Question

(A) Given: C = 100 + 0.75Yd (where Yd = Y-T)

 I = 120-600i

 G = 200

 T = 20 + 0.2Y

 Ms/P = 300

Md/P = 50+0.5Y-600i

Where: C = Consumption

Y = Income

 I = Investment

G = Government spending

T = Taxes

i = interest rate

Ms/P = RealMoney Supply

Md/P = Real Demand for Money

(a) Derive the IS and LM curves

 

(b) Obtain the equilibrium:

i. Interest rate

ii. Income and consumption

Answer 1

(a)

$Y = C+I+G$

$Y = 100 + 0.75(Y-20-0.2Y) + 120-600i + 200$

$Y = 420+0.6Y-15-600i$

$0.4Y = 405-600i$

$IS\space curve : Y = 1012.5 - 1500i$

 

Money Demand = Money Supply,

$50+0.5Y-600i = 300$

$LM\space curve : i =\frac{(0.5Y-250)}{600}$

 

(b)

(i)

$i =\frac{ (0.5Y-250)}{600}$

$i = 0.189$

Equilibrium interest rate : $i = 18.9\%$

(ii)

Substituting value of i in IS curve equation, we get,

Substituting value of i in IS curve equation, we get,

$Y = 1012.5 - 1500 \times \frac{ (0.5Y-250)}{600}$

$Y = 1012.5 - 1.25Y + 625$

$2.25Y = 1637.5$

Equilibrium Income : $Y = 727.7$

 

$C = 100+0.75(Y-20-0.2Y)$

$C = 100+0.6Y-15$

Equilibrium Consumption : $C = 521.6$