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

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

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

Group 3's 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.