Question 2

This question illustrates the workings of automatic stabilisers. Suppose the components of planned spending in an economy are given by:

• C=C₀+c(Y-T)
• I^p =I₀
• G=G₀
• T=tY
• M=mY
• X=X₀
• m=0

wheretis the tax rate andm the marginal propensity to import is zero (i.e.M = 0). In this economy, the tax system acts as an automatic stabiliser, because tax revenues automatically decline when national income falls.

1. Solve for an equation that determines the short-run equilibrium output for this economy.
2. Find the expression for the multiplier, i.e. the amount that output changes when exogenous expenditure changes by one unit.
3. Compare the formula for the multiplier in (ii) with the case when taxes are exogenous. Show that making taxes proportional to income (i.e. endogenous) reduces the size of the multiplier.
4. Explain how reducing the size of the multiplier (or increasing the tax rate t) helps to stabilise the economy.
5. Suppose that c=0.8andt=0.25, calculate the multiplier.