Question

Consider a closed economy income-expenditure model of the economy where the country begins in a long-run equilibrium. • Investment (I) and government spending (G) are fixed: I = 41.5, G = 26. • The income tax rate is t = 6.25%, so tax revenue equals T = tY . • The consumption function is C = 12 + 0.8Yd, where Yd = (1 − t)Y . For the calculations below, write your answers as either a fraction or to two decimal places. (a) Write down the aggregate expenditure (AE) function using the above values. What is the value of the AE function’s intercept term? What is the value of the AE function’s slope term? What is equilibrium output? (b) Plot the aggregate expenditure function on a chart, with output (Y ) on the horizontal axis, in increments of 100 from 0 to 600. (c) In equilibrium, what is the level of consumption? What is the level of private saving? (d) What is the value of tax revenue, T? What is the value of government savings (T G)? Is the government running a surplus or deficit? (e) Suppose that the government reduces expenditure by 9.75 to 16.25. Suppose that this results in lower interest rates so that investment increases by 0.375 to 41.875. Following these changes, what is the new equilibrium level of output? (f) At the new level of equilibrium output, what is the new level of tax revenue? What is the new level of government savings? Is the surplus/deficit larger or smaller than it was in question (d)? (g) Simple income-expenditure models keep both the price level and interest rates fixed. In question (e), the interest rate was allowed to change. Discuss how allowing the price level to vary also would have changed output and tax revenue in equilibrium.

Answer 1

a) Equation of the aggregate expenditure AE = C+I+G (NX = 0 for a closed economy)

or, AE = 12 + 0.8Y_d + 41.5 + 26

or, AE = (12+41.5+26) + 0.8(1-0.0625)Y

or, Y = 79.5 + 0.95Y

Hence, intercept term is 79.5 and slope term is 0.95

For equilibrium, AE=Y = 79.5+0.95Y

or, Y(1-0.95) = 79.5

or, Y = 79.5/0.05 = 1,590

b) In the diagram below, we have plotted the aggregate expenditure function:

Here, we have hypothetically drawn the aggregate expenditure AE function. The vertical intercept of the AE curve is 79.5 and its slope is 0.75.

c) Level of consumption C = 12+0.8(1-t)Y = 12+0.8*(1-0.0625)*1590 = 12+1192.5 = 1,204.5

Level of private saving = Y-T-C = 1,590 - (0.0625*1590) - 1,204.5 = 286.125

d) Tax revenue T = tY = 0.0625*1590 = 99.375

Government savings or public savings = T-G = 99.375 - 26 = 73.375

Thus, government is running a surplus.

e) If government expenditure decreases to 16.25 and investment increases to 41.875,

Aggregate expenditure Y = C+I+G

or, Y = 12+0.8(1-t)Y + I+G

or, Y = 12+0.8(1-0.0625)Y + 41.875+16.25

or, Y = (12+41.875+16.25) + 0.8*0.9375*Y

or, Y = 70.125 + 0.75Y

or, 0.25Y = 70.125

or, Y = 280.5

f) At the new output level, tax revenue T = tY = 0.0625*280.5 =17.53125

At the new output level, government savings = T-G = 17.53125 - 16.25 = 1.28125

Thus, the government savings have decreased.