Consider a finance economy with T = L = 1 and S = J = 3, where the security payoff matrix is given by Z = 2 1 2 2 2 3 0

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Consider a finance economy with T = L = 1 and S = J = 3, where
the security payoff
matrix is given by
Z =
2 1 2
2 2 3
0 3 3
(Recall that rows correspond to states and columns to
securities.)
(a) Are markets complete or incomplete and why?
(b) What are the payoffs of the following two portfolios: a =
(1/3,1/3, 0)^T and a' =
(1/6, 1/3, 0)^T
(c) Is it possible that at an equilibrium the security prices are
given by p = (p1; p2; p3) =
(1; 1; 2)?
(d) Do the three Arrow-Debreu securities and the risk-free asset
(which pays 1 in each
state) lie in the asset span?