All societies must take decisions on collective resources should be allocated. In democratic societies such decisions are often taken by majority voting, as a matter of fact democracy is often associated with majority voting. However, it has for a long time been known that this way of taking collective decisions is associated with certain problems.

(a) Assume that a small city should decide whether they should build a new public library (x), a new public swimming pool (y), or improving the street lightning along the city's main street (z). Only one of these alternative can be started during the next budget year. The city population can be divided into three equally large groups, the members of each group has the following preference ordering for these alternatives:

1 : x > 3 > z,

2 : y > z > x,

3 : z > x > y.

Show that with majority voting between pairwise alternatives, each alternative can win dependent on the order in which the pairwise voting take place (the winner in the first vote goes on to a second round of voting against the remaining alternative).

(b) The problem that the above example illustrates is that majority voting is vulnerable to manipulation. Assume that the person that decides the voting-order between pairwise alternative, belongs to group

3. Show how this person (the "agenda setter") can determine the voting-order so that he/she can assure that his/her best alternative

(z) wins.

(c) According to the first fundamental theorem of welfare economics, a general equilibrium allocation in a perfectly competitive market economy is Pareto efficient. However, this allocation can be very unequal e.g., one person can get everything and all other nothing. The society's preferences other equality can be summed up in a so called social welfare function. Discuss different forms of such a function and what they imply about the inequality of the final allocation.Discuss also how an allocation, which is optimal according to the social welfare function, can be implemented as a perfectly competitive market equilibrium.

(d) Discuss with the help of a so called Edgeworth box-diagram and a diagram where the consumers' utility possibility sets are illustrated, where a conflict can emerge between efficiency- and equality goals. When can it, even in the most egalitarian societies, be optimal with different distribution of the final utility between citizens.