Question

9.13 An economy is described as follows:

C^d = 170 + .6(Y-T) - 1400r                I^d = 120 - 1000r

L = 0.25Y - 1000(i)                 p^e = 0%              G = 110           T = 100

M = 75                         NFP = 0                      i = r + p^e

(a)If long run Y(i.e., Y full employment) is 370, what are the long run levels of r and P?
(b) In the problem above, if the central bank were to increase the money supply to 150, what would happen to Y and r in the short run before P adjusts? (#’s please)
(c) In the problem above, if the central bank were to increase the money supply to 150, what would happen to Y and P in the long run? (#’s please)

Answer 1

Answer - 9.13

(a)

C^d = 170 + .6(Y-T) - 1400r , I^d = 120 - 1000r , L = 0.25Y - 1000(i) , p^e = 0% , G = 110 , T = 100 , M = 75 , NFP = 0 and i = r + p^e

Goods market is in equilibrium when ; Y = C + I + G

=> Y = 170 + .6(Y-100) - 1400r + 120 - 1000r + 110

=> 0.4Y = 340 - 2400r ------------IS Equation

In the Long run Y = 370

=> 0.4*370 = 340 - 2400r => r = 0.08

Hence r = 0.08 ~ 8% => i = r + pe = 0.08 + 0 = 0.08 = 8%

Money Market is in equilibrium when M/P = L

=> M/P =  0.25Y - 1000(i) ---------------LM equation

As calculated above in the long run Our Y = full employment output = 370 and i = 0.08

=> 75/P =  0.25*370 - 1000(0.08)

=> P = 6

Hence In the long run, r = 0.08 and P = 6

(b)

Now P = 6 , M = 150

From IS and LM equation derived above we have :

0.4Y = 340 - 2400r and 150/P =  0.25Y - 1000(i) and i = r + pe = r + 0 = r

=> 0.4Y = 340 - 2400(i) and 150/6 =  0.25Y - 1000(i)

=> 2400(i) +0.4Y = 340 and  25 =  0.25Y - 1000(i)

=> Y = 850 - 6000(i) and Y = 100 + 4000i

=> Y = 850 - 6000(i) = 100 + 4000(i)

=> 750/10000 = i

=> i = 0.075 => r = i - pe = 0.075

=> Y = 850 - 6000(0.075) = 400

Hence In the short run before price adjustment r = 0.075 and Y = 400

(c)

In the Long run Real Output(Y) = Full employment output = 370. Hence In the Long Run After increase in Money supply Our real Output(Y) = 370

Goods market is in equilibrium when ; Y = C + I + G

=> Y = 170 + .6(Y-100) - 1400r + 120 - 1000r + 110

=> 0.4Y = 340 - 2400r ------------IS Equation

In the Long run Y = 370

=> 0.4*370 = 340 - 2400r => r = 0.08

Hence r = 0.08 ~ 8% => i = r + pe = 0.08 + 0 = 0.08 = 8%

Money Market is in equilibrium when M/P = L

=> M/P =  0.25Y - 1000(i) ---------------LM equation

As calculated above in the long run Our Y = full employment output = 370 and i = 0.08

=> 150/P =  0.25*370 - 1000(0.08)

=> P = 12

Hence In the long run, Y = 370 and P = 12