Public goods

Consider the market for police protection

Suppose there are three equal-size groups in the economy with the following demand curves:

Group 1s demand for police protection is P= 70-10 Q

Group 2s demand for police protection is P=50-10 Q

Group 3s demand for police protection is P=44-10

Q where Q refers to the quantity of police protection (i.e. number of police officers) and P refers to the price.

Assume that each group includes 3,000 people and that the social marginal cost is $40,000.

What is the efficient quantity of police protection? Hint: Remember that to build the SMB for a public good, you need to take the vertical sum of individual demand curves. In other words, you need to add the prices that consumers are willing to pay: that is, add how much money each person would be willing to pay. Note that there are 3000 people in each group.

If the people in groups 1 and 2 are free-riders, how many police officers will the private sector provide?

Show the efficient quantity, the equilibrium quantity and the deadweight loss on a graph. Remember to label the axes and the curves.