Question

1. Suppose the autonomous spending is 20, MPC is 0.75. Government spending and tax are unknown. Investment is following the function:

I(r) = 200 - 50r.

If the Government want to close the output gap of -30 by changing tax. Suppose Fed's monetary policy is fixing the real interest rate at 2%, thus the LM curve is horizontal. What is the change in tax the government should aim at?

2. Suppose the production function of a close economy is

F(K, L) = K^.5L^.5.

The full emloyment labor force, L, of the economy is 120 and the stock level of capital, K, is 30 at steady state. Suppose the money supply is 50, velocity is 2 and the current price level is 2.5. What is the output gap?

Answer 1

(1) Output gap = -30

In order to close the output gap of -30, there is a need to increase the output by 30.

=> ΔY = 30

tax multiplier = -MPC / (1 - MPC)

tax multiplier = -0.75 / (1 - 0.75)

tax multiplier = -0.75 / 0.25

tax multiplier = -3

tax multiplier = (ΔY / ΔT)

=> -3 = (30 /ΔT)

=> ΔT = 30 / -3

=> ΔT = -10

hence, there is a need to decrease the taxes by 10 in order to close the output gap of -30.

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(2)

Y = F(K,L) = K^0.5 L^0.5

Full employment level of L = 120 and K = 30

=> Y = (30)^0.5 (120)^0.5

=> Y = 60

Hence, full employment level of output is 60 units.

According to QTM

MV = PY

where M = money supply = 50

V = velocity of money = 2

P = price level = 2.5

Y = real GDP (output)

=> MV = PY

=> 50 * 2 = 2.5 * Y

=> Y = 100 / 2.5

=> Y = 40

Actual output is 40 units

Output gap = Actual output - full employment level of output

Output gap = 40 - 60

=> Output gap = -20

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