Question

The following equations describe your economy:

Y = C + I + G

C = c(bar) +cYD

YD = Y + TR – TA

I = I(bar)

G = G(bar)

TA = tY

TR = TR(bar) – rY

(NOTE: c(bar), I(bar), TR(bar)= C-Bar, I-bar TR-BAR ---- The bar across the top variables indicates its autonomous)

(Also, ‘t’ is a proportional tax on income, and governs the inverse relationship between transfers and income)

a) Suppose that the government adopts a proposal to impose a tax on transfer payments to its citizens such that TA = t (Y + TR) (note: TR still TR(bar). Using this expression for taxes and the same expression for transfers as given in the model, derive an expression for equilibrium output.

b) Does a tax on transfer payments increase, decrease or leave unchanged the extent of automatic stabilization? Explain!

Answer 1

(a) Expression for equilibrium output

Y = C + I + G

Y = c(bar) + cYD + I(bar) + G(bar)

Y = c(bar) + c(Y + TR(bar) - rY - tY - tTR(bar)) + I(bar) + G(bar)

Y = c(bar) + cY + cTR(bar) - crY - ctY + ctTR(bar) + I(bar) + G(bar)

Y = cY(1-r-t) + c(bar) + cTR(bar) + ctTR(bar) + I(bar) + G(bar)

Y - cY(1-r-t) = c(bar) + cTR(bar) + ctTR(bar) + I(bar) + G(bar)

Y(1-c(1-r-t)) = c(bar) + cTR(bar) + ctTR(bar) + I(bar) + G(bar)

Y = c(bar) + cTR(bar) + ctTR(bar) + I(bar) + G(bar)/ (1-c(1-r-t))

(b) Tax on transfer payment will decrease the extent of automatic stabilization. This is because tax on transfer payments is an extra tax that consumers have to pay. This will reduce their marginal propensity to consume and inturn will reduce their disposable income. Further, it will reduce the impact of multiplier. and hence the extent of automatic stabilization will fall.