A large number of fishermen live around a lake. Each day the fisherman can decid

Question

A large number of fishermen live around a lake. Each day the fisherman can decide whether or not to fish in the lake. The fishermen face no opportunity cost, but must pay $10 for gas for their boats. As the lake gets crowded, it becomes more difficult for fisherman to catch fish. This relationship is captured by the following table:

NumberofBoats 1 2 3 4 5 6 7 8 9 10

TotalFishCaught 12 25 37 45 50 54 58 62 56 50

(a) If the price of fish is $1 per fish and the lake is open-access, how many fisherman will fish in equilibrium? What are the total profits made by fishermen?

b) If the price increases to $2 per fish and the lake is open-access, how many fisherman will fish in equilibrium? Are fisherman better off with the higher price?

c.) If the lake was managed by a sole-owner who could choose the number of boats to send out, how many boats would she send if the price of fish is $1? What are her total profits?

d.) If the lake was managed by a sole-owner who could choose the number of boats to send out, how many boats would she let go fish if the price of fish is $2? Is she better off with the higher price?

f.) Why does an increase in the price of the resource have different effects on profits in the open-access scenario vs the sole-owner scenario?

Explanation / Answer

1. The fishermen will fish until their Marginal Revenue is 0.

For both question a) and b), 8 fishermen will fish because as we can see above that if more fishermen fish, the marginal revenue will be negative in both the cases.

The total profit, when $1 is the price of the fish is the sum of the Marginal revenues until 8 units of good minus the marginal cost.

(12+13+12+8+5+4+4+4) - 10 = $52

The total profit when $2 is the price, (24+26+24+16+10+8+8+8) - 10 = $114

As can be seen, the profit that is earned is higher at higher prices and thus the fishermen are better off with higher prices.

3. The no. of boats that would be sent at P=$1 would be when MR=MC

MC is $10

Thus, between 3 to 4 boats will be sent

Her profit would be when 3 boats are sent, 3(12+13+12) - 3(10) = $81

Here we assume that the revenue received and the cost incurred on all three boats will be incurred by the sole-owner.

4. 5 boats will be sent out in case the price is $2. This is because as can be observed above, MR=MC=$10 at 5 units of boats.

5(24+26+24+16+10) - 5(10) = $450

As can be observed, the sole-owner is better off with $2 as the price.

5. The increase in the price has different effects on profits in open access vs closed access because in the case of open access, the quantity of boats is maximized at MR = 0, whereas in case of the closed access, the profits are maximized at MR=MC.

Number of Boats Marginal Product Marginal Revenue(Price=1) Marginal Revenue(Price =2) 1 12 12 24 2 13 13 26 3 12 12 24 4 8 8 16 5 5 5 10 6 4 4 8 7 4 4 8 8 4 4 8 9 -6 -6 -12 10 -6 -6 -12

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