Paragraph: A lake supports a 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.
Question: What is the total number of fish by both Fisherman A and Fisherman B in the Nash equilibrium (calculated response)?
Each fisherman maximizes profit according to the rule, MR =
MC
(As both are free to fish so MC = 0)
Firsherrman A:
MR = MC gives,
100 - 2FA - FB = 0
2FA = 100 - FB
So, FA = (100/2) - (FB/2)
So, FA = 50 - 0.5FB
This is the best response function of fisherman A.
Firsherrman B:
MR = MC gives,
100 - FA - 2FB = 0
2FB = 100 - FA
Now, we substitute best response function of fisherman A. We
get,
2FB = 100 - (50 - 0.5FB) = 100 - 50 + 0.5FB
So, 2FB - 0.5FB = 50
So, 1.5FB = 50
So, FB = 50/1.5 = 100/3 = 33.33
Now, FA = 50 - 0.5FB = 50 - 0.5(100/3) = 50 - 16.67 = 33.33
Total number of fish = FA + FB = 33.33 + 33.33 = 66.66 (or approximately 67 if exact number is required.)
Paragraph: A lake supports a variety of fish. The land around the lake is owned by...
Paragraph: A lake supports a 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...
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