Question

3. 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.

1. Assume that Tasty Tuna currently has only one vessel, but can hire alternative numbers of fisherman to help with the catch. Completely explain why it is appropriate to view this scenario as short run production.
2. Using the concepts of the Law of Diminishing Returns and the three Stages of Production in the Short Run, discuss why the following levels of input and output are important:
   • The variable input labor level (L = # fishermen) where the Daily Tuna Marginal Catch per unit of Labor (DQ/DL) is at its maximum. What is this (DQ/DL) amount?
   • The variable input labor level (L = # fishermen) where the Daily Tuna Average Catch per unit of Labor (Q/L) is at its maximum. What is this (Q/L) amount?
   • The variable input labor level (L = # fishermen) where the Daily Total Tuna Catch (Q), is at its maximum. What is this Q amount?
   • The variable input labor level (L = # fishermen) where the Daily Tuna Marginal Catch per unit of Labor (DQ/DL) is negative. What is this (DQ/DL) amount?

3. 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

4. What is the new optimal number of fishermen to hire for maximum Total Profit, under these two alternative Market Price (P) scenarios:

• The Market Price (P) of Tuna falls to $2.75 per pound
• The Market Price (P) of Tuna rises to $5.00 per pound
• Do these alternative levels of optimal hiring occur within Stage 2 of short run production? Should they? Explain.

5. If the demand for tuna caught via pole-and-line were to become popular, and Tasty Tuna would soon need to be catching a minimum of 1,000 pounds per day, why would this new scenario require a long run production function? Explain your reasoning. Why would the questions about the “Expansion Path” and “returns-to-scale” begin to become relevant? Explain your reasoning.

Answer 1

a. By definition, short run is a period of time where some factors of production remain fixed and are flexible (or variable). This is because the fixed factors of production require relatively more investment and have a positive value even at zero level of production. On the contrary, all factors are variable in the long run. Since Tasty Tuna have only one vessel but can hire alternative number of fisherman, it could be rightly viewed as short run production function.

b.  Daily Tuna Marginal Catch per unit of Labor (DQ/DL) is at its maximum at 3 fishermen per vessel.

Daily Tuna Average Catch per unit of Labor (Q/L) is at its maximum at 5 fisherman per vessel.

Daily Total Tuna Catch (Q), is at its maximum at 8 fishermen per vessel.

Daily Tuna Marginal Catch per unit of Labor (DQ/DL) is negative at 9 fisherman per vessel.

c. Total Profit is maximum at 7 fishermen per vessel.

The maximum total profit does occur within the boundaries of stage 2 of production function as it should since it is the economically rational range where every producer would like to produce. This is so because the Total Product is increasing at increasing rate in the first stage so the producer would not want to stop production whereas it is decreasing in the Third Stage, using the same fixed factors but by altering the variable factors.

d. Optimal number of fisherman at P= $2.75 is 6 and at P=$5 is 8. These alternative levels of optimal hiring do occur within Stage 2 of short run production.

e. According to Tasty Tuna's production function, one vessel can only carry up to 9 fishermen and correspondingly catch 710 pounds per day. To catch a minimum of 1000 pounds per day, they would have to increase their number of vessels. Since number of vessels are a fixed factor in the short run, this scenario would enter the long run production function where all fixed factors turn variable and can be increased. Long run production function is explained by the concepts of expansion paths and returns to scale.