Model

There are two types of agents: employed and unemployed. Since the model is closed, the fraction of the employed is k / n, where k is the number of employed, and n is the fixed total number of agents.

Each of the n - k unemployed persons independently encounters a produc­tion opportunity that appears at the rate of a At in a small time interval At.If the opportunity is accepted, it yields the unit output and at the cost c, which is a nonnegative random number with a known distribution function G. There is a reservation or threshold cost c*(k), to be determined endogenously later, above which the opportunity is rejected as being too costly When the opportu­nity is accepted, the person's status changes from being unemployed to being employed. Each of k employed persons independently encounters a trading op­portunity at the rate b(k/n) per unit time. When an employed person encounters a trading opportunity, he forms a pair with another randomly selected employed person, the pair trade, each of the pair consumes the output of the partner to receive instantaneous utility v, and their status changes from being employed to being unemployed. See Diamond (1982) for some explanations for these assumptions.

9.2