The market has 200 individuals that currently each of whom is an expected utility maximizer with utility of consumption given by ui(xi) = log (xi). There are two states of nature (A and B). The probability of state A is 2/3, and the probability of state B is 1/3. Individuals i = 1, ..., 50, have an endowment of 1 in state A and 4 in state B. Individuals i = 51, ..., 200, have an endowment of 2 in state A and 0 in state B. 1- Define a competitive equilibrium for this economy. 2- Calculate the competitive equilibrium price vector and allocation