Question

19. Consider a closed economy where the consumption function is C = 100+ 0.8(Y – T), where T represents lump sum taxes. Investment is fixed at 100, and government spending is also 100. a. Assuming that the budget is balanced, calculate the equilibrium income for this economy. b. Suppose the government is committed to a balanced budget, but it sees that the economy is overheating (growing too fast). It decides to lower both government spending and taxes by 50 each. What will be the resulting change in equilibrium Y? c. Although the government was concerned about overheating, it did not wish to cause equilibrium income to fall. Assuming that tax cuts are still at 50, by how much should the government have changed G in order to ensure that equilibrium income stays at the level you found in part (a)?

Answer 1

(a) With balanced budget, G = T = 100

In equilibrium, Y = C + I + G

Y = 100 + 0.8 x (Y - 100) + 100 + 100

Y = 300 + 0.8Y - 80

0.2Y = 220

Y = 1100

(b) When both G and T are decreased (increased) by same amount, Y will decrease (increase) by same amount, since balanced budget multiplier is 1.

Decrease in Y = 50

(c) MPC = 0.8

Spending multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1/0.2 = 5

Tax multiplier = - MPC / (1 - MPC) = - 0.8/0.2 = - 4

When Tax is decreased by 50, Y has increased by (50 x 4) = 200.

To keep Y unchanged, government spending has to be decreased by (200/5) = 40.