There are three households in a community. Their individual marginal benefit for hours (H) per week of public television is given by MB₁=30-H, MB₂= 60-2H and MB₃=70-H. Suppose that public television is a pure public good that can be produced at a constant marginal cost of $100 per hour.

(a) Sketch the three marginal benefit schedules and the aggregate marginal benefit schedule. Draw the marginal cost schedule, and find the efficient level of provision for hours per week of public television. What would be the net benefit to the community if the efficient number were provided?

(b) Suppose that the local government finances the hours per week of public television out of taxes. Show that the local government can achieve the social optimum by setting the correct tax prices t₁, t₂ and t₃ on individuals 1, 2 and 3, respectively. What taxes should it set?

(c) Explain why a set of tax prices such as the one proposed in (b) is unlikely to provide the proper incentives for individuals to reveal their true preferences for the public good.