Consider a money search model. Time is discrete and infinite. There is a continuum of infinitely-lived agents with unit mass. Assume there are N types of agents and N goods, where type n agents consume good n but produce good n +1 modulo N i.e., type N agents produce good N +1 = 1). The fraction of type n is 1/N for n = 1, 2, ...N. Agents meet bilaterally in each period with probability 1. Each agent has preferences given by E EG-) u(a), 0 1+r/ where r > 0, C is consumption and u() is a strictly increasing function. A fraction M of the population is endowed with one unit of fiat money in period 0. Goods and money are indivisible. An agent can store at most one unit of any good (including money) at zero cost. Assume free disposal. Let u" = u(1) and normalize u (0) to 0.

1. Solve for all of the symmetric stationary equilibria.

2. If there are multiple equilibria, can these be Pareto-ranked? Explain.

3. Derive the optimal quantity of money that maximizes the ex-ante expected utility of the agents.

My question: how can I set up for solving this problem?