Question

Consider a fishery where fishers can either apply one unit of labor (fishing effort) for fishing from a fixed stock, or work in another industry and earn c dollars from one unit of effort.

Assume:

L is the total fishing labor hours (fishing effort)

p is the price for a unit of fish (we assume that the fishery cannot affect the price – too small relative to the overall market to count)

c is the cost of working an hour in the fishery (the opportunity cost, calculated as the highest wage the worker could get in another job)

F(L) is the response function of fish catch to L.

L is total hours fishing at the lake yield F(L) units of fish to be shared equally per hour.

The total catch of fish is given by the relation F(L)=110L-L^2.

Assume constant price p=1 and a labor cost of c = $10 per hour. Assume fishers are identical, and are employed by a profit-maximizing monopolist of the total particular fishing ground.

(i) Calculate equilibrium fishing effort and fish catch, and profit. Then graph the relation between total revenue and L, and between total labor cost and L, and identify the equilibrium total labor cost and total revenue, and show maximum profit on the diagram.

Answer 1

Q = F(L) = 110L - L²

(a) Profit is maximized when (p x MPL) = c

MPL = dQ/dL = 110 - 2L

1 x (110 - 2L) = 10

110 - 2L = 10

2L = 100

L = 50

Q = (110 x 50) - (50 x 50) = 5,500 - 2,500 = 3,000

Profit = Total revenue - Total cost = (p x Q) - (c x L) = (1 x 3,000) - (10 x 50) = 3,000 - 500 = 2,500

(b)

Data table for graphs:

Q	L	TR	TC
0	0	0	0
1000	10	1000	100
1800	20	1800	200
2400	30	2400	300
2800	40	2800	400
3000	50	3000	500
3000	60	3000	600
2800	70	2800	700
2400	80	2400	800
1800	90	1800	900
1000	100	1000	1000

Graph:

(c) Equilibrium labor cost & total revenue are indicated as ponts A and B respectively in above diagram.

(d) Maximum profit equals area ABCD.