Question

Given: C = 100 + 0.65Yd (where Yd = Y-T) I = 120-400i G = 200 T = 20 + 0.2Y Ms/P = 200 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 level of: i. Income (4 marks) ii. and consumption

Answer 1

a.

The equation of IS curve is derived as follows:

$Y= AE$

$Y=C + I + G$

$Y= 100 + 0.65 Yd + 120 − 400i + 200$

$Y=100 + 0.65 (Y − T) + 120 − 400i + 200$

 $Y=100 + 0.65 (Y − 20 − 0.2Y) + 120 − 400i + 200$

$Y= 847.91 − 833.33 i ... (1)$

 The equation of LM curve is derived as follows:

$\frac{Md}{P} =\frac{ms}{p}$

$50 + 0.5Y − 600i = 200$

$Y = 300 + 1200i ... (2)$

b.

The equilibrium level of income and interest rate is calculated using the equation (1) and (2) as follows:

$300+1200i=847.91-833.33i$

$1200i+833.33i=847.91-300$

$2033.33=547.91i$

$i= 0.2694$

$Y=300+1200i$

$Y=300+(1200\times0.2694)$

$Y =623.36$

The equilibrium level of consumption is calculated as follows:

$C= 100 + 0.65 (Y − T)$

$=100 + 0.65 (Y − 20 − 0.2Y)$

$=87 + 0.52Y$

$= 87 + 0.52 (623.36)$

$= 411.14$