Assume the consumption function in an economy is given by C=200+0.8(Y-T) where C

Question

Assume the consumption function in an economy is given by C=200+0.8(Y-T) where C is consumption, Y is GDP and T is a lump-sum tax. Use the Keynesian-cross model to predict the impact on equilibrium GDP of the following changes. Give a formula for the size of the impact on GDP.

a. (8 points) An increase in government purchases.

b. (8 points) An increase in taxes.

c. (8 points) How would consumption respond to changes in GDP if, instead of assuming that taxes are a fixed amount, taxes increase with the income level so that tax revenue is given by T=100+0.3Y?

d. (8 points) How would your answer to (a) change if, instead of assuming that taxes are a fixed amount, they increase with the income level so that tax revenue is given by T=100+0.3Y?

Explanation / Answer

a) Expenditure multiplier = 1 / (1 - MPC) = 1/0.2 = 5

Change in equilibrium GDP = Increase in government purchases x expenditure multiplier

b) Tax multiplier = - MPC / (1 - MPC) = -4

Change in equilibrium GDP = Increase in taxes x tax multiplier

c)

T = 100 + 0.3Y

C = 200 + 0.8 x (Y - (100 + 0.3Y)) = 120 + 0.56Y

d)

Expenditure multiplier (new) = 1 / (1 - MPC x (1 - t)) = 1 / (1 - 0.56) = 2.27

Change in equilibrium GDP = Increase in government purchases x expenditure multiplier (new)

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