Question

Consider a closed economy with a fixed price:
Consumption function: ? = 1+(3/4)(? − ?)
Investment function: ? = 10
Money demand function: (M/P) = ? − 2?
Tax and government spending: ? = ? = 12
Money supply: ? = 500
Where C is consumption, Y is production, I is investment, ? is real interest rate expressed in percent, ? is tax, ? is government spending, ? is money supply. The price level of this economy is fixed at 10 in the short term and there are many idle production facilities.

(a) Describe the shape of the IS curve (showing the combination of output in product market equilibrium and real interest rates). (Hint: do not derive the IS equation, describe the shape.)
(b) Find the short-term equilibrium income and real interest rate for a closed economy expressed by the above equations.
(c) The economy's policy makers are said to be debating the effectiveness of fiscal and monetary policy to boost the economy. The government considers the income level in (b) to be in a recession and intends to increase fiscal expenditure from 12 to 14 by issuing government bonds. Then, how much the equilibrium income and real interest rate changed from the initial equilibrium income and real interest rate due to the government's expansive fiscal expenditure? Show the results of this economy's expanding fiscal policy as an IS-LM graph. (Put the output on the horizontal axis and the real interest rate on the vertical axis.)
(d) The central bank considers the income level in (b) to be in a recession and wants to increase the money supply from 500 to 520. At this time, answer how much the equilibrium income and real interest rate have changed from the initial equilibrium income and real interest rate due to the central bank's expanding monetary policy. Show the outcome of this economy's expanding monetary policy on an IS-LM graph. (Put the output on the horizontal axis and the real interest rate on the vertical axis.)
(e) If the government sought advice on the effectiveness of fiscal and monetary policy in this economy, please answer which of the two policies would you recommend. And briefly describe the intuitive reason for that.

Answer 1

a) The IS curve is drawn for real interest rate on vertical axis and output on horizontal axis. It is a downward sloping curve indicating an inverse relationship between real interest rate and output. The slope of the IS curve depends on interest elasticity of investment. the IS curve is steep when the interest elasticity is low and will be flat when interest elasticty is high.

b) To solve for the short- term equilibrium income and real interest rate, we need to solve the IS(goods market) and LM(money market) equations.

The IS equation is given as

Y= C+I+G

Where C is Consumption function

I is Investment function

G is government spending

Substituting the values from the information given, we get,

Y= 1+3/4(Y-T) +10+12

Y=1+ 3/4(Y-12) +10+12

Y= 1+0.75Y-9 +10+12

Y-0.75Y=14

0.25Y=14

Y=56  

The money market equation or LM is when demand for real balances equal supply of real money balances.

(M/P)^s= (M/P)^d

500/10=Y-2r

Substitute Y=56 in above equation.

50=56-2r

2r=56-50

r=3

c)

Expansion of government spending to G=14

The new IS equation with expansionary fiscal policy is:

Y= 1+3/4(Y-T) +10+14

Y=1+ 3/4(Y-12) +10+14

Y= 1+0.75Y-9 +10+14

Y-0.75Y=16

0.25Y=16

Y=64  

The new LM equation is:

(M/P)^s= (M/P)^d

500/10=Y-2r

Substitute Y=64 in above equation.

50=64-2r

2r=64-50

r=7

d) Expansionary monetary policy by increasing money supply to 520 affects the money market or the LM equation.

(M/P)^s= (M/P)^d

520/10=Y-2r

Substitute Y=56 in above equation.

52=56-2r

2r=56-52

r=2

The investment function in the IS equation does not depend on the real rate of interest. Thus, there is no change in the the IS equation. In this case, the output(Y) remain the same. Only the real rate on interest declines.

e) The expansion of fiscal policy would be better even though there is an increase in the real rate of interest and can lead to crowding out effect. Since, the IS is insensitive to real rate of interest, any change in r will not affect output. Thus an expansionary monetary policy will not work in this case.