Suppose that the components of planned spending in an economy are C=500 +0.8(Y-T), I=1500, G=2000, X=0, T=0.25Y, where t is the fraction of income paid in taxes (the tax rate). As we will see in this problem, a tax system of this sort serves as an automatic stabilizer, because taxes collected automatically fall when incomes fall.

a) Find a short-run equilibrium output in this economy.

b) Calculate the multiplier.

c) Explain how reducing the size of the multiplier helps to stabilize the economy, holding constant the typical size of fluctuations in the components of exogenous expenditure.