Question

A5-9. Suppose the following aggregate expenditure model describes the US economy:

C = 1 + (8/9)Yd T = (1/4)Y I = 2 G = 4 X = 3 IM = (1/3)Y

where C is consumption, Yd is disposable income, T is taxes, Y is national income, I is investment, G is government spending, X is exports, and IM is imports, all in trillions $US.

                  

(a) Derive a numerical expression for aggregate expenditure (AE) as a function of Y. Calculate the equilibrium level of national income. Illustrate in a diagram with AE on the vertical and Y on the horizontal axis. [Hint: While solving, do not convert the fractions to decimals.] [6]

                      

(b) Calculate the equilibrium levels of consumption spending and private saving (S) [Hint: Recall that C and S are functions of disposable income.]. Is the government running a surplus or deficit? Does the country have a trade surplus or deficit? [8]

                      

(c) Now imagine that as a result of a world-wide financial crisis, both investment exports decrease by 1 each. What is the new level of national income? Illustrate the effects in your diagram. What is effect on the government’s budget? [Hint: Using the multiplier simplifies the calculations.] [6]

  

(d) The government decides to use an increase in government spending to restore national income to its original level. By how much would it have to increase spending? What happens to the government’s budget balance? Explain why the government’s deficit does not increase by the full amount of the increase in spending. [6]  

Answer 1

We know that the equation for aggregate expenditure is AE = C + I + G + X - IM

C = 1 + (8/9)Yd T = (1/4)Y I = 2 G = 4 X = 3 IM = (1/3)Y

(a) Use the equation to find the equilibrium income

Y = AE

Y =  1 + (8/9)*(Y - (1/4)Y) + 2 + 4 + (3 - (1/3)Y)

Y = 10 + (2/3)Y - (1/3)Y

This gives Y - (1/3)Y = 10

or Y* = 15

The equilibrium level of national income is 15

(b) The equilibrium level of consumption spending is 1 + (8/9)*(15 - (1/4)15) = 11

and private saving (S) = Y - C - T = (15 - 11 - 15/4) = 0.25

The government is running a deficit because G is 4 while taxes are 15/4 = 3.75 so there is a budget deficit of 0.25. Trade surplus/deficit = net exports = (X - IM) = (3 - (1/3)15) = -2. Hence there is a trade deficit.

(c) Now imagine that as a result of a world-wide financial crisis, both investment exports decrease by 1 each.

Y = AE

Y =  1 + (8/9)*(Y - (1/4)Y) + 1 + 4 + (2 - (1/3)Y)

Y = 8 + (2/3)Y - (1/3)Y

This gives Y - (1/3)Y = 8

or Y* = 12

AT this level T is 12/4 = 3 and G is 4 so there is still a budget deficit.

(d) The government decides to use an increase in government spending to restore national income to its original level. This means change in income should be 3. Multiplier is 1/(1 - mpc(1 - t) + mpm) = 1/(1 - 8/9*(1 - 1/4) + 1/3) = 1.5. To raise income by 3, G should increase by 2 so that the multipleir effect is 2*1.5 = 3.

New G is 2 + 4 = 6. Hence there is an increased budget deficit. the government’s deficit does not increase by the full amount of the increase in spending because AS is not horizontal but upward sloping and some increase is absorbed by price level.