Question

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1. Consider an economy described by the following equations:

1. Real Sector                                      b. Monetary Sector

Y=C + I +G                            Demand for Money; r = 100 - M

C = 100 + 0.8 (Y –T)                    Supply of Money : M* = 90

I = 400 – 20 r

G =120

T = 100

Where Y is GDP, C is consumption, I is investment, G is government purchases, T is taxes, and r is the interest rate (%). And M is the stock of money. If the economy were at full employment (that is at its natural rate), GDP would be 2,000.

1. Assuming no change in monetary policy, what change in government purchases would restore full employment?                           

ΔG =_______________

2. Assuming no change in fiscal policy, what change in interest rate (Δ r) would restore full employment?                                        

Δ r =________________

3. In case of (5), assume that the inrease in government purchases raises the demand for money in (b) monetary sector from r= 100 - M to r = 110 – M. This causes the equilibrium interest rate to rise to a new level (r**) and the investment to be reduced to a new level (I**).                  

Find out r** __________ and I**___________

4. Continuing from (7), the increase in interest rate implies the cost of borrowing will increase and therefore, it will reduce investment which is defined as________________
5. Draw two diagrams (a) The Money Market and (b) The Aggregate Demand Curve below to explain (7) and (8):

1.                                   (b)

Answer 1

1) For the IS curve,

Y = C+I+G

or, Y = 100+0.8(Y-T)+400-20r+120

or, Y = 100+0.8(Y-100)+400-20r+120

or, 0.2Y = 100-80+400-20r+120

or, 0.2Y = 540-20r

or, Y = 2700-100r

or, r = 27-0.01Y ...(i)

For the LM curve,

r = 100-M

or, r = 100-90

or, r = 10 ...(ii)

Equating (i) and (ii),

27-0.01Y = 10

or, 0.01Y = 17

or, Y = 1700

In this economy, GDP at full employment level = 2000

Then, output gap = 2000-1700 = 300

Here, value of the multiplier = 1/(1-mpc) = 1/(1-0.8) = 1/0.5 = 5

Then, increase in government purchase (G) to fill the output gap = Output gap / value of the multiplier

or, G = 300/5

or, G = 60

2) Again, when GDP is 2000,

Then, Y = C+I+G

or, 2000 = 100+0.8(2000-100)+400-20r+120

or, 2000 = 100+1600-80+400-20r+120

or, 2000 = 2140-20r

or, 20r = 140

or, r = 7

Then, r = 3

Thus, decreasing the interest rate by 3, will close the output gap.

3) If the new LM curve becomes, r = 110-M

or, r = 110-90

or, r = 20

Thus, new r** = 20

and I** = 400 -20r

or, I** = 400-(20*20)

or, I** = 0

The increase in interest rate implies the cost of borrowing will increase and therefore, it will reduce investment which is defined as crowding out effect.