Question #20316

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?

Expert's answer

a.& Aggregate expenditure function = C + I + G + X - M = 480 + 0.9Yd +200 +100 + 200 -100 - 0.1Yd = 880 + 0.8Yd

b.& Equilibrium level of real GDP = Y = 480 + 0.9(Y - 100) + 200 +100 + 200 -100 - 0.1(Y - 100) = 2,000

c.& Spending multiplier = 1/(1-MPC) = 1/(1 - 0,5) = 2

Tax multiplier = - MPC/(1-MPC) = -0,5/(1-0,5) = -1

d.& Show that leakages = injections at equilibrium.&

& Injections are increases in spending = additions to the flow of income.

Govt spending (G) and Investment are injections.

Leakages are reductions to the flow.

Taxes (T ) and Saving (S) are leakages from the flow of income.

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

Y = 480 + 0.9(Y - 200) + 200 +100 + 200 -100 - 0.1(Y - 200) = 3,600

b.& Equilibrium level of real GDP = Y = 480 + 0.9(Y - 100) + 200 +100 + 200 -100 - 0.1(Y - 100) = 2,000

c.& Spending multiplier = 1/(1-MPC) = 1/(1 - 0,5) = 2

Tax multiplier = - MPC/(1-MPC) = -0,5/(1-0,5) = -1

d.& Show that leakages = injections at equilibrium.&

& Injections are increases in spending = additions to the flow of income.

Govt spending (G) and Investment are injections.

Leakages are reductions to the flow.

Taxes (T ) and Saving (S) are leakages from the flow of income.

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

Y = 480 + 0.9(Y - 200) + 200 +100 + 200 -100 - 0.1(Y - 200) = 3,600

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