Question

A. Given that in an economy, , I, MS =300, Mt = 0.4Y, and Mz=125-200r where, Y= income, C= consumption, I= investment, MS= money supply, Mt= transactional-precautionary money demand, Mz= speculative money demand and r= interest rate. Calculate;

 i. The equilibrium level of income and interest rate in this economy.  

 ii. The level of C, I, Mt, and Mz when the economy is in equilibrium

B. Now, assuming the economy is open with government (G) participation and  external trade which is summarized as follows; export(X)= 100-0.10Y, import(M)=50, G=100, Taxes(T)= 100 and C, I, MS, Mt, and Mz the same as defined in (a) above. Calculate;

 i. The equilibrium income and interest rate in this new economy.

 ii. The level of C, I, Mt, and Mz when the economy is in equilibrium

 iii. What exchange rate policy should government implement in (iii) to enhance income and why?

Answer 1

a)

i)

$Y=C+I\\Y=102+0.7Y+150-100r\\Y-0.7Y=252-100r\\0.3Y=252-100r\\Y=840-333.3r\\$

$MS=Mt+Mz\\300=0.4Y+125-200\\0.4Y=300-125+200r\\0.4Y=175+200r\\Y=437.5+500r$

$437.5+500r=840-333.33r\\833.3r=402.5\\r=0.48\\Y=840-333.3(0.48)\\=840-160\\=680$

ii)

$C=102+0.7(680)\\=102+476\\=578\\I=150-100(0.48)\\=150-48\\=102\\Mt=0.4(680)\\=272\\Mz=125-200(0.48)\\=125-96\\=29$

b)

i)

$C=102+0.7Y\\I=150−100r\\MS=300\\Mt=0.4Y\\Mz=125−200r$

MD(Total money demand)$=Mt+Mz$

$MD=0.4Y+125−200r\\Export(X)=50\\Import(M)=100−0.10Y$

IS curve equation

$Y=C+I+G+X−M\\Where,\\C=102+0.7(Y−T)\\C=102+0.7(Y−100)\\$

Let us substitute all the given values:

$Y=102+0.7(Y−100)+150−100r+100+50−(100−0.10Y)\\Y=102+0.7Y−70+150−100r+150−100+0.10Y\\Y=102+0.8Y+130−100r\\Y=232+0.8Y−100r\\Y−0.8Y=232−100r\\0.2Y=232−100r$

$Y=1160−500r$ (IS curve equation)

LM curve equation:

Money demand=Money supply

$0.4Y+125−200r=300\\ 0.4Y−200r=300−125\\ 0.4Y−200r=175\\ 0.4Y=175+200r\\$

$Y=437.5+500r$   (LM curve equation)

At equilibrium,

IS curve=LM curve

$1160−500r=437.5+500r\\ 1160−437.5=500r+500r\\ 722.5=1000r\\ r=\frac{722.5} {1000}\\ r=0.7225$

Substitute r=0.7225 in the IS curve equation for equilibrium income:

$Y=1160−500×0.7225\\Y=1160−361.25\\Y=798.75$

ii)

$C=102+0.7×798.75\\C=102+559.125\\C=661.125$

The value of consumption is 661.125

$I=150−100r\\I=150−100×0.7225\\I=150−72.25\\I=77.75$

The value of an investment is 77.75

$Mt=0.4×798.75\\Mt=319.5\\And,\\Mz=125−200×0.7225\\Mz=125−144.5\\Mz=19.$

iii)

The government should devalue its currency (under a fixed exchange rate system) against the foreign currencies. In this case, domestic goods will become cheaper. As a result, the export will increase and it will lead to an increase in the aggregate demand and domestic income.

Note: devaluation means reducing the value of own country's currency to make export cheaper. 

Under the floating exchange rate regime, the government should buy more foreign currency. As a result, the domestic currency will depreciate. The exchange rate faced by foreign consumers will fall. As a result, domestic export will increase and it will increase the domestic income.