Consider an economy with I consumers and L goods, where, for all i, the endowment vector of consumer i is ei , and the utility function of each consumer i is of the form Iui(xi , ) xn), i=1 where xi is the consumption vector of the ith consumer. Assume that ui is increasing with respect to the components of xi.
(a) De?ne a notion of competitive equilibrium.
(b) Is an equilibrium necessarily Pareto optimal? Give an argument.