Question

1. An economy has full-employment output of 5000. Government purchases are 1000. Desired consumption and desired investment are given by

C^d= 3600 - 2000r + 0.10Y

I^d = 1200 - 4000r

where Y is output and r is the expected real interest rate.

(a) Find the real interest rate that clears the goods market. Assume that output equals full-employment output.

(b) Calculate the amount of saving, investment, and consumption in equilibrium.

Answer 1

(a) Y = C^d + I^d + G^d

Where Y= output

C^d= consumption

I^d= Investment purchases

G^d=Government purchases

Y= (3600 - 2000r + 0.10Y) + (1200 - 4000r) + 1000

Y=5800-6000r+0.10Y

0.9Y=5800-6000r

At full employment Y=5000

Putting the value of Y in the above equation

0.9*5000=5800-6000r

5800-4500=6000r

r=0.217

Therefore real interest rate is 0.217 or 21.7%.

(b) S^d = Y - C^d - G

where S^d is national saving

S^d = Y - (3600 - 2000r + 0.1Y) - 1200

S^d = 5000-(3600 - 2000*0.217 + 0.1*5000) - 1200 =5000-3600+434-500-1200 = 134

Therefore, saving = 134

I^d= 1200-4000*0.217 =332

Therefore, investment is 332

C^d= 3600-2000r+0.10Y=3600-434+500=3666

Therefore, consumption is 3666.