Below are some definitions and examples in different scenarios regarding the Arrow-Debreu Equilibrium, hope that they are helpful. The first question is asked to write down the max function given some variable(s) for i=... and the allocation(s), as well as providing a constraint function and a feasibility equation.

Preferences (1(6) 2 i ,6; log(c:),with ,8 6 (0,1) Endowments 1' i \"9 e ={er} r:o Information: no uncertainty about anything, full information A simple economy - Time is discrete and indexed by :2 0,1,2,... - Two types of individuals 1' 21,2 (continuum of mass 1), that live forever - No firms nor governments - Agents trade a non-storable consumption good every period A competitive Arrow-Debreu equilibrium is a consumption allocation and prices { pis such that: 1 = 0 i= 1,2 1 = 0 Given ( p.) , for i = 1,2, the allocation solves: 1= 0 max EB' log(c,) 1= 0 1=0 s.t. 1=0 1= 0 c' 20. Feasibility: ato sete, Vt = 0,1,2,...OO OO Proposition: Let and be an A-D 1= 0 i=1,2 competitive equilibrium. Then, there exists A, A and a corresponding Sequential Markets equilibrium OO and interest rates such that t+1 ) += 0 i=1,2 The same is true the other way around.Alternative market arrangement: Sequential Markets In A-D equilibrium trade only at I: 0 One period bonds. Let 1; denote the interest rate on a bond contracted in period {1 to deliver return in period t Household 1' budget constraint in period t c: +61!i