### Consumption vector of the ith consumer

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##### Reference no: EM13887980

Consider an economy with consumers and goods, where, for all i, the endowment vector of consumer is e, and the utility function of each consumer is of the form Iui(xi , ) xn), i=1 where xis the consumption vector of the ith consumer. Assume that uis 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.

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