Question

The next several questions refer to the case of an economy with the following equations:

Y = 3K + 2L, with K = 1000 and L = 1500

G = 1230, T = 500

I = 1020 - 1000r

C = 1070 + 0.5(Y-T)

(Assume a closed economy: Y = C + I + G; NX = 0)

Compute the equilibrium level of the interest rate.

compute the equilibrium level of investment.

compute teh equilibrium level of consumption.

suppose government spending is raised to 1250 (instead of 1230). Compute the amount by which investment falls.

the amount by which investment falls is _____ the amount by which government spending rises.

Now change the model above so that the consumption function involves the interest rate as follows:

C = 1070 + 0.5(Y-T) - 1000r

Compute the equilibrium values of the interest rate and investment for the cases of G=1230 and G=1250. How much is investment crowded out now by the rise in G? Report below the amount by which investment falls when G rises from 1230 to 1250.

Answer 1

In a closed economy, Y = C + I + G - T

Given Y = 3K + 2L = 3*1000 + 2*1500 = 6000

Hence, at equilibrium, 6000 = 1070 + 0.5 (6000 - 500) + 1020 - 1000r + 1230

or, 6000 = 1070 + 2750 + 1020 - 1000r + 1230

or, 1000r = 70

or, r = 7%

I = 1020 - 1000r = 1020 - 70

or, I = 950

C = 1070 + 0.5 (6000 - 500)

or, C = 3820

If G = 1250, at equilibrium,

6000 = 1070 + 2750 + 1020 - 1000r + 1250

or, 1000r = 90

or, r = 9%

I = 1020 - 1000r = 1020 - 90

or, I = 930

Therefore, I falls by 20 when G rises by 20

The amount by which investment falls is equal to the amount by which government spending rises.

Now if C = 1070 + 0.5(Y-T) - 1000r,

For G = 1230, at equilibrium,

6000 = 1070 + 0.5 (6000 - 500) - 1000r + 1020 - 1000r + 1230

or, 2000r = 70

or, r = 3.5%

I = 1020 - 1000r = 1020 - 35

or, I = 985

For G = 1250, at equilibrium,

6000 = 1070 + 0.5 (6000 - 500) - 1000r + 1020 - 1000r + 1250

or, 2000r = 90

or, r = 4.5%

I = 1020 - 1000r = 1020 - 45

or, I = 975

Therefore, I falls by 10 when G rises by 20

The amount by which investment falls is less than the amount by which government spending rises.