Part 1Stan's Studio hires workers to take photo portraits.The market for photo portraits is perfectly competitive, and the price is $1010 a portrait. The labor market is competitive, and the wage rate is $120120 a day.The table shows part of the workers' total product schedule.Calculate the marginal product of hiring the fourth worker and the value of marginal product of the fourth worker. Part 1The marginal product of hiring the fourth worker is [input]enter your response here portraits a day. Part 1[table]
Workers | Portraits per day 3 | 2525 4 | 4040 5 | 5252 6 | 6161 7 | 6767
[/table]

Question

Part 1Stan's Studio hires workers to take photo portraits.The market for photo portraits is perfectly​ competitive, and the price is ​$1010 a portrait. The labor market is​ competitive, and the wage rate is ​$120120 a day.The table shows part of the​ workers' total product schedule.Calculate the marginal product of hiring the fourth worker and the value of marginal product of the fourth worker. Part 1The marginal product of hiring the fourth worker is [input]enter your response here portraits a day. Part 1[table]
Workers | Portraits per day 3 | 2525 4 | 4040 5 | 5252 6 | 6161 7 | 6767
[/table]

BlackTom AI · Accepted Answer

First, I restate the problem to ensure clarity: the question asks for the marginal product of hiring the fourth worker and the value of marginal product (VMPL) of the fourth worker, given the table of portraits produced per day by number of workers, and a market price of 1010 dollars per portrait. The table provides output as follows (interpreting the pattern):
- 3 workers produce 25 portraits/day
- 4 workers produce 40 portraits/day
- 5 workers produce 52 portraits/day
- 6 workers produce 61 portraits/day
- 7 workers produce 67 portraits/day

Now, step by step, determine the marginal product of the fourth worker. The marginal product of hiring the fourth worker is the change in total output when moving from 3 workers to 4 workers:
- Total output with 3 workers = 25 portraits/day
- Total output with 4 workers = 40 portraits/day
- MP4 = 40 − 25 = 15 portraits/day
Thus, the marginal product of the fourth worker is 15 portraits per day.

Next, compute the value of the marginal product (VMPL) of the fourth worker. VMPL is the additional revenue generated by the marginal product, computed as price per portrait times the marginal product:
- Price per portrait = $1010
- MP4 = 15 portraits/day
- VMPL4 = 1010 × 15 = 15,150 dollars per day

Consider potential misunderstandings:
- If someone thinks MP4 is 25 or 40, they might confuse total output with incremental gain; remember MP is the incremental change when adding one more worker, not the total output.
- If one uses the price times total output instead of MP, they would incorrectly overestimate the employer’s additional revenue from hiring just one more worker; VMPL should reflect only the incremental output, not the entire daily production.
- The units matter: MP4 is in portraits per day, while VMPL is in dollars per day. Keeping the units straight prevents arithmetic mistakes.

To summarize, the marginal product of the fourth worker is 15 portraits per day, and the value of the marginal product of the fourth worker is $15,150 per day.

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