In a world with two states of nature, g and b, occurring with probabilities 0.4 and 0.6 respectively, there is a market for two types of contingent claims.

The first type, pays 1 if and only if state g occurs and is denoted by (1, 0)

The second kind, pays 1 if and only if state b occurs and is denoted by (0, 1)

The market prices of (1, 0) and (0, 1) are 0.3 and 0.5 respectively.

Dave is a risk-averse expected utility maximiser who is initially endowed with equal amounts of the two types of contingent claims.

(i) Derive and graph Daves budget constraint

(ii) Show that, given an actuarially fair line, the point at which Daves indifference curve is tangential to the line must be a certainty point

(iii) Graphically demonstrate that he will decide to sell some of his (0, 1)s in order to buy more (1, 0)s.