The Reservation Wage Curve Equation (Utility-Based)

A firm has ranked its potential employees in ascending order based on the minimum wage each would accept. The term α_N represents the value (or utility) of being unemployed for the Nth individual in this ranking. To hire exactly N workers, the firm must offer a single wage to all of them. How does the value of α_N directly influence the minimum wage the firm must set?

Hiring Decision at a Startup

Determining the Minimum Hiring Wage

A firm has ranked its potential employees in ascending order of their utility from being unemployed (α_1 < α_2 < ... < α_N < ...). If the firm sets a single wage for all employees that provides a utility level exactly equal to α_N, it will successfully hire all workers from 1 to N, and no workers with an index greater than N.

A firm has ranked four potential employees (1, 2, 3, 4) by their ascending utility from being unemployed (α). The values are α₁=10, α₂=15, α₃=22, and α₄=30. The utility a worker gets from a wage (W) is simply equal to the wage amount (U(W) = W). Match each wage the firm could offer to the total number of employees who would accept the job.

The Role of the Marginal Worker's Utility in Wage Setting

A company ranks potential employees by their ascending reservation wages. To determine the single wage necessary to hire exactly 15 employees, the company must focus on the unemployment utility of the ________ potential worker in the ranking.

A company wishes to hire 50 new employees and has ranked 100 potential candidates in ascending order of their utility from being unemployed (α₁ < α₂ < ... < α₁₀₀). To hire the first 50 candidates, the wage offered must provide a utility level at least equal to α₅₀. A manager suggests that to save costs, the company should instead offer a wage that provides a utility level equal to the average unemployment utility of the first 50 candidates. Why is this suggestion fundamentally flawed for achieving the goal of hiring 50 employees?

A firm wants to hire a specific number of employees and has a list of all potential candidates and the value each candidate places on being unemployed. Arrange the following steps in the logical order the firm must follow to determine the single wage it needs to offer to achieve its hiring goal.

A company ranks its potential employees in ascending order of their unemployment utility (α). It sets a single wage for all hires, calculated to provide a utility level just sufficient to attract the 50th person on the list (α₅₀), with the goal of hiring exactly 50 people. After making the offers, the company discovers that the 20th person on the list (α₂₀) actually had a much higher unemployment utility than initially recorded, a value greater than α₅₀. Assuming all other α values were correct, what is the most likely outcome?