State whether the following statements are true or false. Explain your way of thinking.

The ecient quantity of a public good is provided if the marginal cost equals the sum of consumers marginal willingness to pay. This rule will be satisfied by the majority voting about the level of government services.

Multi-peaked preferences is an indication of individuals irrational preferences and hence always lead to intransitive social preferences.

An increase in government spending over time may be justified with increased income of the median voter in time, if the income elasticity of demand for public goods is less than unity.

A utilitarian social welfare function will favour income redistribution even if redistribution reduces the total available income.

Logrolling by allowing voters to register how strongly they feel about various issues always brings about socially desirable outcomes.