Question

Assume the following equations summarize the structure of an economy.

C =Ca +0.7(Y-T) Ca = 2,000 - 5r T = 150 + 0.15Y (M/P)d = 0.3Y - 10r MS/P = 3,000 i = 2,000 -10r G = 4,000- .2y NX = 1,500 - 0.1Y- 5r

A. Calculate the equilibrium real output (Y) and (r).

B. If government spending increases by 100, compute by how much the fed must increase the money supply if it wants to avoid the crowding out of expansionary fiscal policy. Make sure to support your answer with the relevant graph.

Answer 1

(A)

Goods market equilbrium condition: Y = C + I + G + NX

Plugging all equations,

Y = 2,000 - 5r + 0.7[Y - 150 - 0.15Y] + 2,000 - 10r + 4,000 - 0.2Y + 1,500 - 0.1Y - 5r

Y = 9,500 - 20r + 0.7(0.85Y - 150) - 0.3Y

Y = 9,500 - 20r + 0.595Y - 105 - 0.3Y

Y = 9,395 - 20r + 0.295Y

0.705Y = 9,395 - 20r

Y = (9,395 - 20r) / 0.705................(IS curve)

Money market equilibrium condition: (M/P)d = Ms/P

0.3Y - 10r = 3,000

Y = (3,000 + 10r) / 0.3...................(LM curve)

Equating IS = LM,

(9,395 - 20r) / 0.705 = (3,000 + 10r) / 0.3

2,818.5 - 6r = 2,115 + 7.05r

13.05r = 703.5

r = 53.91

Y = [3,000 + (10 x 53.91)] / 0.3 = (3,000 + 539.1) / 0.3 = 3,539.1 / 0.3 = 11,797

(A)

After G increases by 100,

From IS curve:

0.705Y = (9,395 - 20r) + 100

0.705Y = 9,495 - 20r

Y = (9,495 - 20r) / 0.705................(New IS curve)

Equating New IS = LM,

(9,495 - 20r) / 0.705 = (3,000 + 10r) / 0.3

2,848.5 - 6r = 2,115 + 7.05r

13.05r = 733.5

r = 56.21

Y = [3,000 + (10 x 56.21)] / 0.3 = (3,000 + 562.1) / 0.3 = 3,562.1 / 0.3 = 11,874

These interest rate and income illustrate crowding out.

Interest rate is unchanged if money supply is higher.

From new IS curve, putting initial value of r,

Y = [9,495 - (20 x 53.91)] / 0.705 = (9,495 - 1,078.2) / 0.705 = 8,416.8 / 0.705 = 11,938.72

This is the increased value of Y, when crowding out effect is zero.

From LM curve:

Ms/P = (0.3 x 11,938.72) - (10 x 53.91) = 3,581.62 - 539.1 = 3,042.52

Increase in money supply = 3,042.52 - 3,000 = 42.52

In following graph, IS0 & LM0 are initial IS & LM curves intersecting at point A with initial interest rate r0 and output Y0. When government spending rises, IS0 shifts right to IS1, intersecting LM0 at point B with higher interest rate r1 and higher output Y0. To keep interest rate same, money supply is increased so that LM0 shifts right to LM1, intersecting IS1 at point C with further higher output Y2 but initial interest rate r0.

X 151 LMO 15. sy B LM А. ro Yo Yo Y2 Y