Question

Exercise goals: Be able to solve the profit maximization problem of a monopolist with third-degree price discrimination.
Understand the differences between 3DPD and single-pricing. You own a monopoly that produces cars to be sold in two countries: Freedonia and Sylvania. Demand for cars in Freedonia is given by PF = 16,000-20Q_F, while demand in Sylvania is given by P_S = 20, 000 - 10QS. You own a single plant in Sylvania that produces cars for both countries. Your cost function is C (Q) = 8, 000Q, where Q = Q_F + Q_S.

1. (1 point) Initially, these two countries have a peaceful relationship, and free trade exists between them, therefore you can only charge a single price between the two countries. What price do you set? How much profit do you collect? [Hint: it may be easier to solve this maximization problem in terms of P. To do so, you can first obtain the demand functions (i.e. Q(P) = . . .), and then write the cost function in terms of P using the demand functions]

2. (1 point) How much consumer surplus is generated in each country?

3. (1 points) The Freedonian government finds out that Sylvania is secretly plotting to invade Freedonia. This discovery leads to an interruption in free trade between the two countries. That’s good news for you: it means you can now sell cars in Freedonia at a different price than in Sylvania. However, in order to do so, you have to build a factory in Freedonia as well. Suppose that you can build a factory for free (the Freedonian government is giving you a generous handout because they like your cars). The plants are identical, so you have the same cost function in both countries (C (Q) = 8, 000Q). What prices do you set? How much profit do you collect?

4. (1 point) How much consumer surplus is generated for each country in this new scenario? Comment on whether you think 3DPD is good or bad for society as a whole (i.e. Freedonia + Sylvania) in this case.

5. (1 point) Suppose that the cost of building a factory is 300,000. Does it make sense for the Freedonian government to subsidize the plant? Why or why not? [When answering this question, assume that the Freedonian government only cares about the well-being of its citizens]

Answer 1