Three shipping companies would like to build lighthouses on the rocks in the local harbor to protect their ships. Altogether there are 25 locations that might require lighthouses. The cost to build and maintain each lighthouse is $60. Qd_A=25-(1/2)P, Qd_B=25-(1/10)P and Qd_C=25-(1/3)P.

a. If each company ignores the other companies in deciding to build, how many lighthouses will each company erect? How much net benefit does each company think (incorrectly) they will receive by erecting these lighthouses? (HINT: This is the amount they would build if this was a private good)

b. But in this case, lighthouses are both non-rivalrous and non-excludable. Explain why.

c. How much net benefit will each company actually receive if the number of lighthouses erected is the total calculated (in #1)? (Actually because this is a public good, not a private good)

d. Now suppose all the companies know that lighthouses are public goods. If company A was the first company to open, how many lighthouses will it erect? Then company B opens. How many lighthouses will B add? When company C opens for business, how many new lighthouses will company C add? Under these conditions, how many lighthouses in total will be erected? How much net benefit will each company receive with this many lighthouses?

e. What is the optimal number of lighthouses to erect? How much total benefit will each company receive at this optimal number of lighthouses?

f. What is the dead weight loss that is produced if the companies erect the number of lighthouses in #1?

g. What is the dead weight loss that is produced if the companies erect the number of lighthouses in #3?

h. The companies decide to meet to try to increase the number of lighthouses (from your answer to #3) to the optimal level. Will all the companies be willing to pay an equal share of the increase in cost? Which ones will and which ones wont? Explain.

i. Can you suggest a payment scheme in which all the companies will voluntarily agree to fund the increase in the number of lighthouses to the optimal level? (Many answers are correct) Explain.