a) Discuss whether bike paths can be considered a public good. Now consider a hypothetical town. Suppose that there are three equal-size groups in the economy with the following demand curves: Group 1's demand for bike paths is P=70-5 Q Group 2's demand for bike paths is P=55-5 Q Group 3's demand for bike paths is P=40-5 Q where Q refers to the number of kilometers of bike paths in the town and P refers to the price per km. Assume that each group includes 1,000 people and that the social marginal cost is $20,000. 

b) What is the efficient number of kilometers of bike paths? 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. Note that there are 1000 people in each group.

c) Now suppose that 50% of the town residents are free riders. Assume that this percentage is the same for each group. How many kilometers of bike paths will the private sector provide?

d) On a graph, show the efficient quantity,