Consider a small freshwater lake on the shore of which there are three occupied homes. The people living in the house use the lake for recreational purpose but, unfortunately, the water quality of the lake is contaminated by an old industrial plant that has since been closed. The contamination is measured in parts per million (ppm). At present the lake contains 5ppm of containment.

Is it possible to clean the water by using an expensive treatment process. Each homeowner is willing to pay a certain amount to have the water quality improved. The table below shows the marginal and aggregate willingness to pay for different levels of water quality. The marginal cost (MC) of treatment process for cleaning up the lake is also shown in the last column of the table (MC increases as the water becomes cleaner).

Level of contaminant (ppm): 4,3,2,1,0

Owner A (marginal willingness to pay $ per year): 110,85, 70,55,45

Owner B (marginal willingness to pay $ per year): 60,35,10,0,0

Owner C (marginal willingness to pay $ per year): 30,20,15,10,5

Aggregate MWTP: 200,140,95,65,50

MC of clean up: 50,65,95,150,240

Suppose the lake was cleaned up to the efficient level of 2 ppm and that the total cost of cleanup was shared equally among the homeowners (consider integer values only)

What problem does this bring up about sharing the costs of public goods?