how does government intervention (thru tax) affect the efficient allocation of resources?

Answer 1

by altering relative prices

by altering relative incomes

by providing the govt with money to buy things or to subsidise people or (un)economic activities

Answer 2

Under the normal assumptions of welfare economics, (1) all consumers facing the same prices and purchasing goods to maximise utility, (2) all producers facing the same input costs and prices and producing to maximise profits, (3) perfectly competitive markets leading to prices equalling marginal costs, and (4) no externalities: it can be shown that the economic system will produce an efficient allocation of resources in the Pareto sense (no individual can be made better off, without making anyone else better off). In such a system, a tax on production or consumption of any good drives a wedge between price and marginal cost leading to a less efficient allocation of resources.

For example, if a good was taxed, price would exceed marginal cost, and less of the good would be produced than otherwise. For the lost production, consumers' valuation of the output exceeds the cost of production so there is a loss of economic welfare. For taxes on labour (income taxes), workers are induced to substitute leisure for work, yet the value of the work forgone, exceeds the value workers place on the additional leisure taken.

In some cases taxes can improve resource allocation. A Pigouvian tax on an externality is an example.

Government intervention to reduce monopoly power (anti-trust) can improve resource allocation by bring prices closer to marginal costs.