Consider an economy with two periods (today and tomorrow), two physical goods (? and ?), and two consumers (1 and 2). There is no production in the economy. Consumption takes place tomorrow after all uncertainty is resolved and realized, but choices are made today. There are two equally likely states (1 and 2) tomorrow. Let

(Xis, Vis) be consumer i's consumption bundle of the physical goods x and y when the realized state is s and i's utility function be given as below: Ui (Xis, Vis) = a; In(xis) + (1 -a;)In (Vis) where a, E (0,1) and a, # @2. Both consumers have no endowment today. For tomorrow, in state $ = 1, consumer 1 has (1 - =) units of good x and (1 - z) units of good y, and consumer 2 has & units of good x and & units of good y, in state $ = 2, consumer 1 has & units of good x and & units of good y, and consumer 2 has (1 - 8) units of good x and (1 - z) units of good y, where & E (0,1). Both consumers are expected utility maximizers. For this economy, (i) Define the Arrow-Debreu (Contingent Market) equilibrium. (ii) Determine the Arrow-Debreu equilibrium