Question

1.     The following functions are given:

        C = 100 + 0.8Y

I = 120-5r

M_s = 120

M_d = 0.2y-5r

A.   develop the Investment saving curve and draw the curve

B.    write the LM equation and draw the curve

C.    find the equilibrium income and interest rate

D.   what is the  equilibrium income if the equilibrium interest rate increased by 25%

Answer 1

$$solution$$

$given:\\ C=100+0.8Y\\ I=120-5r\\ M_s=120\\ M_d=0.2Y-5r$

$[A]\ IS \ curve: \\ Y=C+I\\ Y=100+0.8Y+120-5r\\ Y-O.8Y=220-5r\\ 0.2Y=220-5r\\ Y=1100-25r$

$[B]\ LM\ equation: \\ M_d=M_s\\ 0.2Y-5r=120\\ 0.2Y=120+5r\\ Y=600+25r$

[C] Equilibrium income and interest rate:

interest rate at equilibrium $IS=LM$

$1100-25r=600+25r\\ 1100-600=25r+25r\\ 500=50r\\ r=10$

income at equilibrium:

substitute:

$Y=600+25r\\Y=600+(25\times 10)\\ Y=600+250\\ Y=850$

$Y=1100-25r\\ Y=1100-(25\times10)\\ Y=1100-250\\ Y=850$

Therefore the equilibrium income is $\$850$

[D] Equilibrium income if equilibrium interest rate increased by 25%

$0.1=850\\ 0.25=?\\ \frac{0.25}{0.1}\times 850=\$2125\\$