Questions: Search and Matching Models

Question 1

The matching function M(U, V) in the Mortensen-Pissarides model takes as inputs...

• A. Wages and productivity
• B. The number of unemployed workers (U) and the number of job vacancies (V), producing the flow of new matches per unit of time
• C. GDP and the interest rate
• D. Worker education levels and firm sizes

Answer: (B)

The matching function is the core technology of search models — it determines how many new worker-firm matches form per period given the stocks of searching workers and open vacancies. It is typically assumed to be increasing in both arguments (more searchers or more vacancies produce more matches) with constant returns to scale. The ratio V/U (labor market tightness) is a key variable: when tightness is high (many vacancies per unemployed worker), workers find jobs quickly but firms take longer to fill positions.

Question 2

In search and matching models, unemployment exists even when the number of vacancies equals the number of unemployed workers.

• T. True
• F. False

Answer: True

This is a fundamental insight of search theory. Even when U = V, matching takes time due to information frictions, geographic mismatch, skill mismatch, and the stochastic nature of the search process. Not every worker-vacancy pair is a suitable match, and even suitable pairs take time to find each other. The matching function captures this: even with many searchers on both sides, the flow of new matches per period is finite. This 'frictional' unemployment exists at all points on the Beveridge curve and is a permanent feature of any labor market with search frictions.

Question 3

How is the wage determined in the Mortensen-Pissarides model, and why does this differ from the competitive model?

Model answer: Wages are determined by Nash bargaining between the matched worker and firm, splitting the match surplus (the value of the match above each party's outside option). The worker's outside option is the value of unemployment (search income, UI benefits, leisure); the firm's outside option is the value of an unfilled vacancy. The surplus is divided according to bargaining power parameters. This differs from the competitive model where the wage equals MRPL — in search models, bilateral monopoly after matching creates surplus to be divided, and the wage depends on bargaining power, outside options, and labor market tightness.

The Nash bargaining solution splits surplus proportionally to each party's bargaining power. When the labor market is tight (many vacancies, few unemployed), workers' outside options improve (they can find another match quickly if this one fails), shifting bargaining power toward workers and raising wages. When the market is slack, firms' outside options improve, reducing wages. This endogenous wage determination links wages to aggregate labor market conditions and creates a channel through which macroeconomic shocks transmit to wages and employment.