A lake supports a delicious variety of fish. The land around the lake is owned by two fisherman,so by state law both are free to fish as much as they like. Let FA and FB be the number of fish each catches,respectively. Suppose the price of fish is 100 - FA - FB. Given this demand curve,it turns out that marginal revenue is 100 - 2FA - FB for fisherman A and 100 - FA - 2FB for fisherman B. What is the total number of fish by both in the Nash equilibrium?
A)30
B)45
C)60
D)90

Question

Quizplus · Accepted Answer

The Nash equilibrium is found by solving the system of equations:```MR_A = 100 - 2FA - FB = 0MR_B = 100 - FA - 2FB = 0```Solving this system of equations gives:```FA = 20FB = 10```Therefore, the total number of fish caught by both fishermen in the Nash equilibrium is 20 + 10 = 30.

A Lake Supports a Delicious Variety of Fish