Question

9.5 A closed economy is described as follows:

C^d = 70 + .6(Y-T) - 300r                I^d = 100 - 500r

L = .2Y - 250i     p^e = 0%       G = 40     _      T = 50

M = 120                          NFP = 0         Y = 210

(a) What will the interest rate be in the long run? SHOW YOUR WORK.
(b) What will the price level be in the long run? SHOW YOUR WORK.
(c) Given an equation for the AD curve for this economy in the form Y = …………. (The answer will not have round, pretty numbers. But, if you have time, you can double check your answer to verify that it is the correct equation another way.)

Answer 1

(a)

C^d = 70 + .6(Y-T) - 300r                I^d = 100 - 500r

G = 40 and  T = 50 Also i.e. Potential Output = 210

In the Long Run Real GDP = Potential Output.

=> Y = C + I + G = 70 + 0.6(Y-50) - 300r + 100 - 500r +40

=> Y = 210 + 0.6Y - 30 - 800r => 0.4Y = 180 - 800r => Y = 450 - 2000r

As in the long run Real GDP = Potential output = 210

=> Y = 450 - 2000r = 210

=> 240/2000 = r => 0.12

=> r = 12%

Hence Interest rate in the long run = 12%

(b)

Money market is in the equilibrium when Real Money supply = real money demand

=>M/P = L = .2Y - 250i Also Note that Inflation rate = 0 => i = r +pe = r = 0.12 (In the Long run as calculated above)

=> 120/P = 0.2*210 - 250*0.12 = 12

=> P = 10

Hence, the price level in the long run = 10

(c)

AD shows the relationship between Y and P such that both goods and Money market is in equilibrium

GOOD MARKET:

Y = C + I + G = 70 + 0.6(Y-50) - 300r + 100 - 500r +40

=> Y = 210 + 0.6Y - 30 - 800r => 0.4Y = 180 - 800r => Y = 450 - 2000r => r = (1/2000)(450 - Y) ----(1)

MONEY MARKET :

M/P = L = .2Y - 250i => 120/P = 0.2Y - 250r --------------(2)

=> Putting values of r from (1) in (2) we get:

=> 120/P = 0.2Y - 250*(1/2000)(450 - Y)

=> 120/P = 0.2Y - 0.125(450 - Y) = 0.325Y - 56.25

=> Y = (1/0.325)(56.25 + 120/P) -----------Equation of AD Curve