Part 1Greg's Grooming hires workers to groom dogs.The market for dog grooming is perfectly competitive, and the price of a grooming is $10.0010.00. The labor market is competitive, and the wage rate is $9090 a day.The table shows part of the workers' total product schedule.To maximize profit, how many workers does Greg's hire and how many groomings does Greg's produce? Part 1Greg's will hire [input]enter your response here workers to maximize profit. Part 1[table]
Workers | Groomings per day 3 | 2121 4 | 3636 5 | 4848 6 | 5757 7 | 6363
[/table]

Question

Part 1Greg's Grooming hires workers to groom dogs.The market for dog grooming is perfectly​ competitive, and the price of a grooming is ​$10.0010.00. The labor market is​ competitive, and the wage rate is ​$9090 a day.The table shows part of the​ workers' total product schedule.To maximize​ profit, how many workers does Greg's hire and how many groomings does Greg's ​produce? Part 1Greg's will hire [input]enter your response here workers to maximize profit. Part 1[table]
Workers | Groomings per day 3 | 2121 4 | 3636 5 | 4848 6 | 5757 7 | 6363
[/table]

BlackTom AI · Accepted Answer

We start by restating the scenario and the data provided. Greg's Grooming operates in a perfectly competitive market, with price per grooming at $10.00 and wage rate at $9.00 per day. The partial table shows workers and corresponding groomings per day:
- 3 workers → 21 groomings/day
- 4 workers → 36 groomings/day
- 5 workers → 48 groomings/day
- 6 workers → 57 groomings/day
- 7 workers → 63 groomings/day

To determine the profit-maximizing number of workers, we compare the marginal revenue product (MRP) of each additional worker to the wage. In a competitive market, MRP = marginal product (additional groomings) × price per grooming.

Compute the incremental output (marginal product) for each step:
- From 3 to 4 workers: 36 − 21 = 15 additional groomings
- From 4 to 5 workers: 48 − 36 = 12 additional groomings
- From 5 to 6 workers: 57 − 48 = 9 additional groomings
- From 6 to 7 workers: 63 − 57 = 6 additional groomings

Now convert these into MRP by multiplying by the price $10:
- MRP of the 4th worker (additional 15 groomings): 15 × $10 = $150
- MRP of the 5th worker (additional 12): 12 × $10 = $120
- MRP of the 6th worker (additional 9): 9 × $10 = $90
- MRP of the 7th worker (additional 6): 6 × $10 = $60

Compare each MRP to the wage of $90:
- 4th worker: $150 > $90, hire
- 5th worker: $120 > $90, hire
- 6th worker: $90 = $90, hire (ties are typically included in profit-maximization, depending on convention; hiring the worker does not reduce profit here)
- 7th worker: $60 < $90, do not hire

Thus, the profit-maximizing hiring level is 6 workers. The corresponding daily groomings produced at 6 workers is 57 groomings per day, as shown in the table.

Therefore, the blanks should be filled with: 6 workers and 57 groomings per day.

Homework:ch18_homework

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