Question

2. Assume a consumption function C = 100 + 0.8(Y-T), and let G = 200, T = 200, I = 100. a. First, suppose there is just a tax cut alone, increasing T from 200 to 250. Use the relevant Keynesian multiplier to compute the change in output. (5 pts)

b. If instead, there is an increase in government spending from 200 to 250. By how much will output change? (5 pts)

c. Now suppose there is a simultaneous action so that both government spending and taxes are increased from 200 to 250. What will be the total change in output as a result? (5 pts)

Answer 1

C = 100 + 0.8 * (Y - T)

In the above consumption fundtion, MPC (Marginal Propensity to consume) = 0.8

Aggregate output (Y) = C + I + G

Y = 100 + 0.8 * (Y - 200) + 100 + 200

Y = 100 + 0.8Y - 160 + 100 + 200

0.2Y = 240

Y = 1,200

a) If T increases from 200 to 250,

New output would be: Y = 100 + 0.8 * (Y - 250) + 100 + 200

Y = 100 + 0.8Y - 200 + 100 + 200

0.2Y = 200

Y = 1,000

Tax Multiplier = (MPC / MPS) where MPC + MPS = 1

Tax multiplier = (0.8 / 0.2) = 4

Rise in tax by 50 will reduce aggregate demand by 50 * 4 = 1,000

b) Spending multiplier = [1 / (1 - MPC)] = [1 / (1 - 0.8)] = 5

Rise in governemnt spending from 200 to 250 will raise aggregate demand by 50 * 5 = 250

c) Net multiplier effect = Spending multiplier - Tax multiplier = 5 - 4 = 1

Rise in government spending as well as taxes by 50 will raise aggregate demand by 50 * 1 = 50 because government spending will raise aggregate demand by 250 and tax reduce aggregate demand by 200. Therefore, net effect on aggregate demand is 250 - 200 = 50.