Question

Suppose a = 70; b = ¼; and I = 50. Use the Keynesian cross and its associated equations to answer the following question.

What is the affect on consumption if investment goes from 50 to 80?

Answer 1

Solution:

The consumption function can be written as:

C = a + b*Y, where C is consumption and Y is income

So, C = 70 + (1/4)*Y or C = 70 + 0.25*Y and I = 50; where I is investment

Keynesian cross implies that income equals aggregate expenditure at equilibrium. Aggregate expenditure in this case (assuming a closed economy) = C + I + G

With no information on government expenditure, we take G = 0, so AE = (70 + 0.25*Y) + 50

With Y = AE

Y = 120 + 0.25*Y

Y*(1 - 0.25) = 120

Y = 120/0.75 = $160

So, consumption = 70 + 0.25*160 = $110

With investment increased to 80, new equilibrium income can be found as: Y = (70 + 0.25*Y) + 80

Y*(1 - 0.25) = 150

Y = 150/0.75 = $200

So, new consumption level = 70 + 0.25*200 = $120

Thus, affect of investment going from 50 to 80 is consumption going from 110 to 120.

(Shortcut: change in equilibrium income = (1/(1 - b))*change in autonomous expenditure. In this case, change in autonomous expenditure = 80 - 50 = 30)