Question

Suppose there is a jalapeño farmer that wants to use water from the Rapid River to irrigate her land. Further, suppose there is a fisherman who likes to fish in the Rapid River. As the amount of water in the river increases, the fishing improves. We can represent the marginal benefit the fisherman has for river water with a demand curve. If the farmer leaves water in the river, she can’t use it to irrigate her crop. We can represent her marginal cost of leaving water in the river with a supply curve. The demand schedule and supply schedule are given in the following table:

Units of water left in the river	Marginal Benefit for Fisherman (Demand)	Marginal Cost for Farmer (Supply)
0	-	-
1	21	4
2	17	8
3	13	12
4	9	16
5	5	20

c) Suppose that the fisherman holds property rights to 5 units of water from the Rapid River, but can sell these water rights to the farmer. If transaction costs are zero, how many units of water will the fisherman trade to the farmer? Does this result in the socially optimal quantity of water left in the river?

Answer 1

Units of water left in the river	Marginal Benefit for Fisherman (Demand)	Total Benefit	Marginal Cost for Farmer (Supply)	Total cost
0	-		-
1	21	21	4	4
2	17	38	8	12
3	13	51	12	24
4	9	60	16	40
5	5	65	20	60

The fisherman would trade two units of water to the farmer because at 4th unit of water, his marginal benefit from water becomes lower than marginal cost that farmer is bearing. By giving away 2 units of water, he operates at 3 units of water.

Yes, this is socially optimal as earlier, when fisherman was operating at 5 units of water, his benefit was 65, while total cost for farmer was 60, giving net benefit of 5. But at 3 units, total benefit is 51 and total cost is 24, giving net benefit of 27, which is highest at any level of water units.