Question

For a real Keynesian model of a mixed economy with a marginal propensity to consume equal to .8 and autonomous consumption equals 600 billion, planned investment equals 100 billion, government spending equals 300 billion, and taxes equal 300 billion:

a. Calculate the equilibrium level of Ye or real output.

b. Draw a diagram that illustrates the equilibrium condition for the model, the equilibrium level of output, and the level of autonomous spending. Be sure to carefully label your diagram, including the axes and the slopes of the lines you draw.

c. Troubled by a persistent recession gap of S200b, government authorities decide to cut taxes to close the recession gap.   By how much should they cut taxes to close the recession gap?

d.   Now illustrate the effect of the tax cut you recommended in an intermediate-range IS/LM diagram. Be sure to illustrate the original equilibrium level of output and the full employment level of output and the effect of your recommended tax cut.

e. Further research reveals that the change in taxes that you recommended to increase real output has driven up real interest rates from 2% to 3%. Those higher real interest rates reduced investment by $25b.

Calculate the effect of the decline in investment on Ye (equilibrium level of output after your tax cut) and illustrate your answer in your IS/LM diagram being sure to indicate the full multiplier, investment crowding out, and the net multiplier.

f. Finally, calculate the net multiplier and the size tax cut would be necessary to close the recessionary after taking into account the effect of investment crowding out.

Answer 1

Sol : (a) Equilibrium level of an output or income is the total quantity of goods demanded by the consumers in aggregate.

At, Equilibrium level of output , Y = AD

    And, AD = C + I +G + NX

( where, AD = Aggregate Demand

                C = Consumption

                I = Investment

                G = Government Expenditure

               NX = Net Exports  

                 Y = Income

Y = AD = C + I + G + NX                ............................................(1)

Consumption Function =

           C = Autonomous C + (MPC)Y

             = 600 + (0.8)Y

Putting the value in (1)

Y = AD = 600 + 0.8Y + 300 + 0

0.2Y = 900

Y = 900/0.2

Y = $4500 billion or equilibrium level of output

(b)

Date: Page No: Equiliboium Tevel of output AD=Y=AS ate demand (billion) - AD=ct cY c-ctcy The level 600 of autonomous spending 45 Yo $4500 (Billion) Income, Output Billion)

(c) As, there is a recessionary gap of $200 b and government wants to cut the tax by the following amount as calculated :

in this relationship , we assume that relationship to be constant.

As, we have value of MPC = 0.75 and value of △ Y should be equal to $200 b because we have to raise the AD level by $200b

Multiplier between the Real GDP and taxes is = △ Y / △ Taxes

△ Y/ △ T = -m / (1-m)              m = MPC

200 / △ T = -0.75 / (1 - 0.75)

200 / △ T = -0.75 / 0.25

200 / △ T = -3

-(200/3) = △ T

-$66.67b taxes. So, government should decrease the taxes by $66.67b and Ad becomes equal to the full employment level.

(d)

full employement Y=AS Eg ultibrium PPA AD (full employment Aggregate demand (AD) Actual) Dy tnderemployment equilibrium 145 45 o output 1 Employment

in the above given diagram , Full Employment level is at point P where AD = Y and Actual level of employment (i.e Underemployment due to recession gap of $200b is at point P' )

After , cutting of taxes by the government , AD level should rise by $200b (i.e from point P' of underemployment to point P of Full Employment ) .

So , Effect of taxes is equal to PP'