1. An economy has full-employment output, Y, of 6,000. Government purchases, G, are 1,200. Desired consumption and desired investment are:

Question

1. An economy has full-employment output, Y, of 6,000. Government purchases, G, are 1,200. Desired consumption and desired investment are:

C^{d = 3600 – 2000r + 0.1Y}

I^d = 1200 – 4000r

where Y is output and r is the interest rate.

a. Find an equation relating desired national saving, S^d_, to r and Y

b. Using both versions or forms of the goods market equilibrium, find the real interest rate that clears the goods market. Assume that the output equals full-employment output.

c. Government purchases rise to 1,440. How does this increase change the equation describing desired saving? Show the change graphically. What happens to the market-clearing real interest rate?

Answer 1

a. Find the equation:

S = Y - C = -3600 +2000i +.9Y

b. Solve

We have Y=6000 and G=1200

market clearing equation is Y=C + l + G

Y = 3600 - 2000i + .1*6000 + 1200 - 4000i

Y = 5400 - 6000i

6000 = 5400 - 6000i

i = 600/6000

= 0.10

Now, for S-I

-4800 + 2000r + 0.9Y = 1200 - 4000r

0.9Y = 6000 - 6000r

=.10

c. If G=1440, savings is S = Y-C - G = Y - (3600 - 2000r + 0.1Y) - 1440 = -5040 + 2000r + 0.9Y

Having 240 less for r and Y, will shift the demand curve.

S - I is,

-5040 + 2000r + 0.9Y = 1200 - 4000r

6000r + 0.9Y = 6240

=.9(6000)

=840/6000

=.14

The market clearing real interest rate increases from 10% to 14%.