Question

solve the following:

a. In the Keynesian cross model, assume that the consumption function is given by 

C=120+0.8(Y-T). 

Planned investment is 200; government purchases and taxes are both 400. Y, C, I G&T are all in billions. 

i Graph planned expenditure as a function of income. 

ii. What is equilibrium income?

 iii. If government purchases increase to 420, what is the new equilibrium income? What is the multiplier for government purchases? 

iv. What level of government purchases is needed to achieve an income of 2,400? (Taxes remain at 400.) 

v. What level of taxes is needed to achieve an income of 2,400? (Government purchases remain at 400.) 

vi. If you were the economic adviser to the president and the government's goal is to stimulate the economy by increasing GDP by $2,400 billion, which one

will you recommend to achieved this GDP target? Government spending or tax cut? Why?

Answer 1

The Keynesian model is given as:

Consumption function: C = 120 + 0.8(Y-T)

Planned Investment I = 200

Government Purchases = Taxes = 400

1. The aggregate expenditure function can be derived as:

AE = C + I + G

AE = 120 + 0.8(Y-T) + 200 + 400

AE = 120 + 0.8(Y – 400) + 600

AE = 120 + 0.8Y -320 + 600

AE = 400 + 0.8Y

The below figure shows an upward sloping planned expenditure curve as function of income. The X-axis shows the income level and the Y-axis shows the Aggregate expenditure. The intercept of the curve is equal to 400 i.e. the level of aggregate expenditure when income is equal to zero. The slope of the aggregate expenditure curve is equal to 0.8 i.e. the ratio of the change in aggregate expenditure due to change in the income levels.

2. At equilibrium, the aggregate output is equal to the aggregate expenditure:

Y = AE

Y = 400 + 0.8Y

Y – 0.8Y = 400

0.2Y = 400

Y = 400/0.2

Y = 2000     {Equilibrium income}

3. If the government purchases increases to G’ = 420 (all other things being constant) the new aggregate expenditure function would change to:

AE’ = C + I + G’

AE’ = 120 + 0.8(Y-T) + 200 +420

AE’ = 740 + 0.8(Y- 400)

AE’ = 740 + 0.8Y – 320

AE’ = 420 + 0.8Y

At the equilibrium:

Y = AE’

Y = 420 + 0.8Y

Y – 0.8Y = 420

0.2Y = 420

Y = 420/0.2

Y = 2100

Given the marginal propensity to consume (MPC) = 0.8, the government spending multiplier “aG” is:

aG = 1 / 1 – MPC

aG = 1/ 1- 0.8

aG = 1/ 0.2

aG= 5     { Multiplier of government purchases}

4. If income is Y = 2000 then the government purchases required to achieve Y= 2400 be:

Multiplier = aG = ΔY/ΔG = 5

ΔY/ΔG = 5

(2400-2000) / ΔG = 5

400/ ΔG = 5

400/ 5 = ΔG

ΔG = $80 Billion

Hence, the government purchases should be increased to $480 billion in order to achieve an income level of $2400 billion.

5. If income is Y = 2000 then the change in tax required to achieve Y= 2400 be:

Tax Multiplier (Kt) =    -MPC /1-MPC

ΔY/ΔT = -0.8/1-0.8

(2400-2000)/ ΔT = -0.8/0.2

400/ ΔT = - 4

400/4 = - ΔT

ΔT = (-) 100 billion

Thus, the taxes should be reduced by $100 billion i.e. reduced to $300 billion in order to achieve

6. In order to stimulate the economy and achieve an income of $2400 billion, the government can either increase its spending by $80 billion or could reduce taxes by $100 billion.

Taxes are the source of government revenue which it uses for economic development and welfare projects. By increasing the government purchases by $80 billion, the government can save additional $20 billion revenue which it will lose in the form of cutting $100 billion taxes. Since both the policy tools would achieve the same level of income, the government would be betteroff to increase the government spending rather than cutting taxes.