New Year's Countdown Day 9: Ninth Worker

Quantitative Finance Level 2

Brilliant Problem Writing is a firm that sells a consumer product called problems . Each problem it produces sells on the market for $5, regardless of quantity produced.

Suppose that Brilliant Problem Writing is looking to hire more workers over the short run in order to boost production and profits. Each worker that the firm hires is paid an hourly wage of $11, regardless of the number of workers. Currently, the firm has eight workers working eight hours a day, and the daily production quantity is 64 problems. If the firm were to hire an additional worker while retaining the eight hour workday, the daily production quantity will increase to 81 problems.

Should Brilliant Problem Writing hire the ninth worker?

Details and Assumptions:

  • Assume that all the problems Brilliant Problem Writing produces will be sold at the market price.
  • Assume that only the quantity of workers affects production quantities.
This problem is part of the set New Year's Countdown 2017 .
No Not enough information Yes

Steven Yuan by Steven Yuan , 20, USA

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1 solution

Steven Yuan
Dec 9, 2017

Since the goal of Brilliant Problem Writing is to maximize profits, it will hire the extra worker iff marginal revenue product (the additional revenue from hiring the worker) is greater than or equal to marginal resource cost (the additional cost of hiring the worker). The MRC per day is simply the hourly wage times the number of working hours, which is $ 11 × 8 = $ 88. \$11 \times 8 = \$88. Because the market price of each problem does not change, the MRP per day is equal to the price times marginal product, which is $ 5 × ( 81 − 64 ) = $ 5 × 17 = $ 85. \$5 \times (81 - 64) = \$5 \times 17 = \$85. Since, $ 88 > $ 85 , \$88 > \$85, we conclude that no , Brilliant Problem Writing should not hire the ninth worker, because the MRC exceeds the MRP.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Why does the 9th worker produce 17 problems the the current workers are only producing 8 per worker. There needs to be more information

John Howey - 3 years, 6 months ago

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It's possible that the addition of the ninth worker boosts productivity among all the other workers (e.g. division of labor), so the per worker efficiency rate increases. Besides, we are only interested in the additional costs and benefits from hiring the worker, which in this case do not justify the hire.

Steven Yuan - 3 years, 6 months ago

The current revenue is 64 x 5 is $ 320 and the labour costs are 8 x 11 x 8 is 704. That means a daily loss of $ 384. An additional worker would lead to a revenue of 81 x 5 is $ 405 and the labour cost would be 9 x 11 x 8 is 792, leaving a loss of $ 387. So the ninth worker would increase the loss by another $ 3. Hiring the 9th worker would increase the loss so no, not a good idea.

Fokko Veenstra - 3 years, 5 months ago

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Yeah, I didn't think through the pre-existing revenue and costs while making this problem, the numbers just happened to work out well...

Steven Yuan - 3 years, 5 months ago

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From my point of view, yes.9th worker should be hired. Because, when labour costs is $704, and total sale is $320.So, ratio of labour costs to total sales is 2.2. But by hiring ninth worker, ratio of labour costs to total sales is reduced to 1.9555555. [ $ 792 $ 405 ] \left[\frac{\$792}{\$405}\right] . In other words, when the total sales are $320, total losses are 120%($384). But when the total sales are $405. total losses are 95.555%($387)

So, from my point of view, the answer to this question is 'Yes'.

Winod DHAMNEKAR - 1 year, 4 months ago

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