Question

Suppose that I = 100, G = 75 and T = 100. There was a fall in autonomous level of consumption because of which the consumption function changed from C = 20 + 0.6YD to C’ = 10 + 0.6YD.

a) Calculate the equilibrium level of incomes associated with C and C’? Show your work. Does this change match up to what you calculated using the multiplier?

b) Calculate the equilibrium level of incomes associated with C and C’? But, this time use S + T = I + G condition. Show your work. Do you obtain the same conclusions as you did in part (a)?

c) What was C and what was S at the two equilibrium income levels?

d) Suppose the income associated with C was the full employment level of output and now you are at an output level associated with C’. By how much should G change to reach the full employment level? By how much should T change to reach the full employment level?

e) If the government wants to balance budget and at the same time reach the full employment level of output, what should it do?

Answer 1

a)

At C = 20+0.6Yd

Y = C + I + G

Putting the values we get

Y = 20+0.6Yd + 100 + 75

Y = 20+0.6(Y-T) + 175

Y = 20 + 0.6(Y-100) + 175

Y = 20 + 0.6Y - 60 + 175

0.4Y = 135

Y = 337.5

When C =10+0.6Yd

Putting the values we get

Y = 10+0.6Yd + 100 + 75

Y = 10+0.6(Y-T) + 175

Y = 10 + 0.6(Y-100) + 175

Y = 10 + 0.6Y - 60 + 175

0.4Y = 125

Y = 312.5

Change in Y = 312.5 - 337.5 = -25

The value of multiplier = 1/1-MPC = 1/1-0.6 = 2.5

Change in consumption = C' - C = 10+0.6Yd - 20-0.6Yd = -10

Hence change in Y = -10*2.5 = -25.

hence we get the same answer.

c)

C + S = Yd
At C = 20+0.6Yd

20+0.6Yd + S = Yd

S = -20 + 0.4Yd

Now

S + T = I + G

-20 + 0.4Yd + 100 = 100 + 75

0.4(Y-T) + 80 = 175

0.4(Y-100) = 95

0.4Y - 40 = 95

0.4Y = 135

Y = 337.5

At C = 10+0.6Yd

10+0.6Yd + S = Yd

S = -10 + 0.4Yd

Now

S + T = I + G

-10 + 0.4Yd + 100 = 100 + 75

0.4(Y-T) + 90 = 175

0.4(Y-100) = 85

0.4Y - 40 = 85

0.4Y = 125

Y = 312.5

Hence we get same conclusion

c)

At Y = 337.5

C = 20+0.6Yd = 20+0.6(Y-T) = 20+0.6(337.5-100) = 20 + 0.6*237.5 = 162.5

S = -20 + 0.4Yd = -20 + 0.4(Y-T) = -20 + 0.4(337.5-100) = -20+0.4*237.5 = 75

At Y = 312.5

C = 10+0.6Yd = 10+0.6(Y-T) = 10+0.6(312.5-100) = 10 + 0.6*212.5 = 137.5

S = -10 + 0.4Yd = -10 + 0.4(Y-T) = -10 + 0.4(312.5-100) = -10+0.4*212.5 = 75

d)

Change in Income has been of 25.

Government expenditure multiplier = 1/1-mpc = 1/1-0.6 = 2.5

Hence change in Y = multiplier*change in government expenditure

25 = 2.5*change in government expenditure

change in government expenditure = 10

Tax multiplier: = -mpc/1-mpc = 0.6/0.4 = -1.5

change in Y = multiplier*change in taxes

25 = -1.5* change in taxes

change in taxes = -16.67

e)

The balanced budget multiplier has the value 1. Hence if government expenditure is increased by 25 and taxes are increased by 25, Y will increase by 25.