Question

The information below describes the current state of the economy of a country called “Macroland.” Assume that in the short run, prices are fixed, so that the Keynesian model of the economy applies. 

C = 800 + mpc(Y – T) “C” is consumption, and “Y” is real GDP 

T = 1000 “T” is taxes minus transfers 

G = 900 “G” is government purchases 

IP = 600 “IP” is planned investment 

NX = 0 “NX” is net exports  mpc = 0.8 “mpc” = the marginal propensity to consume

a. Calculate the short-run equilibrium level of real GDP.

b. Calculate the income-expenditure multiplier.

Suppose that the economy started out at its potential, so that the short-run equilibrium level of GDP that you found above is equal to potential GDP. Now suppose that businesses suddenly become pessimistic about future consumer demand, and planned investment (IP) falls from 600 to 500. Prices, wages, and interest rates are stuck at their old levels, and the marginal propensity to consume does not change. (Assume that all of these things are true for the rest of the question).

c. Calculate the short-run equilibrium level of GDP now.

d. Calculate the output gap.

e. The government decides to return the economy to potential GDP (Y*) by changing taxes. In what direction should taxes change (up or down), and by how much should they change, to return the economy exactly to Y*?

f. Illustrate what happened in part (e) on a carefully labeled “Keynesian cross” diagram. Label (with numbers) the intercepts, the equations of the PAE lines, the short-run equilibrium levels of output before and after the policy change, and the potential output.

Answer 1

Ans)- Given,

C = 800 +mpc(Y-T)

T = 1000

G= 900

IP =600

NX =0, mpc =0.8

a) Short-run equilibrium attains in the economy where

Aggregate income (GDP) = Aggregate expenditure

Where, Aggregate expenditure = Aggregate demand = C +IP +G +NX

Y = C+IP+G+NX

Put the values of C,IP,G and NX

Y = [800 +mpc(Y-T)] + 600 + 900 +0

Put T =1000 and mpc =0.8

Y = [800 +0.8(Y-1000)] +1500

Y = 800 +0.8Y – 800 +1500

Y-0.8Y = 1500

0.2Y = 1500

Y = 1500/0.2

[Y=7,500]----------------------------short-run equilibrium level of real GDP

b) Income-expenditure multiplier: The Income-expenditure multiplier is defined as the ratio of the change in GDP (ΔY) to the change in autonomous expenditure (a).

The income-expenditure multiplier can be calculated by differentiating standard IS equation w.r.t. autonomous expenditure.

So, we have formula for income-expenditure multiplier-

Where, autonomous consumption (a) = C₀ + IP +G -mpc*T, and C₀ is autonomous consumption (800)

So, put mpc = 0.8

Hence income-expenditure multiplier is 5.

c) Now if Planned investment fall from 600 to 500.

i.e. change in IP = 500-600 =-100

So, the change in autonomous expenditure (da) = change in IP

i.e. da = -100

Now, using income-expenditure multiplier

So,

Put da=-100

Hence the new short-run equilibrium of real GDP will be (Y_New) = Y – dy

Y_New = 7,500 -500 = 7,000

Hence, new Equilibrium GDP will be 7,000.

d) Output Gap:

Output gap = Old real GDP(Y) – New Real GDP(Y_New)

                       = 7,500 – 7,000

                  = 500.