The Richardson Brothers, Prodigal and Miser, are "almost identical twins".

However, their utility genes were quite different at birth. Miser has been able to

amass and hold a fortune consisting of KES 15 million in cash and a home worth

KES 10 million, while Prodigal owns only a KES 10 million worth of a house

inherited from their father. Prodigal has recently undergone a major change in

priorities and decided to "straighten up and fly right" like his brother. This means

that both now share the same utility for wealth, that is,

() =

Prodigal has learned that all is not great when one decides to squander one's

wealth and that the risk of its loss is one of the unfortunate facts of life. For

Prodigal, this means that there is, say, a 0.5 probability of losing his home to fire

next year. Prodigal has been advised by his brother to buy fire insurance.

a) How much would Prodigal be willing to pay to insure against the prospect of

losing the house to a fire?

b) How much would Miser be willing to pay for the same coverage?

c) (Exercise). Graph Prodigal's and Miser's utility functions and illustrate

graphically your answers to parts (a) and (b).

d) (Exercise). Repeat parts (a), (b) and (c) above assuming that the Richardson's brothers' utility for wealth function is given by () = ,

where = ..