Problem 5: (Internalizing) external costs

Cardinal Crust (CC) produces tavern-style pizzas that can be sold in a competitive market at the price of $40 each; CC incurs no fixed costs, and the daily marginal production cost (in dollars) of producing each pizza (q) is given by MPC=8 + q. Unfortunately, CC's production process emits pollution that harms the neighboring community of Palo Alto, in an amount equal to $8 per pizza.

a. How many pizzas will CC produce each day, if it acts purely in its own self-interest? What will be CC's daily profits? How much will Palo Alto endure in "external costs" each day? Illustrate your answers with a well-labeled diagram, and note that your diagram will be very useful in computing the firm's profits.

b. What would be the efficient number of pizzas produced daily, considering all relevant costs (including those borne by the residents of Palo Alto)? Show this efficient outcome in your diagram from part a).

c. Suppose CC has the legal right to choose its production level, and is not required to consider Palo Alto's wellbeing in doing so.Describe a private agreement between CC and Palo Alto that could bring about the efficient outcome and make both entities "better off" compared to the outcome you described in part a).

d. Now suppose Palo Alto has the legal right to an environment free of pollution. Describe a private agreement between CC and Palo Alto that could bring about the efficient outcome and make both of them "better off" compared to a scenario in which CC shuts down production completely.

e. Finally, describe a "Pigovian tax" that would bring about the efficient outcome, as compared to a scenario in which CC is able to do whatever it wants.