Question

You are given the following equations for the Aggregate Demand (AD) and short-run Aggregate Supply (SAS), AD Y = 2 Ap + 4 (Ms / P) SAS Y = 750 + 250 P Y N = 1250 Natural Real GDP Ap = 250 Autonomous Spending Ms = 125 Nominal Money Supply

1- Find the equilibrium Price level and Real GDP in the short run.

2- Determine the recessionary or inflationary gap if exist and by how much at short run equilibrium price levels.

3- Calculate the equilibrium price level and real GDP, if the nominal supply increases to 375.

Answer 1

AD: Y = (2 x 250) + 4 x (125/P) = 500 + (500/P)

(1) In equilibrium, AD = SAS.

500 + (500/P) = 750 + 250P

500/P = 250 + 250P

2/P = 1 + P [Dividing by 250]

2 = P + P²

P² + P - 2 = 0

P² + 2P - P - 2 = 0

P(P + 2) - 1(P + 2) = 0

(P + 2) (P - 1) = 0

P = 1 [Since P is non-negative]

Y = 750 + (250 x 1) = 750 + 250 = 1000

(2) Since YN > Y, there is a recessionary gap equal to

Recessionary gap = YN - Y = 1250 - 1000 = 250

(3) When MS = 375,

AD: Y = (2 x 250) + 4 x (375/P) = 500 + (1500/P)

500 + (1500/P) = 750 + 250P

1500/P = 250 + 250P

6/P = 1 + P [Dividing by 250]

6 = P + P²

P² + P - 6 = 0

P² + 3P - 2P - 6 = 0

P(P + 3) - 2(P + 3) = 0

(P + 3) (P - 2) = 0

P = 2 [Since P is non-negative]

Y = 750 + (250 x 2) = 750 + 500 = 1250