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

Cd = 3600 - 2000r + 0.10Y

Id = 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.

a. real interest rate is 0.217 or 21.7%.

b. saving = 134, investment is 332, consumption is 3666.

Explanation:

a) Y = Cd + Id + Gd

Where Y = output

Cd = consumption

Id = Investment purchases

Gd=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) Sd = Y - Cd - G

where Sd is national saving

Sd = Y - (3600 - 2000r + 0.1Y) - 1200

Sd = 5000 - (3600 - 2000*0.217 + 0.1*5000) - 1200 = 5000-3600+434-500-1200 = 134

Therefore, saving = 134

Id = 1200-4000*0.217 = 332

Therefore, investment is 332

Cd = 3600-2000r+0.10Y=3600-434+500=3666

Therefore, consumption is 3666.