Question

In the Keynesian cross, assume that the consumption function is given by: C(Y-T)=210+0.5(Y-T)

and government purchases and taxes are both 100. Current planned investment is 750.

A) Plot the Keynesian cross with both axes going from 0 to 8000. Be sure to label the axes and the planned expenditure function as PE₀.

B) What is the equilibrium level of income? Show this on your graph as Y₀.

C) Give the formula for the government purchase multiplier and compute it for this economy.

D) Give the formula for the tax multiplier and compute it for this economy.

E)  Use the government multipler and tax multiplier to explain the net effect on output, Y₀, if both government expenditures and taxes change to 75.

Answer 1

AE = C + I + G

AE = 210 + 0.5(Y - 100) + 750 + 100

AE = 1,060 + 0.5Y - 50

AE = 1,010 + 0.5Y

(A) The Keynesian cross is as follows.

Data table:

Y	AE
0	1010
1000	1510
2000	2010
3000	2510
4000	3010
5000	3510
6000	4010
7000	4510
8000	5010

Graph:

(B) In equilibrium, Y = AE

Y = 1,010 + 0.5Y

0.5Y = 1,010

Y = 2,020

In above graph, equilibrium is at point E where AE0 intersects 45⁰ line with equlibrium Y being Y0 (= 2,020).

(C) MPC = 0.5

Government purchase multiplier = 1 / (1 - MPC) = 1 / (1 - 0.5) = 1 / 0.5 = 2

(D) MPC = 0.5

Tax multiplier = - MPC / (1 - MPC) = - 0.5 / 0.5 = - 1

(E) Both G and T decrease by 25 (= 100 - 75).

When G decreases by 25, Y decreases by (2 x 25) = 50 units.

When T decreases by 25, Y increases by (1 x 25) = 25 units.

Net decrease in Y = 50 - 25 = 25 units