Question

Consider a world with only two countries, which are designated the home country (H) and the foreign country (F). Output equals its full-employment level in each country. You are given the following information about each country: Home Country Consumption: CH = 100 + 0.5YH - 500rw Investment: IH = 300 - 500rw Government Purchases: GH = 155 Full-employment Output: YH = 1000 Foreign Country Consumption: CF = 225 + 0.7YF - 600rw Investment: IF = 250 - 200rw Government Purchases: GF = 190 Full-employment Output: YF = 1200 a. Write national saving in the home country and in the foreign country as functions of the world real interest rate rw. b. What is the equilibrium value of the world real interest rate? c. What are the equilibrium values of consumption, national saving, investment, the current account balance, and absorption in each country?

Answer 1

a.

$S_H=Y_H-C_H-G_H=1000-[100+(0.5\times1000)-500_r]-155\\=245+500r\\ S_F=Y_F-C_F-G_F=1200-[225+(0.7\times1200)-600_r]-190\\=-55+600r$

b.

$NX_H=S_H-I_H\\=245+500r-(300-500r)=-55+1000r\\ NX_F=S_F-I_F\\=-55+600r-(250-200r)=-305+800r$

In equilibrium, one country's CA surplus should equal to the other country's CA deficit, thus we have

$NX_H+NX_F=0\\so\\-55+1000r+(-305+800r)=0\\1800r=360\\r=0.20$

c.

$C_H=100+(0.5\times 1000)-(500\times 0.2)=500\\S_H=245+(500\times o.2)=345\\I_H=300-(500\times 0.2)=200\\ CA_H=NX_H=-55+(1000\times 0.2)=145 (assuming \space NPF=0)$

$Absorption \space H=C_H+I_H+G_H=500+200+155=855\\C_F=255+(0.7\times 1200)-(600\times 0.2)=945\\S_F=-55+(600\times 0.2)=65\\I_F=250-(200\times 0.2)=210\\CA_F=NX_F=-30+(800\times 0.2)=-145(assuming \space NPF=0)\\absorption=C_F+I_F+G_F=945+210+190=1345$