Take the market for public schools. In the absence of any government intervention, private schools would arise to meet the demand for all people who want to send their children to school and have positive willingness to pay for schooling. However, it is widely regarded that there is a positive externality to providing schooling at low or zero cost, stemming from the fact that greater levels of learning among the population have many positive externalities in the labor market, political processes, and so forth. If this is true, the market will under-supply the education of students relative to the social optimum.

1. Using whatever (nonzero!) numbers you choose, write equations for:

• A private demand curve;
• A private supply curve; and
• An external marginal benefit curve showing this.

Using these equations, find the social optimal quantity supplied of students, and the government expenditure necessary to reach it.

2. Show your answer to a. graphically, also indicating:

• Consumer surplus;
• Producer surplus;
• Government expenditure; and
• Equilibrium before and after the government intervention.