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In search-and-matching models, wages emerge from bilateral bargaining over the surplus from a job match. The wage is a weighted average of the worker's reservation value and the firm's productivity minus its hiring cost. Tighter labor markets (higher vacancy-unemployment ratio) increase workers' bargaining power and equilibrium wages.
In search-and-matching models, a job match generates a surplus — the difference between the value of a filled position and what both parties would get if they walked away. The worker's outside option is continued unemployment (collecting benefits, searching for another job). The firm's outside option is an unfilled vacancy (paying posting costs, waiting for another applicant). The wage must fall somewhere between these two outside options, because both sides prefer a deal to no deal. The question is where exactly in that range the wage lands.
The standard approach uses Nash bargaining, which you can think of as splitting a pie. The worker and firm each have a bargaining power parameter — typically denoted β for the worker and (1 − β) for the firm — that determines their share of the match surplus. The resulting wage equation takes the form: wage equals the worker's reservation value plus β times the total surplus. Equivalently, the wage is a weighted average of what the worker could get elsewhere and what the firm can afford to pay. When β is high, workers capture most of the surplus and wages are closer to productivity; when β is low, firms capture most of it and wages hover near the reservation value.
What makes this more than a static bargaining problem is the feedback through labor market tightness — the ratio of vacancies to unemployed workers (v/u). When the market is tight (many vacancies relative to job seekers), unemployed workers find jobs quickly, which raises their outside option. A worker who can credibly walk away and find another match soon has more leverage. Simultaneously, firms find it harder to fill vacancies in a tight market, which lowers their outside option. Both effects push the negotiated wage upward. The wage-setting curve plots this positive relationship: as tightness rises, equilibrium wages rise.
The wage-setting equilibrium emerges where the wage-setting curve intersects the job-creation condition — the requirement that firms find it profitable to post vacancies. Higher wages reduce the profitability of vacancies, so fewer are posted, which reduces tightness. The intersection pins down both the equilibrium wage and the equilibrium level of labor market tightness, and from tightness you can derive the equilibrium unemployment rate. This is why policy changes — like higher unemployment benefits raising the worker's reservation value, or productivity shocks shifting what firms can pay — propagate through the entire system: they shift the wage curve, change tightness, and alter unemployment in equilibrium.