Question

2) Consider the following economy with an income-tax rate of 20% as well as fixed (or lump-sum) taxes of 50 and where the level of Government expenditure is fixed in part but also increases during recessions and thus is negatively related to the level of aggregate output. (For example this would be the case when government programs like employment insurance and job-retraining are in higher demand during recessions, when incomes are low, than during booms when incomes are high.) Z = C + I + G C = 250 + 0.70YD I = 200 + 0.1Y T = 50 + tIY, tI = 0.2 G = 200 − 0.15Y

a) What would the equilibrium level of output be in this economy?

b) Is the government running a deficit or a surplus at this equilibrium?

c) What is the value of the aggregate expenditure multiplier for this economy?

d) Everything else equal, what income tax rate (tI) would produce a balanced budget for the government in equilibrium in this economy?

Answer 1

Solution:

a) At equilibrium, Z =Y, or Y = C + I + G

Y = 250+ 0.70YD + 200 + 0.1Y + 200 - 0.15Y

= 650 + 0.70(Y-T) - 0.05Y

= 650 + 0.70(Y-50 - 0.2Y) - 0.05Y

= 650 + 0.56Y - 35 - 0.05Y

Y = 615 +0.51Y

0.49Y = 615

Y = 615/0.49 = $1255.1

b) At equilibrium, T = 50 + 0.2Y = 50 + 0.2*1255.1 = $301.02

And G = 200 - 0.15Y = 200- 0.15*1255.1 = $11.73

Since tax revenue is more than government expenditure, the government is running a surplus of 301.02-11.73 = $289.29.

c) The value of aggregate expenditure multiplier = 1/0.49 = 2.04

d) For balanced budget, T = G

50+tl*1255.1 = 200 - 0.15*1255.1

tI = (11.73 - 50)/1255.1 which is negative. Hence even at zero tax rate the budget will be surplus budget. It will not balance.