Question

Assume the following model of the economy, with the price level fixed at 1.0:

C = 0.8(Y – T) i = 1000 – 20r

T = 500

G = 1,000

Ms = 1,000

Md/P = 0.5Y – 50ra

A) What are the short-run equilibrium values of Y, and r.

B) Assume that T decreases by 100. By how much will Y increase in short-run equilibrium?

C) Assume that T is back at its original level of 500, but Ms (money supply) increases by 100. By how much will Y increase in short-run equilibrium?

Answer 1

A) C = 0.8(Y-T) = 0.8(Y-500) = 0.8Y - 400
IS: Y = C + i + G = 0.8Y - 400 + 1000 – 20r + 1000 = 1600 + 0.8Y - 20r
So, Y - 0.8Y = 0.2Y = 1600 - 20r
So, Y = (1600/0.2) - (20r/0.2)
So, Y = 8000 - 100r

LM: Md = Ms/P. P = 1
So, 0.5Y – 50r = 1000
So, 0.5(8000 - 100r) – 50r = 1000
So, 4000 - 50r - 50r = 1000
So, 100r = 4000 - 1000 = 3000
So, r = 3000/100
So, r = 30

Y = 8000 - 100r = 8000 - 100(30) = 8000 - 3000
So, Y = 5000

B) MPC = 0.8
According to tax multiplier,
Change in Y/Change in T = -MPC/(1-MPC) = -0.8/(1-0.8) = -0.8/0.2 = -4
So, change in Y = change in T*(-4) = (-100)*(-4) = 400
So, Y will increase by 400

C) MS = 1,000 + 100 = 1100
LM: Md = Ms/P. P = 1
So, 0.5Y – 50r = 1100
So, 0.5(8000 - 100r) – 50r = 1100
So, 4000 - 50r - 50r = 1100
So, 100r = 4000 - 1100 = 2900
So, r = 2900/100
So, r = 29

Y = 8000 - 100r = 8000 - 100(29) = 8000 - 2900
So, Y' = 5100

Change in Y = Y' - Y = 5100 - 5000 = 100
So, Y increases by 100.