Chapter 5, Problem 4NP

a)

To determine

To evaluate the equilibrium interest rate in the international capital market and the equilibrium values of national saving, consumption, investment, and current account balance in each country.

Explanation of Solution

  $\begin{array}{c}{\text{C}}^{\text{d}} = \text{32}0 + 0.\text{4}(\text{1}000 - \text{2}00) - \text{2}00r^w\\ = \text{32}0 + \text{32}0 - \text{2}00 r^w\\ = \text{64}0 - \text{2}00 r^w\\ CA = NX = S^d – I^d = Y –(C^d + I^d + G)\\ = \text{1}000–(\text{64}0–\text{ 2}00 r^w + \text{15}0–\text{ 2}00r^w + \text{275})\\ = –\text{65} + \text{4}00 r^w\end{array}$

  ${\text{C}}^{\text{d}}$ is desired consumption, $r^w$ is world real interest rate, CA is current account ,NX is national income ,y is output, $I^d$ is desired investment, T is taxes $s^d$ desired saving rate, Government spending.

 Foreign:

  $\begin{array}{c}{\text{C}}^{\text{d}}{}_{\text{For}}=\text{48}0+0.\text{4}\left(\text{15}00–\text{ 3}00\right)-\text{3}00{\text{p}}^w \\ =\text{ 48}0+\text{48}0-\text{3}00r^w \\ =\text{96}0-\text{3}00r^w\\ {\text{CA}}_{\text{For}}={\text{NX}}_{\text{For}}=S^d{}_{\text{For}} - I^d{}_{\text{For}} = Y_{\text{For}} - (C^d{}_{\text{For}} + I_{\text{For}}{}^d + G_{\text{For}}) \\ = \text{15}00 - (\text{96}0 - \text{3}00r^w + \text{225} - \text{3}00r^w + \text{3}00) \\ = \text{15} + \text{6}00 r^w \end{array}$

At equilibrium, 

  $\begin{array}{c}CA + C{A}_{\text{For}} = 0,\text{ so}: \\ –\text{65} + \text{4}00 r^w + \text{15} + \text{6}00 r^w = 0 \\ –\text{5}0 + \text{1}000 r^w = 0 \\ r^w = 0.0\text{5}\\ C = \text{64}0 - \text{2}00 r^w = \text{63}0 \\ C_{\text{For}} = \text{96}0 - \text{3}00 r^w = \text{945}\\ S = Y - C - G = \text{1}000 - \text{63}0 - \text{275} = \text{95} \\ S_{\text{For}} = Y_{\text{For}} - C_{\text{For}} - G_{\text{For}} = \text{15}00 - \text{945} - \text{3}00 = \text{255} \\ I = \text{15}0 - \text{2}00 r^w = \text{14}0 \\ I_{\text{For}} = \text{225} - \text{3}00 r^w = \text{21}0 \\ CA = S - I = \text{95} - \text{14}0 = -\text{45} \\ C{A}_{\text{For}} = S_{\text{For}} - I_{\text{For}}= \text{255} - \text{21}0 = \text{45}\end{array}$

For stands for foreign country. ${\text{C}}^{\text{d}}$ is desired consumption, $r^w$ is world real interest rate, CA is current accountNX is national income,y is output, $I^d$ is desired investment, T is taxes, S is saving, $G_{for}$ is foreign government spending

b)

To determine

To evaluate the equilibrium interest rate in the international capital market and the equilibrium values of national saving, consumption, investment, and current account balance in each country assuming that in the home country government purchases by 50 to 325 and taxes also increase by 50 to keep the deficit from increasing.

Explanation of Solution

For stands for foreign country. ${\text{C}}^{\text{d}}$ is desired consumption, $r^w$ is world real interest rate, CA is current account, NX is national income, y is output , $I^d$  is desired investment, T is taxes, S is saving. People’s income tends to increase when the government expenditure on socio economic sectors increase, increase in incomes leads to increase in demand for imports as a result the home has to face deficitin current account.