that the money of country A is the only currency that currently circulates in the two countries. There are $1000 of country A money split equally among the initial old of both countries.

a. Find the value of a country A dollar.

b. Find the consumption of the initial old. Now, suppose country B issues its own money, giving €12 to each of the initial old of country B. To ensure a demand for its currency, country B imposes foreign-exchange controls.

c. Find the value of one euro and the value of one dollar.

d. Find the consumption of the initial old in country A and in country B. Who has been made better off by this policy switch?

Answer 1

Given data are:

N^a = N^b= 200, ( N^A = N^a +N^b) for country A and B Money balance after cunsumption , Y^a - C^a = Y^b - C^b = 40,

Money given to both country, M^a = M^b =1000/2 = 500

Answer A ) valuation fo fiat money as whole issued by A,

V^A = N^A ( Y^A - C^A ) / M^A =400 *40/ 1000 = 16

Answer B)

With foreign currency controls in effect value of .consumption of money in country B

V^b = N ( Y^b - C^b ) / M^b = 200 * 40 /500 = 16

New currency issued by country B , against old currency in ratio 0f 1:12

Answer C) The exchange is made as fixed exchange as 1:12

I Euro = 1/12 $

1 $ = 12 Euro .

Answer d)Consumption of old intial currency in Country A

V^a = N ( Y^a - C^a ) / M^a = 200 * 40 /500 = 16

Consumption of old intial currency in Country B

V^b = N ( Y^b - C^b ) / M^b = 200 * 40 /500 = 16

by the change of policy , there will no change to any currency status as it is fixed exchange rate .