Chapter 26 Equilibrium Search and Matching . Introduction This chapter presents various equilibrium models of search and matching. We describe (1) Lucas and Prescott’s version of an island model, (2) some matching models in the style of Mortensen, Pissarides, and Diamond, and (3) a search model of money | Chapter 26 Equilibrium Search and Matching . Introduction This chapter presents various equilibrium models of search and matching. We describe 1 Lucas and Prescott s version of an island model 2 some matching models in the style of Mortensen Pissarides and Diamond and 3 a search model of money along the lines of Kiyotaki and Wright. Chapter 5 studied the optimization problem of a single unemployed agent who searched for a job by drawing from an exogenous wage offer distribution. We now turn to a model with a continuum of agents who interact across a large number of spatially separated labor markets. Phelps 1970 introductory chapter describes such an island economy and a formal framework is analyzed by Lucas and Prescott 1974 . The agents on an island can choose to work at the market-clearing wage in their own labor market or seek their fortune by moving to another island and its labor market. In an equilibrium agents tend to move to islands that experience good productivity shocks while an island with bad productivity may see some of its labor force depart. Frictional unemployment arises because moves between labor markets take time. Another approach to model unemployment is the matching framework described by Diamond 1982 Mortensen 1982 and Pissarides 1990 . These models postulate the existence of a matching function that maps measures of unemployment and vacancies into a measure of matches. A match pairs a worker and a firm who then have to bargain about how to share the match surplus that is the value that will be lost if the two parties cannot agree and break the match. In contrast to the island model with price-taking behavior and no externalities the decentralized outcome in the matching framework is in general not efficient. Unless parameter values satisfy a knife-edge restriction there will either be too many or too few vacancies posted in an equilibrium. The efficiency problem is further exacerbated if it is assumed that heterogeneous jobs must be .
