Answer to Question #193997 in Macroeconomics for Nkeletsang Marupin

Question #193997

(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 (10 Marks) (b) Obtain the equilibrium: i. Interest rate (5 Marks) ii. Income (3 marks) iii. and consumption (2 marks) 


1
Expert's answer
2021-05-18T12:13:43-0400

(a)

Y=C+I+GY = C+I+G

Y=100+0.75(Y200.2Y)+120600i+200Y = 100 + 0.75(Y-20-0.2Y) + 120-600i + 200

Y=420+0.6Y15600iY = 420+0.6Y-15-600i

0.4Y=405600i0.4Y = 405-600i

IS curve:Y=1012.51500iIS\space curve : Y = 1012.5 - 1500i

 

Money Demand = Money Supply,

50+0.5Y600i=30050+0.5Y-600i = 300

LM curve:i=(0.5Y250)600LM\space curve : i =\frac{(0.5Y-250)}{600}

 

(b)

(i)


i=(0.5Y250)600i =\frac{ (0.5Y-250)}{600}

i=0.189i = 0.189

Equilibrium interest rate : i=18.9%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=1012.51500×(0.5Y250)600Y = 1012.5 - 1500 \times \frac{ (0.5Y-250)}{600}

Y=1012.51.25Y+625Y = 1012.5 - 1.25Y + 625

2.25Y=1637.52.25Y = 1637.5

Equilibrium Income : Y=727.7Y = 727.7

 

C=100+0.75(Y200.2Y)C = 100+0.75(Y-20-0.2Y)

C=100+0.6Y15C = 100+0.6Y-15

Equilibrium Consumption : C=521.6C = 521.6

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