2.(15 points) Tom and Al are two neighbors who live on opposite ends of a very small...

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2.(15 points) Tom and Al are two neighbors who live on opposite ends of a very small lake that neither of them own. The lake has fish in it and both Tom and Al are both avid fishermen. They each derive benefit from fishing, but the more fish they catch now, the fewer fish there will be next season. Suppose Tom and Al have the same preferences for fish. For each of them, the total benefit derived from consumption can be described as follows:

Total Benefit for each person derived from consuming 1 fish: $10

Total Benefit for each person derived from consuming 2 fish: $15

Total Benefit for each person derived from consuming 3 fish: $18

While Tom and Al individually only get the benefits from fish they actually catch, they both bear costs (in terms of lost benefits from future fish) regardless of who catches the fish. The cost of the first fish is $2, but this cost is shared equally between them, so they each bear a cost of $1. The cost of two fish removed is $6 (marginal cost of $4), but this cost is shared between them, so they each bear a cost of $3. The costs for all fish (1-6) are shown below.

Cost to each person if 1 fish is removed: $1

Cost to each person if 2 fish are removed: $3

Cost to each person if 3 fish are removed: $6

Cost to each person if 4 fish are removed: $10

Cost to each person if 5 fish are removed: $15

Cost to each person if 6 fish are removed: $21

a.Fill in the remaining net payoffs based on the number of fish caught by each person

b. Do Tom and Al have any dominant or dominated strategies? Explain.

c. What is the efficient level of fishing in this situation? Is the efficient level of fishing a Nash equilibrium? Explain.

Now suppose that property deeds are found that indicate that Al actually owns the entire lake and has property rights to all of the fish in it and bears all the costs of any fish removed from the lake (meaning the cost of 1 fish being removed is now $2 to Al, rather than $1 to each person). Al can allow Tom to fish in his lake if he wants to, and he can make Tom pay for any fish he catches. Or he can simply forbid Tom from trespassing on his property and fishing in his lake – whether that is the optimal thing for Al to do is what we will explore now…

d. If there are no transaction costs involved between Al and Tom, what will happen in this situation? How many fish will each person catch? What will the payoffs be to both parties? (Hint: remember that Tom must now purchase the right to fish from Al.) Is this the efficient solution?

e. If the neighbors have an argument and now there are transaction costs preventing Al and Tom from reaching an agreement, what will happen in this situation? How many fish will each person catch? What will the payoffs be to both parties? (Hint: Tom has no right to future fish either, so he no longer bears any costs when Al catches fish.) Is this the efficient solution?