Question

1. A pharmaceutical company currently holds a patent on a cream that removes freckles. They are in the final year of patent protection and have brought down the cost to make a carton of the cream over time to its current C(Q) = 100Q. The inverse-demand for cartons (which contain 10 individual bottles) of this product is P = 1,000 – 10Q.

a. What price will the monopoly set, what quantity (in cartons) will be purchased, and how much profit will they make?

b. The patent is set to expire and another company is considering entering the market. The potential entrant has a cost C(Q2) = 400Q2 as their production process is not as lean as the monopolist’s. The inverse-demand is now P = 1,000 – 10(Q1 + Q2). That is, customers will view the companies as perfect substitutes. You should think about the monopoly as firm 1, so C(Q1) = 100Q1 as before. If the two firms compete by setting quantities simultaneously (Cournot competition), what quantity will each firm set, what will be the market price, and how much profit will each firm make? Show your work on the back then put your answers below.

Q1 = _______________ Q2 = _______________ P = ______________

Profit1 = ____________ Profit2 = ______________

c. Show that if the monopoly is able to set its quantity first (Stackelberg) that they can deter the other firm from entering the market. That is, Q2 = 0. What quantity will the monopolist produce, what will be the market price, and how much profit will they make?

d. Explain why the price charged is not the same in parts a and c even though there is only one firm in each situation.

Answer 1