Lucas and Prescott (1974) propose a model where individuals search for employment. In their model economy there exists a continuum of spatially separated markets, or "islands." Each island is subject to serially correlated productivity shocks that are independent across islands; there is no aggregate uncertainty. At the beginning of a period, a fixed population of infinitely lived workers is distributed in some way across the islands. Shocks are realized on each island, with each island's shocks being common knowledge to workers on every island. Each worker then decides whether to stay where he is, earning a competitively determined local wage, or to migrate to another island of his own choosing. If the chooses to migrate, his earnings for the current period are zero, but he begins the following period on the new island. The fraction of workers in transit can be interpreted as the unemployment rate for the economy. The model determines the stationary equilibrium unemployment rate, the distribution of workers over islands, and the distribution of wages.
Lucas, R. and Prescott, E. (1974) Equilibrium search and unemployment. Journal of Economic theory 7: 188-209.
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