The tradable pollution permit exercise: Three additional tools

Permit trading has been a significant innovation in controlling pollution. Ando and Harrington (2006) developed a classroom exercise demonstrating the effectiveness of a tradable permits market. We provide three additional pedagogical tools. First, we show how intermediate microeconomics students can algebraically and graphically calculate the market-clearing permit price. Second, for advanced students we show how the cost-minimizing allocation of pollution control is achieved using a Lagrangian equation and explain the economic interpretation of the shadow price. Third, we show how to solve the first order conditions using Excel's matrix inverse tool for each firm's emissions reductions and the shadow price.