11 The Ocean Pacific fleet has just decided to use a poleand

11. The Ocean Pacific fleet has just decided to use a pole-and-line method of fishing instead of gill netting to catch tuna. The latter method involves the use of miles of nets strung out across the ocean and therefore entraps other sea creatures besides tuna (e.g. porpoises, sea turtles). Concern for endangered species was one reason for this decision, but perhaps more important was the fact that the major tuna canneries in the United States will no longer accept tuna caught by gill netting. Ocean Pacific decided to conduct a series of experiments to determine the amount of tuna that could be caught with different crew sizes. The results of these experiments follow.

Number of Fishermen

Daily Tuna Catch (lb)

0

0

1

50

2

110

3

300

4

450

5

590

6

665

7

700

8

725

9

710

At what point (what number of fishermen) does diminishing returns occur?

12. Refer to the previous question. Indicate the number of fishermen at the points that delineate the three stages of production. Enter your answers as whole numbers.

13. Refer to question 11. Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100?

14. Refer to question 11. a glut in the market for tuna causes the price to fall to $2.75/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

15. Refer to question 11. Suppose the price of tuna rises to $5.00/pound. At this new price, how many fishermen should the company now use if the daily wage rate remains at $100?

Number of Fishermen	Daily Tuna Catch (lb)
0	0
1	50
2	110
3	300
4	450
5	590
6	665
7	700
8	725
9	710

Solution

(11) MPL starts diminishing when L = 9 & Q = 710

(12) Stages of production are:

Stage 1: L = 0 to L = 3, where MPL is increasing (Q increasing at an increasing rate).

Stage 2: L = 4 to L = 8, where MPL is decreasing (and Q increasing at a decreasing rate).

Stage 3: L = 9 (Q falling after reaching a maximum, MPL is negative).

(13) Firm will hire labor until the point MRPL = wage rate, where MRPL = MPL x Price

When wage = 100, L = 7 or L = 8 (closest to MRPL = 100)

(14) When wage = 100, L = 7 (closest to MRPL = 100)

(15) When wage = 100, L = 8  (closest to MRPL = 100)

No. Of Fishermen (L)	No. Of Tuna (Q)	MPL	Price (P) = 3.5	MRPL = MPL x P	Price (P) = 2.75	MRPL = MPL x P	Price (P) = 5	MRPL = MPL x P
	(A)	(B)	(C)	(D) = (B) x (C)	(E)	(F) = (B) x (E)	(G)	(H) = (B) x (G)
0	0		3.5		2.75		5
1	50	50	3.5	175	2.75	137.5	5	250
2	110	60	3.5	210	2.75	165	5	300
3	300	190	3.5	665	2.75	522.5	5	950
4	450	150	3.5	525	2.75	412.5	5	750
5	590	140	3.5	490	2.75	385	5	700
6	665	75	3.5	262.5	2.75	206.25	5	375
7	700	35	3.5	122.5	2.75	96.25	5	175
8	725	25	3.5	87.5	2.75	68.75	5	125
9	710	-15	3.5	-52.5	2.75	-41.25	5	-75