Question

Two types of consumers (boaters and non-boaters) share a community on the seaside. Boating accidents can be reduced by lighthouse services. The boaters combined inverse demand for the lighthouse is P = 60 − 6Q, and the non-boaters combined inverse demand is P = 20 − 2Q. The cost of providing lighthouse services to the community is TC = Q².

a) Briefly explain why lighthouse services can be considered a public good.

b) Find the optimal provision of lighthouse services (use Samuelson condition).

c) Suppose that no government provides lighthouses. The boaters decide to produce lighthouse services on their own. How much would they produce?

d) Suppose the boaters produce the amount in your answer to part c), and then ask the non-boaters to contribute remainder to get the optimal amount you found in part b). What would the non-boaters say?

Answer 1

A)

A good becomes public good under condition that it's non-rival and non - exclusive. By non rival we mean that everyone can consume or take benefit of the given good . By non exclusive we mean that no one can be barred from using it even when he doesn't pay for the product .

In the above condition lighthouse will come under public good because it's benefits will be enjoyed by all even when they do not pay for it.

B)

Optimum provision of lighthouse service is given by

Here,

Marginal benefit can be found out by summing up the demand function of both baoters and non baoters

Pb = 60-6Q(boaters)

Pn = 20-2Q(non baoters)

Here , TC = 2Q

MC = ∆TC

dtc/dq = 2

Therefore, MC = 2

For efficient condition we will equate the two

80-8Q= 2

8Q= 78

Q= 9.75

C)

Let's see how much the boaters will produce

We will put the value of Q in boaters demand function

60-6×9.75

= 1.5

Thus, the boaters will be able to produce 1.5 lighthouses. As we can see only 1 lighthouse will be able to get constructed .

D)

To complete the other remaining lighthouse boaters will ask non boaters to pay for it but , as lighthouse being a public good and the free rider approach that people have for public goods we can say that convincing non boaters would be difficult .