The table provided shows the daily output for a profit-maximizing T-shirt firm that is operating in a perfectly competitive product market and hires labor from a perfectly competitive labor market. If each T-shirt sells for $10 and the equilibrium daily wage is $100, how many workers will the firm hire to maximize profit?

Question

BlackTom AI · Accepted Answer

To determine the profit-maximizing number of workers, we compare the value of the marginal product of labor (VMPL) to the wage. The price per T-shirt is $10, and the equilibrium wage is $100, with the table giving output for each number of workers.

Now evaluate each option:

- Option 2 (two workers): The table shows 44 T-shirts with 2 workers. The marginal product of the second worker is the additional output from going from 1 to 2 workers, which is 44 − 24 = 20 T-shirts. The VMPL for adding the second worker is 20 × $10 = $200. This exceeds the wage of $100, so hiring the second worker increases profit.

- Option 1 (one worker): The first worker adds 24 T-shirts (from 0 to 1). VMPL = 24 × $10 = $240, which is greater than $100, so hiring the first worker is profitable.

- Option 3 (three workers): The third worker adds 60 − 44 = 16 T-shirts. VMPL = 16 × $10 = $160, still above the wage, so hiring the third worker remains profitable.

- Option 5 (five workers): The fifth worker adds 80 − 72 = 8 T-shirts. VMPL = 8 × $10 = $80, which is below the wage of $100, so hiring the fifth worker would reduce profit; you would not hire a fifth worker.

- Option 4 (four workers): The fourth worker adds 72 − 60 = 12 T-shirts. VMPL = 12 × $10 = $120, which is still greater than the wage, meaning hiring the fourth worker continues to increase profit.

Putting it together, you continue hiring workers as long as VMPL ≥ wage. VMPLs for hires 1 through 4 are $240, $200, $160, and $120, all above $100, while the fifth hire would yield VMPL $80 < $100. Hence, the profit-maximizing number of workers is 4.

Note: Each step uses the given output table to compute marginal increases, then multiplies by the unit price to obtain VMPL, and finally compares to the wage to decide whether to hire that additional worker.

AP Economics-Hillebrand AP Microeconomics Sem 1 Exam 2025 - Requires Respondus LockDown Browser

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