Question

3) The Ocean Pacific fleet has just decided to use a pole-and-line method of fishing instead of gill netting to catch tuna due to a concern for endangered species that can become caught in fishing nets. Ocean Pacific is limited in the short run to the current fleet of boats, and has decided to conduct a series of experiments to determine the impact of changing the crew size. The results of these experiments follow. Number of Fishermen Daily Tuna Catch (lb) 0 0 1 50 2 110 3 200 4 350 5 490 6 565 7 600 8 625 9 610

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

b) Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100? (Hint: Calculate MRP for each fisherman at $3.50.)

c) Suppose 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?

d) 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? e) In the long run, Ocean Pacific could acquire more boats or sell some of their existing boats. What factors might influence the decision whether to acquire boats, sell boats, or remain at the current number of boats? Explain.

Answer 1

a) When the number of fishermen is 5, we can see diminishing returns to occur. Note that this happens when marginal product starts falling as more and more labor units are employed. Here as more and more fishermen are available for a catch after 5 fishermen, the marginal catch starts falling.

b) Given that the market price of tuna is $3.50/pound. Find the value of marginal product which is done by finding Price x MP. When the number of fishermen is 7, MRP exceeds the wage rate of 100 and the difference is minimum. Hence the company should use 7 fishermen if the daily wage rate is $100.

c) When the price falls to $2.75/pound, there is a new MRP schedule given in the table. At this new price, the company should now use 6 fishermen because the MRP exceeds the daily wage rate of $100 when there are 6 fishermen.

d) Suppose the price of tuna rises to $5.00/pound. At this new price, a total of 7 fishermen should be used by the company now given that the daily wage rate remains at $100. This is because MRP is 125 for 8th fishermen

e) In the long run, the company can acquire more boats or sell some of their existing boats. This decision will then depend the quantity of fixed inputs which will become variable in the long run. The short run decision of production was taken on the basis of number of fishermen but in the long run when number of boats become variable, they both will determine the optimum input mix.

Number	Daily catch (TP)	MP	MRP	New MRP	MRP for part e)
0	0		0	0	0
1	50	50	175	137.5	250
2	110	60	210	165	300
3	200	90	315	247.5	450
4	350	150	525	412.5	750
5	490	140	490	385	700
6	565	75	262.5	206.25	375
7	600	35	122.5	96.25	175
8	625	25	87.5	68.75	125
9	610	-15	-52.5	-41.25	-75