1. Suppose you are given the following fixed-price Keynesian model: C = 480 + 0.

Question

1. Suppose you are given the following fixed-price Keynesian model:

            C = 480 + 0.9Yd

            I = 200

            G = 100

            X = 200

            M = 100 + 0.1Yd

            T = 100

            a. Find the aggregate expenditure function.                                        

            b. Find the equilibrium level of real GDP.                                           

            c. What is the spending multiplier in this model? Tax multiplier?

            d. Show that leakages = injections at equilibrium.                               

            e. If taxes increase by $100, what is the new equilibrium level of

                 GDP?                                                                                             

            f. Show your answers to b) and f) graphically.

Explanation / Answer

a. Find the aggregate expenditure function.   

AE = C + I + G + X - M

AE = 480 + 0.9*(Y - 100) + 200 + 100 + (200 - 100 - 0.1(Y - 100))

AE = 800 + 0.8Y   

b. Find the equilibrium level of real GDP.         

Y = AE

Y = 800 + 0.8Y

Y* = 800/0.2 = $4000   

c. What is the spending multiplier in this model? Tax multiplier?

Spending multiplier = 1/1-MPC-MPM = 1/1 - 0.9 + 0.1 = 5

Tax multiplier = -MPC/1-MPC-MPM = -0.9/1 - 0.9 + 0.1 = -4.5

d. Show that leakages = injections at equilibrium.   

Savings + Taxes + Imports = Investment + G + exports

(4000 - 100) - (480 + 0.9*(4000 - 100)) + 100 + 100 + 0.1*4000 = 500

500 = 500

e. If taxes increase by $100, what is the new equilibrium level of GDP?

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