(a) If the government raises taxes on labour income and interest income, explain how potential GDP and economic growth are…

(a) Taxes on labour and interest income. Potential GDP is the output the economy can sustain with full use of labour and capital at existing technology. A tax on labour income lowers the after-tax wage. The substitution effect (leisure becomes cheaper) reduces labour supply and the income effect may raise it, so the net effect is ambiguous; it is usually negative for the participation and hours of secondary earners and it discourages skill formation, so effective labour input and potential output fall. A tax on interest income lowers the after-tax return to saving, so saving and capital formation fall. In the Solow model this lowers the steady-state capital stock and output, a level effect with only a temporary fall in the growth rate along the transition path; in endogenous-growth models, where investment or human capital drives growth, it can lower the long-run growth rate. Dynamic analysis (Chamley–Judd) finds a capital income tax costly in the long run because it taxes future consumption more heavily than present consumption. The deadweight loss rises roughly with the square of the tax rate, and at very high rates the base may shrink so that revenue falls (Laffer). If the revenue funds productive public investment, part of the loss is offset.

(b) Private provision at a lower price. Assume the same service is supplied and the government saves the difference, so government expenditure G falls by ΔG and the saving is not passed on to private demand; aggregate demand shifts left. (i) Fixed wages: money wages cannot fall, so the price level adjusts little and the real wage stays high; output falls by the multiplier times ΔG, ΔY = ΔG/[1 − c(1 − t)], and employment falls, creating unemployment. Part of this is offset only if consumers who earlier bought the service privately gain disposable income and spend it. (ii) Flexible wages: the excess supply of labour pushes money wages and prices down, real balances M/P rise, the interest rate falls and private investment and consumption rise (the Keynes and Pigou effects), until output returns to the full-employment level Y*. The price level is lower and the composition of spending shifts from public to private, so there is only a price adjustment and no lasting output loss. The efficiency gain of a cheaper provider is thus realised fully only with flexible wages or when the saving is recycled into demand.

(c)(i) Buchanan's criticism of Arrow. Arrow's theorem says that, with unrestricted domain, the Pareto principle, independence of irrelevant alternatives and a complete, transitive social ordering, the only rule is dictatorship. Buchanan (1954) argued that this treats society as an organic entity with its own preferences, whereas only individuals choose; a collective decision is the outcome of a procedure, which need not be a consistent ordering. The demand for "overall consistency" (transitivity of social preference) is therefore unwarranted, and cycles under majority rule (Condorcet) are not a defect, since the procedure only has to produce a decision. He favoured constitutional rules, such as near-unanimity (Wicksell), instead of searching for a social ordering.

(c)(ii) Sen's response. Sen (with Gibbard) tested Arrow's result after dropping full transitivity. With only quasi-transitivity (strict preference transitive, indifference not), the rules that satisfy the remaining Arrow conditions give power to an oligarchy: a group that is collectively decisive, and each member of which has a veto. With only acyclicity, which guarantees a best element in every finite set and so a workable choice, the rules yield a veto group (a collegium). The dictator is gone, but concentration of power remains. So even if overall consistency is relaxed as Buchanan wished, the difficulty persists in weaker form; Sen's later liberal-paradox result shows that minimal liberty with the Pareto principle can generate cycles.