Questions: Wage-Setting Equilibrium and Wage Bargaining

Question 1

An economy experiences a surge in job vacancies while the number of unemployed workers stays constant, raising labor market tightness (v/u). According to the wage-setting model, what happens to the equilibrium wage and why?

• A. The wage rises, because workers find new jobs faster (higher outside option) and firms fill vacancies slower (lower outside option) — both effects push wages up.
• B. The wage falls, because more vacancies mean firms are desperate to hire and will accept lower-wage workers.
• C. The wage is unchanged, because the Nash bargaining power β is a fixed parameter that doesn't depend on market conditions.
• D. The wage rises only if workers have bargaining power β > 0.5; otherwise firms capture the extra surplus.

Answer: (A)

Tighter labor markets work on both sides of the table simultaneously. Workers' outside option improves (they find jobs faster), and firms' outside option worsens (they wait longer to fill a vacancy). Both effects increase the negotiated wage. This is the key insight of the wage-setting curve: tightness translates directly into wage pressure, regardless of the fixed bargaining power parameter.

Question 2

In Nash bargaining, the worker's bargaining power β approaches 1. What does the equilibrium wage approach?

• A. The worker's reservation value (unemployment benefit plus value of job search).
• B. The firm's productivity minus its vacancy-posting cost — essentially the maximum the firm can pay.
• C. The average of worker reservation value and firm productivity, unaffected by β.
• D. Zero, because a worker with all the power captures the entire surplus, leaving nothing for a wage.

Answer: (B)

The Nash wage is: w = reservation value + β × (total surplus). As β → 1, the worker captures the entire surplus, so the wage approaches the firm's maximum willingness to pay: productivity minus hiring costs. When β → 0, the wage collapses to the reservation value. This is the surplus-splitting logic at the heart of the model.

Question 3

An increase in unemployment benefits raises the equilibrium wage even if the worker's bargaining power β is unchanged.

• T. True
• F. False

Answer: True

Higher unemployment benefits raise the worker's outside option (the value of staying unemployed and searching). In the Nash wage formula, the wage equals the reservation value plus β times the surplus. A higher reservation value directly raises the wage, even with the same β. This is why policies affecting the outside option of workers — benefits, minimum wages, housing mobility — have wage effects in search-and-matching models.

Question 4

In the wage-setting model, higher labor market tightness lowers the equilibrium wage because firms can fill vacancies more easily.

• T. True
• F. False

Answer: False

This reverses the direction. Higher tightness means MORE vacancies relative to unemployed workers, so firms find it HARDER to fill positions — their outside option worsens. At the same time, workers find jobs faster — their outside option improves. Both effects push wages UP, not down. The wage-setting curve has a positive slope in tightness.

Question 5

Why does a rise in labor market tightness (v/u) push wages up from both sides of the bargaining table simultaneously? Explain using the concept of outside options.

Model answer: Higher tightness means more vacancies per unemployed worker. For workers, this shortens expected unemployment duration — their outside option (the value of continued search) improves. For firms, more vacancies per applicant means longer expected vacancy duration — their outside option (waiting for another candidate) worsens. Since both sides' threat points move in the same direction, the negotiated wage rises. Neither side alone drives the increase; it is a simultaneous tightening of constraints from both parties.

The key is that tightness is a market-wide variable affecting both sides' fallback positions at once. This is why search-and-matching models generate a wage-setting curve with a positive slope — not because bargaining power changes, but because the outside options that anchor the bargaining range shift together.