Quiz I

1. Suppose the state space is finite and that $O=\R^L_+$. In each case on theprevious slide, determine what conditions on $u$, $\mu$, etc., guarantee the existence of equilibrium in the private ownership economy.
2. Minimax Regret Demand. On each budget set $B(p,y) = \{x:\sum_ssp_s\cdot x(s)≤y\}$, let $v(s,p,y)= \max_{x\in B(p,y)}u(x(s))$. State $s$ regret of act $x$ is then $r(x,s,p,y)$ which is $v(s,p,y)−u(x(s))$. Now define max regret $U(x,p,y) = \max_s r(x,s,p,y)$. Demand on the budget set is: \begin{equation*} d(p,y)= \argmin_{x\in B(p,y)} U(x,p,y). \end{equation*} Interpret this. Under what conditions on $u$ will demand be such that aggregate excess demand satisfies assumptions 1, 2, and 3 for the existence of a competitive equilibrium?