Consider a static (one-period) macroeconomic model. Output Y is produced using labour N and

land T according to the production function Y = aN + bT, where a and b are constants. Firms

hire labour in a perfectly competitive market and pay wage w = @Y=@N = a in equilibrium. Land

is in .xed supply. Non-wage income = Y wN is distributed to a representative household.

Goods C are sold to households and G to the government, so Y = C + G holds in equilibrium.

The real wage w adjusts to equalize labour demand and supply. The representative household

enjoys consumption C and leisure l and has a diminishing marginal rate of substitution MRSl,C

between them. With h hours available, labour supply is N = h l. Wage income is taxed at a

proportional rate tw, so the budget constraint is C = (1 tw)wN + .

Sketch the budget constraint and indifference curves in a diagram and write down an equation

for the representative household's optimal consumption-leisure trade-off.

Suppose the government decides to tax non-wage income at a proportional rate t instead

of taxing wages. The representative household's budget constraint is now C = wN + (1 t).

The government must raise suf.cient revenue to pay for the same expenditure G under both tax

systems, so t = G (and twwN = G under the original tax system). Illustrate how your diagram

changes and .nd whether the household is better or worse off under the new tax system. [Hint:

Argue that the original consumption-leisure choice remains affordable under the new tax system.]