To water their vine yards, a group of farmers in Cyprus drill identical wells and draw irrigation water from an underground aquifer. This aquifer has a natural maximum recharge rate of 340,000 liters per day (in others words, a maximum of 340,000 liters of water per day filter into this underground reservoir from natural sources). The table below shows the relationship between the daily total water output (total product) and the number of wells operating.
Common Property and Public Goods Problem
To water their vine yards, a group of farmers in Cyprus drill identical wells and draw irrigation water from an underground aquifer. This aquifer has a natural maximum recharge rate of 340,000 liters per day (in others words, a maximum of 340,000 liters of water per day filter into this underground reservoir from natural sources). The table below shows the relationship between the daily total water output (total product) and the number of wells operating.
|
Number of Wells Operating |
Total Water Output (in 1000s of Liters/Day) |
Total Revenue (TR) |
Total Cost (TC) |
Average Revenue (A VR) |
Profit |
|
0 |
0 |
0 |
0 |
0 |
0 |
|
10 |
100 |
||||
|
20 |
200 |
||||
|
30 |
280 |
||||
|
40 |
340 |
||||
|
50 |
380 |
||||
|
60 |
400 |
||||
|
70 |
400 |
||||
|
80 |
380 |
||||
|
90 |
340 |
(a) The cost of operating a well is €60/day and the value of water to each farmer is €0.1/liter. Using this information and the following formulae, complete the table above (be sure to provide at least one sample calculation for each column): TR = Price x Quantity of water, TC = Number of Wells x Cost/Well, AVR = TR / Number of Wells, and Profit = TR – TC.
(b) Using the data in the table above, sketch a graph that shows the TR, TC and Profit
(c) Assuming each well is privately owned by a different farmer, use the graph you sketched and/or the data in the table to calculate the number of wells that will operate if the extraction of water from the aquifer is not regulated (Hint: The question asks you to calculate the open access equilibrium. Use the fact that at the open access equilibrium, TR=TC. What is the number of wells at this point?
(d) Use your graph and the data in your table to identify the economically efficient number of wells (Hint: What is the profit maximizing number of wells?)
-
(e) Calculate the profits of the 40th well.
-
(f) The government of Cyprus has decided to impose a license fee to limit the number of wells to 40. What should be the price of this license fee? Show all your calculations clearly.
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