Question

Swellingham is a fishing port near the Fishy Banks. There are N fishermen and potential fishermen in Swellingham, and N is very large On any given day, M is less than or equal to N fishermen. take their boats out to Fishy Bankes to fish. The catch per boat per day is 100/M tons of fish. The price of fish on the world market is $100 per ton. The cost to take a boat out on a particular day: fish or do not fish. The payoff to "do not fish" is always 0. Let M be the state variable for this problem.

A. Determine how the profit (per day) of a representative fisherman varies as M changes. This is the payoff to the strategy "fish"

B. On a coordinate graph, draw the curve or line representing the payoff to an agent who fishes as a function of the state variable M. On the same graph, draw the curve or line representing the payoff to a nonfisher.

C. Determine whether the two curves intersect, and if so where; and draw conclusions with respect to the value to the state variable.

Answer 1

Solution:

a) Payoff for fishing :

[ * Not fishing: ]

Thus, for fishing strategy, we can see that is inversly related to M, i.e, profit/ pay off decrease (increase) of representative fisherman, as the number of fishermen fishing increases (decreases)

b) Graph:

c) Graphing the above two equations:

Fishing:

Not fishing:

, we found intersection as shown in graph

[ * Algebrically, the two curve intersect where, P ( from fishing )= P(from non-fishing]

So, the two graphs intersect at No.of fishermen, M=50, where each representative fisherman earns a profit of 0 (also, those who do not fish also earn 0 profit / payoff)

So, at Nash equilibrium (M=50), each fisherman earns a 0 profit, since if M<50, fishermen earn positive profit and then more fishmen are attracted to follow the fishing strategy ( as otherwise their payoff is 0, by not fishing). As a result, due to increased number of fishing men, their individual profits fall, and till they reach 0, fishing men increase. After M has reached 50, each fishermen starts earning. A negative profit, and thus no more than 50 fishing men will enter the strategy.

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