Chapter 5, Problem 5NP

a)

To determine

To ascertain the national saving in the home country and in the foreign country as a functions of the world real interest rate.

Explanation of Solution

  $\begin{array}{c}{S}_H=Y_H-C_H-G_H\\ =1000-\left(100+\left(0.5\times 1000\right)-500r\right)-155\\ =255+500r\end{array}$

  $\begin{array}{c}{S}_H=Y_H-C_H-G_H\\ =1200-\left(225+\left(0.7\times 1200\right)-600r\right)-190\\ =55+600r\end{array}$

H refers to home country, $S_H$ , $Y_H$ , $C_H$ , $G_H$ refers to saving, full employment output, consumption, government purchase of the home country. S_F, Y_F, C_F,G_F refers to the saving, full employment output, consumption, government purchase of the foreign country. And $r^w$ refers to the world real interest rate

Economics Concept Introduction

Introduction: National savings are important for countries' economic development because the savings generate investment. Saving is an important indicator of economic development where it is used in every developing country to achieve economic growth.

b)

To determine

To ascertain the equilibrium values of the world real interest rate

Explanation of Solution

  $\begin{array}{c}N{X}_H=S_H-I_H\\ =245+500r-\left(300-500r\right)\\ =-55+1000r\end{array}$

  $\begin{array}{c}N{X}_H=S_H-I_H\\ =-55+600r-\left(250-200r\right)\\ =-305+800r\end{array}$

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

  $N{X}_H-N{X}_F=0$

So,

  $\begin{array}{c}-55+1000r+\left(-305+800r\right)=0\\ 1800r=360\\ r=0.20\end{array}$

  $N{X}_H$ Refers to the national income of home country, $N{X}_F$ refers to the national income for foreign country, $I_F$ and $S_F$ refers to investment and saving for foreign country, r is real interest rate.

Economics Concept Introduction

Introduction: The real rate of interest is the interest rate that a creditor, saver or lender earns after adjusting for inflation. It is also defined by the Fisher equation, that states the real interest rate is thenominal rate of interest minus the rate of inflation

c)

To determine

To ascertain the equilibrium values of consumption, national saving, investment, the current account balance, absorption in each country.

Explanation of Solution

  $\begin{array}{c}{C}_H=100+\left(0.5\times 1000\right)-\left(500\times 0.20\right)\\ =500\end{array}$

  $\begin{array}{c}{S}_H=245+\left(500\times 0.20\right)\\ =345\end{array}$

  $\begin{array}{c}{I}_H=300+\left(500\times 0.20\right)\\ =200\end{array}$

  $C{A}_H=N{X}_H=-55+\left(1000\times 0.20\right)=145$ (Assume NFP = 0)

  $\begin{array}{c}Absorbtion=C_H+I_H+G_H\\ =500+200+155\\ =855\end{array}$

  $\begin{array}{c}{C}_F=225+\left(0.7\times 1200\right)-\left(600\times 0.20\right)\\ =945\end{array}$

  $\begin{array}{c}{S}_F=-55+\left(600\times 0.20\right)\\ =65\end{array}$

  $S_H$ , $Y_H$ , $C_H$ , $G_H$ refers to saving, full employment output, consumption, government purchase of the home country. S_F, Y_F, C_F,G_F refers to the saving, full employment output, consumption, government purchase of the foreign country. And $r^w$ refers to the world real interest rate

Economics Concept Introduction

Introduction: The growth of an economy is affected by national savings. Consumption, balance of trade, investment and a proper allocation of savings in to efficient investment can lead a country towards better growth.