Part 1Kaiser's Ice Cream Parlor hires workers to produce milk shakes.The market for milk shakes is perfectly competitive, and the price of a milk shake is $4.004.00. The labor market is competitive, and the wage rate is $40.0040.00 a day.The table shows the workers' total product schedule.If the price rises to $5.005.00 a milk shake, how many workers will Kaiser's Ice Cream Parlor hire? Part 1Kaiser's will hire [input]enter your response here workers. Part 1[table]
Number of workers | Quantity produced(milk shakes per day) 2 | 2727 3 | 3939 4 | 4949 5 | 5757 6 | 6161
[/table]

Question

Part 1Kaiser's Ice Cream Parlor hires workers to produce milk shakes.The market for milk shakes is perfectly​ competitive, and the price of a milk shake is ​$4.004.00. The labor market is​ competitive, and the wage rate is ​$40.0040.00 a day.The table shows the​ workers' total product schedule.If the price rises to ​$5.005.00 a milk shake​, how many workers will Kaiser's Ice Cream Parlor ​hire? Part 1Kaiser's will hire [input]enter your response here workers. Part 1[table]
Number of workers | Quantity produced​(milk shakes per​ day) 2 | 2727 3 | 3939 4 | 4949 5 | 5757 6 | 6161
[/table]

BlackTom AI · Accepted Answer

We start by restating the scenario: Kaiser's Ice Cream Parlor operates in a perfectly competitive market with the price of a milk shake at $5.00 and a wage rate of $40.00 per day. The table provides the total output (milk shakes per day) corresponding to different numbers of workers. The firm decides how many workers to hire by comparing the value of the marginal product of labor (VMP) to the wage.

First, we extract the marginal product of labor (MP) from the total product table. MP is the additional milk shakes produced when one more worker is added, i.e., MP for going from n to n+1 workers equals Q(n+1) − Q(n).
- From 2 workers (27) to 3 workers (39): MP = 39 − 27 = 12 milk shakes/day.
- From 3 workers (39) to 4 workers (49): MP = 49 − 39 = 10.
- From 4 workers (49) to 5 workers (57): MP = 57 − 49 = 8.
- From 5 workers (57) to 6 workers (61): MP = 61 − 57 = 4.
Thus the sequence of MP values for the additional workers is 12, 10, 8, and 4 milk shakes per day, corresponding to hiring the 3rd, 4th, 5th, and 6th workers, respectively.

Next, we compute the value of the marginal product (VMP) for each additional worker at the new price of $5. VMP = P × MP, where P is the price per milk shake ($5.00).
- For the 3rd worker (MP = 12): VMP = 5 × 12 = 60.
- For the 4th worker (MP = 10): VMP = 5 × 10 = 50.
- For the 5th worker (MP = 8): VMP = 5 × 8 = 40.
- For the 6th worker (MP = 4): VMP = 5 × 4 = 20.

The wage rate is given as $40 per day. A firm hires workers as long as the VMP of the next worker is at least as high as the wage; it stops hiring when the VMP falls below the wage. Comparing VMP to the wage:
- 3rd worker: VMP = 60 ≥ 40, so hiring is profitable at this point.
- 4th worker: VMP = 50 ≥ 40, still profitable to hire.
- 5th worker: VMP = 40 = 40, break-even; hiring the 5th keeps the firm at least as well off as not hiring.
- 6th worker: VMP = 20 < 40, not profitable to hire.

Therefore, the optimal number of workers is the number after which adding another worker would yield a VMP below the wage. Since hiring up to 5 workers gives a VMP equal to the wage for the 5th worker and the next (6th) would yield a VMP less than the wage, the firm should hire five workers and not hire the sixth.

In summary, the decision hinges on calculating MP from the total product data, converting MP to VMP using the market price, and comparing VMP to the wage to determine the hire level. The jump in price from $4.00 to $5.00 raises the VMPs enough to make hiring up to the fifth worker profitable, but not the sixth.

Homework:ch18_homework

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