Question

In a simple two-sector Keynesian model, if MPC=75%, what is the size of the multiplier?
  
                
                

10. What is the equilibrium level of income in this Keynesian model?

        When DI (AP) = 1000, C=1200, Ip=300, G=200, Exports=100, Imports=50
        When DI (AP) = 2000, C=2000, Ip=300, G=200, Exports=100, Imports=100
        When DI (AP) = 3000, C=2800, Ip=300, G=200, Exports=100, Imports=150
        When DI (AP) = 4000, C=3600, Ip=300, G=200, Exports=100, Imports=200
        When DI (AP) = 5000, C=4000, Ip=300, G=200, Exports=100, Imports=250

  
                              1000          2000          3000          4000          5000

Answer 1

Q1: We know that multiplier = 1/(1-MPC), here MPC=75%

Hence multiplier = 1/(1-75%) = 1/0.25 = 4

Q2: If you see the data you realize that Investment (Ip) is constant, govt expenditure (G) is constant and Exports (E) are also constant.

Consumption (C) is growing with income and we can find out the MPC by taking delta C / delta DI

(2000-1000) / (2000-1000) = 800/1000 = 80% = 0.8

With MPC = 0.8, we can also find out autonomous consumption which is 1200 - 1000*0.8 = 400 (taking consumption over and above what we get by MPC on the lowest income, i.e., 1000)

Similarly Imports are related to Income as follows:

(100-50)/(2000-1000) =50/1000 = 5% or 0.05

There is no autonomous Import.

Now the equation is
Income = 400 + 0.8*Income + 300 + 200 + 100 - 0.05*Income

Income - 0.8 Income + 0.05 Income = 1000

0.25 Income = 1000

Income = 1000/0.25 = 4000