Question

Please answer a, b, c, d

1. For the following question, assume that the consumption function is: C = 200+ 0.75(Y – T) The investment function is: I = 200 – 2.51 Government spending is fixed at G = 100 and the government has a balanced budget. The liquidity function is: L(Y,r) = Y – 10r Nominal money supply is 1,000 and the price level is equal to 2. a) Find the planned expenditure function and plot it on the Keynesian Cross diagram. Hint: PE=C+I+G and output is on the horizontal axis and planned expenditure is on the vertical axis. b) If the real interest rate is 10% then what is output? c) Show the effects of an increase in government spending to G' = 200 on your diagram. What is the new level of output? How is this related to the con- sumption function? Hint: I am asking about the government spending multiplier. d) Discuss the relationship between the multiplier and the marginal propensity to consume.

Answer 1

(a)

PE = 200 + 0.75(Y - 100) + 200 - 2.5r + 100 [since balanced budget means T = G = 100]

PE = 500 + 0.75Y - 75 - 2.5r

PE = 425 + 0.75Y - 2.5r

When Y = r = 0, PE = 425 (vertical intercept)

Equilibrium is at point A where 450 line intersects PE0 (with G0 = 100) with output Y0.

PE PE1 525 200 PEO 425 100 Чо .

(b)

When r = 10, setting Y = PE,

Y = 425 + 0.75Y - 2.5r

0.25Y = 425 - 2.5 x 10

0.25Y = 425 - 25 = 400

Y = 1600

(c)

When G = 200, Increase in G = 200 - 100 = 100

PE = (425 + 0.75Y - 2.5r) + 100

Setting Y = PE,

Y = 525 + 0.75Y - 2.5r

0.25Y = 525 - (2.5 x 10)

0.25Y = 525 - 25 = 500

Y = 2000

Multiplier = Change in Y / Change in G = (2000 - 1600) / 100 = 400/100 = 4

Again, using MPC formula, Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.75) = 1/0.25 = 4

New Equilibrium is at point B where 450 line intersects new PE line (PE1) corresponding to higher government spending with G1 = 200 and higher output Y1.

(d)

From formula it is seen that the higher (lower) the MPC, the lower (higher) the value of (1 - MPC) and so, the higher (lower) the multiplier.