Question

Consider a closed economy (no international trade) under a simple Keynesian model. Assume investment is a constant. Tax is a lump-sum that does not depend on income. If a government increases its expenditure by $1 but at the same time increases the lump-sum tax by $1. Will real output be increased or decreased, and by how much?

Answer 1

Closed economy case

Planned Aggregate Expenditure = PAE = C + I + G

C = C0 + c(Y-T)

Where, C0 = AUtonomous Consumption Expenditure

c = Marginal Propensity to consume

Y = Real Output

T = Lumpsum tax

G = Government Expenditure

I = Investment = I0

Consider, the government increases its expenditure by $1

Change in Real Output = delYg = (1/(1-c))*$1

delYg = 1/(1-c)

Now, consider an increase in the lump-sum tax by $1

Change in Real Output = delYt = (-c/(1-c))*$1

delYt = -c/(1-c)

Thus, the total change in Real Output = delYg + delYt

= 1/(1-c) + (-c/(1-c))

= 1

Thus, the real output would increase by $1