Question

Consider the following Keynesian economy.

Consumption function: Ct = 20 + 0.7(Y-T)

Investment Function: It = 42 −100r

Government Spending: Gt = 50

Tax Collections: Tt = 50

Real Money Demand Function: (Mt/Pt) = 6Yt − 2000Rt

Money Supply: = Mt = 2800

Price Level: Pt = 2

i. Derive the equation for the IS curve expressing r as a function of Y only. For interest rates ranging from 0-8, graph the IS curve.

ii. Derive the equation for the LM curve expressing r as a function of Y. For interest rates ranging from 0-8, graph the LM curve.

iii. The point of intersection between the IS-curve and the LM-curve depict short equilibrium interest rate and income. Solve for the short run equilibrium interest rate and income based on the IS and LM equations derived in parts a and b above. Show the short equilibrium values of interest rate, r and income, Y that you have solved for on a graph.

Answer 1

i.

Ct = 20 + 0.7(Y-T)

It = 42 −100r

Gt = 50

Tt = 50

For IS curve derivation:

Y = Ct + It + Gt

Y = 20 + 0.7(Y-T) + 42 −100r + 50

Y = 20 + 0.7(Y-50) + 42 −100r + 50

Y = 20 + 0.7Y - 35 + 42 -100r +50

Y - 0.7Y = 20-35+42+50 - 100r

0.3Y = 77 - 100r

Y = (770/3) - (1000/3)r

For LM curve derivation:

(M/P) = Md

2800/2 = 6Y - 2000r

1400 = 6Y - 2000r

6Y = 1400 + 2000r

Y = (700/3) + (1000/3) r

iii.

The point of intersection between IS and LM curve is:

Thus, the short run equilibrium interest rate is 0.035

The short-run equilibrium income = 245