Farmers in an arid region in Mexico draw their irrigation water from an underground aquifer. The aquifer has a natural maximum recharge rate of 340 gallons per day (that is 340 gallons per day filter into the underground resource), which could be regarded as the maximum sustainable withdrawal. The total product schedule for well operations looks like this:

a. The cost of operating each well is 55 pesos per day and the value to the farmer, in terms of increased crop production and revenue, of each gallon of water is 1 peso. Calculate the total daily revenue (TR = output times value) for each number (N) of wells operating.
b. If each well is privately owned by a different farmer, how many wells will operate? (To calculate this first calculate the average revenue, which is TR/N). Analyze this result in terms of economic efficiency and sustainability.
c. What would be the economically efficient number of wells? (To calculate this you will need marginal revenue, which is given by ΔTR/ΔN.) Show that net social benefit in the present period is maximized at this number of wells.
d. How could the socially efficient equilibrium identified in part c be achieved through taxes? In this case is the socially efficient level also ecologically sustainable?
e. How would the answers to b, c, and d change if costs fell to 38 dollars per well per day?

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Wells operating (N) 12 45 67 8 9 Total Water Output 100 200 280340 380 400 400 380 340 (Gal Day)