Consider an economy with two traded assets and tree possible states of the world, where the dividend matrix \(D\) is given by

\[D=\left[\begin{array}{ll}1 & 0 \\0 & 1 \\0 & 1\end{array}\right]\]

Suppose that there are two agents (i.e., \(I=2\) ), whose utility functions are differentiable, strictly increasing and strictly concave and only depend on consumption at time \(t=1\). The probabilities associated to the three states of the world are given by \((1 / 4,1 / 4,1 / 2)\). The endowment of the first agent is given by one unit of the first asset, while that of the second agent is given by one unit of the second asset. Show that the Pareto optimal allocation is given by the consumption plan \((1 / 4,1 / 4,1 / 4)\) for the first agent and \((3 / 4,3 / 4,3 / 4)\) for the second agent .