Economics question about GDP?

Consider the following money demand function:

M d = 500 ? 20i

where M d is the quantity of money demanded (in billions of dollars), and i is the

interest rate in percentage. For example, i = 2 means the interest rate is 2%.

The supply of money is $400 billion.

The aggregate expenditure function in billions of dollars is

AE = 1000 + 0.8Y

a. Compute the equilibrium interest rate in the money market and find the

equilibrium real GDP.

b. The Bank of Canada decides to increase money supply by $40 billion. For the

time being, assume spending in the economy is not sensitive to changes in the

interest rate. Compute the equilibrium interest rate.

c. Now suppose that each one percentage point decrease in the interest rate

stimulates spending in the economy by $200 billion. Find the equilibrium real

GDP given the change in part b.

Economics question about GDP?yes loans

The aggregate expenditure function in billions of dollars is

AE = 1000 + 0.8Y

a. Compute the equilibrium interest rate in the money market and find the equilibrium real GDP.

Ans: Money market equilibrium requires Md=Ms.ie.,

500 ? 20i = 400 0r, 20r= 100 or, r= 4 ie equlibrium interest is 4%

Real goods sector will be in equilibrium if aggregate expenditure equals aggregate income or GDP,Y. so,

AE = 1000 + 0.8Y =Y or, 0.2*Y= 1000, or, Y= 1000/0.2 = 5000.

Thus equilibrium GDP is $5000 billion.

b. The Bank of Canada decides to increase money supply by $40 billion. For the time being, assume spending in the economy is not sensitive to changes in the

interest rate. Compute the equilibrium interest rate.

Ans: Ms is now 440. So, Md=Ms implies 500-20i=440,

or, 20r= 60, or i- 60/20= 3 So, the equlibrium interest rate is 3%.

c. Now suppose that each one percentage point decrease in the interest rate stimulates spending in the economy by $200 billion. Find the equilibrium real GDP given the change in part b.

Ans: Interest rate has gone down by 2% points from 5% to 3% as a result of increased money supply. This shoukld lead to increase in aggregate expenditure by 2*$200 billion = $400 billion. So, AE will be given by 1000+0.2Y + 400 = 1400 +0.8 Y. For equilibrium, AE should equal Y. So,

1400+0.8Y= Y 0r, 0.2 Y= 1400 or, Y= 1400/0.2= 7000 ie. the equlibrium GDPP is now $7000 billion.

Note that the multiplier being 1-(1-mpc)= 1/0.2=5, a $400 billion extra spensding leads to an additional GDP of 5*400 or, $ 2000 billion of additional GDP.