Question

The Tasty Tuna Fishing Company decided to abandon gill-netting technology because of its adverse environmental side-effects. Tasty Tuna’s management decided to utilize a more traditional pole-and-line fishing method. They utilize a fishing vessel that can accommodate multiple fishermen per day. The managers were unsure of the optimal size of the crew who would man the vessel and catch the tuna. Tasty Tuna’s managers experimented with different size crews on the vessel. They generated the following short-run production relationship between the number of fishermen per vessel, and the daily catch of tuna (in total pounds):

# Fishermen per vessel

# Lbs. / Day Tuna Catch

Tasty Tuna’s Short-Run Production Function

0	0
1	50
2	110
3	300
4	450
5	590
6	665
7	700
8	725
9	710

Based on Tasty Tuna’s production function above, please answer the questions below. Please also consult the companion MS-Excel Spreadsheet file. The spreadsheet file provides some calculations that will assist you to properly respond to the questions posed in this problem.

The daily wage rate for a fisherman is $100/day → this is the Marginal Factor Cost (DTC/DL). A multi-billionaire environmentalist, who was happy to see gill-netting go away, gave Tasty Tuna their vessel at no cost, causing Total Fixed Cost to be Zero. As a result, Total Cost (TC) simply equals Total Variable Cost (Daily Wage x #Fishermen). With these cost conditions identified, if the Market Price (P) of Tuna is $3.50 per pound, then what is the optimal number of fishermen to hire for maximum Total Profit? Does this maximum total profit occur within the boundaries of Stage 2 of short run production? Should it? Explain

Answer 1

Use the following formulae to calculate the marginal product of labor and marginal revenue product of labor: MPL TPn TPn 1 wwwwwwy wwwww MRPL MPL*Price From the given information, it is clear that the wage rate equals to marginal factor cost Calculation:

A В C D E F Lbs./ Day Tuna Fishermen per Price MRPL Catch MFC W MPL 1 vessel 0 3.5 20 100 D3 E3 50 3.5 3.5 |ЕB3-B2 - B4-B3 3 1 100 110 -D4"E4 100 4 2 -D5*E5 -D6 *E6 =D7 E7 -D8 E8 D9 E9 -D10 E10 -D11 *E11 300 3.5 - B5-B4 5 3 100 - 86-B5 450 100 3.5 6 4 590 100 3.5 - 87- B6 -B8-B7 7 5 665 3.5 8 6 100 700 3.5 - B9-B8 9 7 100 -B10-B9 - B11 - B10 725 3.5 10 8 100 11 9 710 3.5 100 Result

A В E Fishermen per Lbs./ Day Tuna Catch MFC W Price 100 100 100 100 1 vessel MPL MRPL 0 2 0 3.5 50 110 300 50 60 175 3 3.5 1 210 3.5 2 190 3.5 665 3.5 525 6 4 450 100 150 100 100 100 490 7 5 590 3.5 140 665 700 725 262.5 122.5 3.5 8 6 75 3.5 3.5 35 25 10 8 100 87.5 710 100 3.5 -15 -52.5 11 According to labor market equilibrium, a firm will get maximum profits by employing the labor where marginal factor cost equals to marginal revenue product Thus, from the above calculations, it is clear that the firm is getting maximum profits by employing 7 fishermen per vessel at the output of 700where marginal factor cost nearly equals to marginal revenue product of labor Thus, the firm will hire more labors when the marginal revenue product of labor is greater than marginal factor cost CO

According to the above calculations, it is clear that the firm in the second stage of production, because the total product is at maximum and marginal product is decreasing, but it is positive