Problem 5.2 For the above problem, imagine that Tracey is offered insurance at unfair odds by her local insurance broker, Ben. Ben sets a price of pi (greater than 112) per unit of compensation.

(a)

(b)

(c)

(d)

(e)

What is the equation of the unfair odds budget line facing Tracey? Show that anywhere along this line WT is given by [T - C + (1 - p')Y] and WNT is given by (T - p'Y).

Explain the meanings of the terms (1 - p')Y and p'y if Tracey takes out insurance.

Tracey complains that the insurance is far too expensive and that at those odds she would rather gamble, making a payment to Ben of B in return for a payment from him of R in the case where her car was not stolen. Show that if Band R are determined by the unfair odds line found in

(a) above, the terms Band R satisfy B = (1 - p/)R.

In the interests of good customer relations Ben agrees to let Tracey take a gamble. Illustrate Tracey's gamble on a state-space diagram.

Find a formula for Ben's expected profits from accepting Tracey's bet.

Why would Ben be unwise to accept too many deals like the one he made with Tracey?