Handout on the Keynesian Model

 

Use the Keynesian Model to answer the next few questions

            Y = C + I

            C = a + b(Y – T)

            I = autonomously given

            T = 0

  1. If C = $200 and I = $100, then Y must equal _$300_.  If the value of a = $100, then the MPC must be equal to ____.33_____.  The slope of the consumption function is ____.33_____.  The marginal propensity to save is __.67______.  Saving equals ___100______ in  equilibrium.
  2. Suppose a = $100, MPC = .8, and I = $50.  Fill in the following table.  There are no taxes.

Y

C

S

I

C + I

Inventory change

Direction of Change in Y

100

180

-80

50

230

-130

Increase

130

204

-74

50

254

-124

Increase

500

500

0

50

550

-50

Increase

650

620

30

50

670

-20

Increase

780

724

56

50

774

6

Decrease

 

The equilibrium level of real GDP is _750___________.

  1. Suppose the MPC = .5 and the autonomous level of consumption increases by $200.  Fill in the following table showing the multiplier effect.

Round

Change in Y

Change in C

Change in S

1

2

3

4

5

…

200

100

50

25

12.5

…

100

50

25

12.5

6.25

…

100

50

25

12.5

6.25

…

Total

400

200

200

What is the multiplier? ____2_______

Use the following Keynesian Model to answer the next few questions.

      Y = C + I + G + (X – M)

      C = a + b(Y – T)

      I, G, (X – M), and T are all autonomously given

  1. If C = $200, I = $100, G =$100, (X – M) = $50, then Y must be equal to _450______.

If the value of autonomous consumption is zero and T = $50, then the MPC must be equal to _.5_______.  The marginal propensity to save is __.5______.  Saving is equal to ____200______ in equilibrium.

  1. Suppose Y is initially at $500.  But suppose the full employment level of Y is $1000.  If the MPS = .5, how much would the increase in government spending have to be in order to move the economy to the full employment level of Y?

The change in Y = [1/(1 – b)](change in government spending)

The change in Y = 1000 – 500

500 = [1/(1 - .5)](change in government spending)

500 = 2(change in government spending)

250 = change in government spending

  1. Instead of a change in government spending as in problem 5, suppose the government implements a change in taxes in order to move the economy to the full employment level of output.  What will be the change in taxes necessary to move this economy to full employment?

The change in Y = [-b/(1 – b)](change in taxes)

500 = [-.5/(1 - .5)](change in taxes)

500 = (-1)(change in taxes)

-500 = change in taxes       

Note:  the negative implies that taxes must decrease in order for Y to increase