Answer to Question #245696 in Macroeconomics for Manish

Question

An economy has full-employment output of 9000, and
government purchases are 2000. Desired consumption
and desired investment are as follows:
Real Interest
Rate (0/o)
2
3
4
5
6
Desired
Consumption
6100
6000
5900
5800
5700
Desired
Investment
1500
1400
1300
1200
1100
a. Why do desired consumption and desired invest-
ment fall as the real interest rate rises?
b. Find desired national saving for each value of the
real interest rate.
c. If the goods market is in equilibrium, what are the
values of the real interest rate, desired national
saving, and desired investment? Show that both
forms of the goods market equilibrium condition,
Eqs. (4.7) and (4.8), are satisfied at the equilibrium.
Assume that output is fixed at its full-employment
level.
d. Repeat Part (c) for the case in which government
purchases fall to 1600. Assume that the amount people desire to consume at each real interest rate
is unchanged

Answer 1

(a)

Desired consumption falls as real interest rate rises because of higher returns from savings which stimulates much greater savings.

Desired investment falls as real interest rate rises because of an inclined user cost of capital, which decreases the desired capital stock and hence the investment.

(b)

Desired national saving is given by:

$S_d=Y-C_d-G$

Thus,

At real interest=2, $S_d= 9000-6100-2000=900$

At real interest=3,

$S_d=9000-6000-2000=1000$

At real interest=4,

$S_d=9000-5900-2000=1100$

At real interest=5,

$S_d=9000-5800-2000=1200$

At real interest= 6,

$S_d=9000-5700-2000=1300$

(c)

Goods market equilibrium is achieved when aggregate demand is equal to income. The aggregate demand is determined by the desired consumption and the desired investment.

$Y_d=Y=C_d+I_d+G_0$

$9000=5800+1200+2000$

$9000=9000$

$\therefore$ the goods market is in equilibrium at:

Real interest rate =5

Desired national saving=1200

Desired investment=1200

(d)

If government purchases fall to 1600,

$Y_d=C_d+I_d+G_0$

$Y=Y_d$

$9000=6000+1400+1600$

$9000=9000$

$\therefore$ the goods market will be in equilibrium at:

Real interest rate=3

Desired national saving=1000

Desired investment= 1400.