Question

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

ANSWER: a

Please explain the answer given and give all the steps. Thanks.

Answer 1

Step 1) Profit is maximised at a point where MR= MC

Since, MC is not given,MC=0

Step 2) For firm 1

MR= 100-2FA-FB

MC=0

So, 100-2FA-FB=0

FA= (100-FB)/2 --------------------------(A)

Step 3) For firm 2

MR= 100-FA-2FB

MC=0

So, 100-FA-2FB=0

FB= (100-FA)/2 -------------------------(B)

Step 4) Putting the value of FA from (A) to (B)

FB= (100-FA)/2

FB= [ 100- ( 100-FB)/2 ]/2

FB= [ 200-100+FB]/4

FB*= 100/3

FA*= (100-FB)/2 = { 100-(100/3) }/2

FA*= 100/3

Total nash Equilibrium quantity=FA*+FB*= 200/3= 66