Practice with the keynesian model. Suppose C = 400 + .75 * DI; I = 250; X = 300;

Question

Practice with the keynesian model.

Suppose C = 400 + .75 * DI;

I = 250; X = 300; M = 100

G = 100; TR = 100; t = 0.2.

(a) Calculate equilibrium output.

(b) Explain in words what would happen if output were above the level you calculated in (a). What would happen if output were below the equilibium level?

(c) Recompute equilibium output assuming that G = 200, holding all else the same as in part (a). Now, recompute equilibium output assuming that the tax rate t = 0.3, assuming that G is 200 and holding all else the same as in part (a).

Explanation / Answer

(a) Y = C + I + G + (X – M)

Y = C = 400 + 0.75(Y – 0.2Y) + 250 + 100 + (300-100)

Y = 400 + 0.75(0.8Y) + 550

Y = 950 + 0.6Y

0.4Y = 950

Y = 950/0.4 = $2,375.

Equilibrium output = $2,375.

(b) If output were above the equilibrium level of $2,375, economic forces would act to reduce output. People wouldn’t want to buy all the output that is being produced, and producers would try to reduce their production, until the equilibrium is reached. On the contrary, if output is below the equilibrium level, people would be trying to buy more goods and services, and as a result, producers would start producing more and continue until the equilibrium level of output is reached.

(c) G increases to 200 and all else remaining constant.

0.4Y = 1,050

Y = 1,050/0.4 = $2,625.

Equilibrium output = $2,625.

Assuming G = 200 and t = 0.3, holding all else the same.

Y = 400 + 0.75(Y – 0.3Y) + 250 + 200 + 200

Y = 1,050 + 0.525Y

Y – 0.525Y = 1,050

0.475Y = 1,050

Y = $2,210.5

Equilibrium output = $2,210.50.

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