8. Consider a hypothetical closed economy with the following functions: C = 50 + 0.75(Y-T); I = 100 – 2r; G = 120; T = 140; Ms = 440; P = 2; (M/P)d = 0.5Y – 1.5r; A. Write down the IS function. B. Write down the LM function. C. Determine the equilibrium levels of income and interest rate. D. What happens to equilibrium r if money supply is raised from 1,000 to 1,200? E. If the central bank wishes to raise the interest rate to 7 percent, what money supply should it set? F. If government purchases increase by 224, what is the impact of this change on the IS curve? and What is the impact of the change on the equilibrium level of income?

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-01-18T14:36:48+01:00

Based on the information given, the IS function will be given as Y = 660 - 8r and the LM function will be Y = 438 + 3r.

Y = C + I + G

Y = 50 + 0.75(Y - T) + 100 - 2r + 120

Y - 0 75Y = 270 - 0.75T + 100 - 2r + 120.

0.25Y = 270 - 0.75T - 2r

Y = 1080 - 3(140) - 8r

Y = 660 - 8r

The LM function will be;

Ms = Md + P

440 = 2(0.5Y - 1.5r) + 2

440 = Y - 3r + 2.

Y = 438 + 3r

The equilibrium level of income and interest rate will be:

IS = LM

660 - 8r = 438 + 3r

8r + 3r = 660 - 438

11r = 222

r = 20.18

Replacing r in the IS equation will be:

Y = 660 - 8(20.18)

Y = 498.6

When money supply is raised from 1,000 to 1,200,the equilibrium interest rate will be:

= 1200/1000 = 1.2

Lastly, the impact of the change on the equilibrium level of income is that the money demand will be 477.6.

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