Consider the same representative agent economy described in Exercise 4.11, but with the expected utility function

\[u\left(x_{0}, x_{1}, x_{2}\right)=x_{0}^{\gamma}+\frac{1}{2} x_{1}^{\gamma}+\frac{1}{2} x_{2}^{\gamma}\]

with \(0)\) of the two Arrow securities as well as the return \(r_{f}\) of the risk free asset with constant payoff 1 .

Data From Exercise 4.11

Transcribed Image Text:

Exercise 4.11 Consider an economy with two possible states of the world, with associated probabilities of occurrence (1/2, 1/2), and a representative agent with expected logarithmic utility function of the form 1 1 u(x0,x1, x2) = log(x0) + log(x1) + = log(x2). In the economy it is possible to trade the two Arrow securities and a risk free asset with constant unitary payoff. Determine the equilibrium prices (91,9%) of the two Arrow securities and the return rf of the risk free asset in the representative agent economy when the aggregate endowment is given by (eo, e1, e2) = (1, 3, 1).