(a) For what values of γ is the utility function well behaved? (i.e. U′ > 0 and U′′ < 0)
(b) Derive an expression for the stochastic discount factor mt+1?
(c)What are the prices q0s1and q0s2 of complex securities s1 and s2 at t = 0?
d) What weights create Arrow-Debreu securities? (hint: What are the weights of the complex
securities that create payoffs (1, 0)′ and (0, 1)′?)
(e) What are the state prices q1 and q2? (hint: State prices are a function of prices from part
c) and the the inverse of the payoff matrix from part d).)
(f) What is the price of a risk free bond qb?
(g) What are the risk neutral probabilities π1RN and π2RN ?
(h) Using the risk neutral probabilities solve for qs1and qs2
(i) Is π2RNgreater than or less than the true probability π2? Why?
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