Question

Suppose that there are only two tour guides, Howe and Joseph, who provide nighttime tours along a certain coast. They would each benefit if lighthouses were built along the coast where they fish. The marginal cost of building each additional lighthouse is $100. The marginal benefit to Howe of each additional lighthouse is 90-Q, and the marginal benefit to Joseph is 40-Q, where equals the number of lighthouses. a. Explain why we might not expect to find the efficient number of lighthouses along this coast. b. What is the efficient number of lighthouses? What would be the net benefit if the efficient number were provided?

Answer 1

a. Here we might not expect to find the efficient number of lighthouses due to this reason:

there will be a problem of externality in this case.

if Joseph pays for building the lighthouses he requires, Howe is going to get benefitted even if doesn't pay anything. Hence there will be some external benefit to the other person if one pays for the lighthouses. then what will happen?

Both of them will try not to reveal their preferences and let the other person pay for the installations hence end result will be both of them not revealing their preference and try to free ride.

hence an efficient number of lighthouses will not be built.

or reverse scenario may happen if they decide according to their own marginal benefit then there will no installation of lighthouses. the cost of installing one lighthouse may be over the individual marginal benefits (we'll see how both of them  won't even consider installing in the next part of the answer.)

b. here lighthouses will be a public good. because they are not excludable(even you don't pay the price you get to enjoy the benefits) and not rival( your consumption of the benefits may not reduce other people's consumption share).

hence here we will have to vertically add the demand curves(marginal benefits curves)

hence equilibrium condition will be,

MB of jospeh+ MB of Howe(Marginal social benefit)=MC

or,90-Q+40-Q=100

or, 130-2Q=100

or, Q=15

15 is the efficient number of lighthouses.

if they go along the private benefit rule then the equilibrium conditions will be,

MB(joseph)=Mc or, 40-Q=100 or Q=-60

and MB(howe)=MC or 90-Q=100 or Q=-10

hence total installed light will be none because Joseph and Howe will not think about installing lights at all because of no positive quantity will be there to MC equalling their individual MBs.

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