An investment project will yield £10,000 or £9000 with equal probability. An individual has a certain income of £10,000 and utility function v( y)  ln y. (a) Show that the individual would turn down...

An investment project will yield £10,000 or £9000 with equal probability. An individual has a certain income of £10,000 and utility function v( y)  ln y. (a) Show that the individual would turn down the project. (b) Suppose that it is possible for a syndicate of n individuals (with the same preferences and certain income as the first individual) to undertake the project. How large must n be before they would be willing to accept the project? (c) What is the size of syndicate which maximizes the expected utility of syndicate members if the project is accepted? (d) If there are N individuals in the community (all identical to the first individual) and all individuals count equally in the social welfare function, what is the socially optimal size of the syndicate? (e) If the first individual owned the project and could not sell shares in it but could give away a proportion l of the project, how much would he give away? (f) If he could sell shares, how much of the project would he sell? Is it better to permit the owner to sell shares or to restrict him to giving away part of the project?