Answer to Question #283696 in Macroeconomics for Sheya

Question

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?

Answer 1

A. Write down the IS function. 

$Y=C+I+G$

$Y=50 + 0.75(Y-T)+100 – 2r+120\\ Y=50+0.75Y-0.75T+100-2r+120\\ Y-0.75Y=270-0.75T-2r\\ 0.25Y=270-0.75T-2r\\ Y=1080-3(140)-8r\\ Y=660-8r$

B. Write down the LM function.

$Ms= Md+ P$

$440=2(0.5Y-1.5r)+2\\ 440=Y-3r+2\\ Y=438+3r$

C. Determine the equilibrium levels of income and interest rate.

At equilibrium;

$IS=LM\\ 660-8r=438+3r\\ 222=11r\\ r=20.18$

Replacing r in the IS equation;

$Y=660-8(20.18)\\ Y=498.6$

D. What happens to equilibrium r if money supply is raised from 1,000 to 1,200? 

The equilibrium interest rate will rise by;

$\frac{1200}{1000}=1.2$

E. 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?

If the central bank wishes to raise the interest rate to 7 percent, money supply should be set at;

$(M/P)d = 0.5Y – 1.5r\\ (M/P)d=0.5(498.6)-1.5(r)\\ M_d=498.6-3(7)\\ =477.6$