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

Taxes on labour and interest income A tax on labour income lowers the after-tax wage. The substitution effect makes leisure cheaper and tends to reduce labour supply; the income effect, by lowering after-tax income, may induce more work if leisure is normal. The net effect on potential GDP is therefore ambiguous, but if the tax discourages effort, skill formation or participation, it lowers the effective labour input and hence the level of potential output. A tax on interest income lowers the after-tax return to saving, reducing savings and capital accumulation; in a Solow-type model this lowers the steady-state capital stock and output, while in endogenous-growth models it can also lower the long-run growth rate. The Laffer curve is relevant to revenue: if the tax rate is already high, a rise may shrink the tax base and reduce revenue. Deadweight loss, however, generally rises roughly with the square of the tax rate even before the revenue peak. Thus the main effect is a level effect on potential GDP, with a growth-rate effect only where incentives for saving, investment or productivity are persistently distorted.

Private provision at a lower price (i) In a closed economy with fixed nominal wages, a cheaper public service raises the real wage and real income. The lower price level can increase real balances and demand for other goods, an expansionary channel; in India, lower electricity tariffs raise real income, but wage rigidity can blunt employment adjustment. At the same time, if the private agency supplies the service more efficiently, it may need fewer workers; because wages cannot fall, displaced workers may become unemployed, and the higher real wage may reduce firms' labour demand. Distributionally, consumers gain, public-sector workers lose, and private owners earn profits. The net output effect is therefore not automatically contractionary: it depends on whether demand and real-balance gains outweigh employment and real-wage rigidity losses.

(ii) With flexible wages, nominal wages adjust downward in response to lower prices and reduced labour demand. This restores labour-market clearing and prevents persistent unemployment. The fall in prices raises real balances, supporting demand, while lower-cost provision raises efficiency. Output is therefore more likely to improve, though workers share the gain through lower nominal wages; the main effect is reallocation toward a more efficient provider with a lower price level.

Buchanan, Arrow and Sen Arrow’s theorem says that, with unrestricted domain, Pareto, IIA, non-dictatorship and a complete transitive social ordering, no non-dictatorial social welfare function exists. Buchanan’s criticism was that the theorem depends on “overall consistency”: it requires a rational, transitive social ordering, which is unrealistic. He preferred procedural rules, especially Wicksellian unanimity, and argued that if collective choice need not be fully transitive, the impossibility might be avoided.

Sen tested this by weakening consistency while retaining IIA and Pareto. Under the Pareto extension, if everyone prefers x to y, society must prefer x to y; if everyone prefers y to x, society must prefer y to x; non-unanimous cases are not settled and need not be indifference. Sen showed that with only quasi-transitive social preference, Arrow’s result still yields a dictator. With mere acyclicity, the result is an oligarchy or veto structure: a non-empty set of individuals whose preferences constrain the social ranking. Thus Sen did not prove a non-dictatorial rule satisfying Arrow’s conditions; he showed the impossibility survives without full collective rationality, so Buchanan’s criticism does not dissolve the theorem. Sen’s liberal paradox reinforces this: minimal liberty plus Pareto can generate cycles, showing partial orderings or acyclicity may fail rather than provide a clean escape. Overall, public policy trades efficiency against distribution, and social-choice theory shows procedural consistency cannot escape impossibility without strong assumptions.