Question

9. 16 A CLOSED economy is described as follows:
C^d = 100 + .6(Y-T) - 200r                I^d = 400 - 1000r
L = 0.25Y - 750(i)       p^e = 0%         G = 70           T = 50
M = 675            P = 6            (NFP = 0, of course, since it is closed)         Ῡ = 810
(a) What is Y in the SR?
(b) What will r be in the LR if laissez-faire policy is followed?
(c) What will P be in the LR if laissez-faire policy is followed?

Answer 1

(a) Since Pe = 0%, i = r (nominal interest rate = real interest rate).

(a)

In goods market equilibrium,

Y = Cd + Id + G

Y = 100 + 0.6(Y - 50) + 400 - 1000r + 70

Y = 570 + 0.6Y - 30 - 1000r

(1 - 0.6)Y = 540 - 1000r

0.4Y = 540 - 1000r

Y = 1350 - 2500r...........(1) [Equation of IS curve]

In money market equilibrium, L = M/P

0.25Y - 750r = 675/6

0.25Y - 750r = 112.5

0.25Y = 112.5 + 750r

Y = 450 + 3000r............(2) [Equation of LM curve]

In SR equilibrium, Y_IS = Y_LM.

1350 - 2500r = 450 + 3000r

5500r = 900

r = 0.16

Y = 450 + (3000 x 0.16) = 450 + 480 = 930

(b)

With lassez-fair, Y will be equal to potential GDP (= 810). Therefore,

Y = Cd + Id + G

Y = 1350 - 2500r [From (1)]

810 = 1350 - 2500r

2500r = 540

r = 0.216

(c)

Plugging in Y = 810 and r = 0.216 in money market equilibrium condition,

(0.25 x 810) - (750 x 0.216) = 675/P

202.5 - 162 = 675/P

675/P = 40.5

P = 675/40.5 = 16.67