Question

A closed economy has full employment output of 6000. Government purchases, G, are 1200. Desired consumption and desired investment are:

Cd= 3600 - 2000r + 0.10Y, and

Id = 1200 - 4000r

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

a. Find an equation relating desired national saving, Sd, to r and Y.

b. Using the goods market equilibrium condition, find the real interest rate that clears the goods market. Assume the output equals full-employment output.

c. Government purchases rise to 1440. How does this increase change the equation describing desired national saving? Show the change graphically. What happens to the market clearing real interest rate?

Answer 1

(a) Sd = Y - Cd - G

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

= -4800 + 2000r + 0.9Y

(b).Y = Cd + Id + G

Y = (3600 - 2000r + 0.1Y) + (1200 - 4000r) + 1200

= 6000 - 6000r + 0.1Y

So 0.9Y = 6000 - 6000r

At full employment, Y = 6000.

Solving 0.9* 6000 = 6000 - 6000r,

we get r = 0.10

(c).Government purchases rise to 1440 i.e. G = 1440,

desired saving becomes Sd = Y - Cd - G

= Y - (3600 - 2000r + 0.1Y) - 1440

= -5040 + 2000r + 0.9Y.

Sd is now 240 less for any given r and Y; this shows up as a shift in the Sd line from S1 to S2 in the Figure

Setting Sd = Id, we get: -5040 + 2000r + 0.9Y = 1200 - 4000r

6000r + 0.9Y = 6240

At Y = 6000, this is 6000r = 6240 - (0.9 ´ 6000) = 840,

o r = 0.14.

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