You are hired as a consultant for a fishing company. They wish to maximize profi

Question

You are hired as a consultant for a fishing company. They wish to maximize profits by determining the ideal number of workers. The number of fish caught per week is a function of the number of crew on the boat, as follows:

The owner tells you that he can sell any fish caught at $750/unit. Each crewmember earns $1500 per week. The owner currently hires 10 crewmembers, since that maximizes output.

a) What is the profit maximizing number of crew? Please show calculation

b) Describe any rule or economic intuition behind how/why you arrived at this number. Please explain

Number of Crew Fish Caught per Week (units of 100lbs) 19 24 28 31 8 10 12 34 34

Explanation / Answer

A.

Profit maximizing number of crew = 9

At this number of crew, the profit is maximized that is $11250

At this number of crew,

Profit = Revenue – cost = 33*750 – 9*1500 = $11250 and it is maximum.

Detailed calculation is put in the above table.

B.

Marginal rule of economic is used that says that profit maximizing output is achieved when MR = MC.

In the given scenario also,

At 9 crew members,

Marginal revenue (MR) = $1500

Marginal cost (MC) = 1500

So, MR = MC when 9 crew members are employed.

At this level the profit is maximized that is $11250.

No. of crew Fish Caught per week Total Revenue Total cost Marginal Revenue Marginal cost Profit = Revenue - cost 2 3 2250 3000 -750 3 6 4500 4500 2250 1500 0 4 11 8250 6000 3750 1500 2250 5 19 14250 7500 6000 1500 6750 6 24 18000 9000 3750 1500 9000 7 28 21000 10500 3000 1500 10500 8 31 23250 12000 2250 1500 11250 9 33 24750 13500 1500 1500 11250 10 34 25500 15000 750 1500 10500 11 34 25500 16500 0 1500 9000 12 33 24750 18000 -750 1500 6750

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