Carol and Deb were once co-owners of a coffee shop. But, they had a falling out,
ID: 1109250 • Letter: C
Question
Carol and Deb were once co-owners of a coffee shop. But, they had a falling out, dissolved their partnership and went their separate ways, with each opening up their own coffee shop. They now own and operate the only two coffee shops in their town. Given that the town is small, they are not concerned about future entry since the town could not support a third coffee shop. Carol and Deb no longer trust each other, so any attempt at colluding to set the price of coffee is sure to fail. They use very similar methods to brew their coffee, so customers always want to simply buy from the low price firm (that is, they have no loyal customers). Let's suppose that the demand for coffee is given by P 500-Q c where P is the price of a cup of coffee (in cents), QD is the number of cups of coffee Deb sells in a day and Qc is the number of cups of coffee that Carol sells in a day. In addition, let's assume that it cost them each 20 cents to brew each cup of coffee. Find the Cournot equilibrium outputs, price and profit levels for Carol and Deb. Show your work. Now, suppose that Deb finds a new supplier that allows her to get some of her coffee beans more cheaply, lowering her cost per cup to 5 cents. Assuming that Carol's cost remains at 20 cents per cup, find the new Cournot equilibrium outputs, price and profit levels for Carol and Deb. Show your work. 0 8Explanation / Answer
Initially the market demand is P = 500 - Qd - Qc. Hence their respective marginal revenue functions are
MRc = 500 - Qd - 2Qc and MRd = 500 - 2Qd - Qc
Equate them with the marginal cost
500 - Qd - 2Qc = 20 and 500 - 2Qd - Qc = 20
Qd + 2Qc = 480 and Qc + 2Qd = 480
Solve them to get Qc = Qd = 160 and common price P = 500 - 320 = 180 cents.
Profits for each firm is (180 - 20)*160 = 25600 or $256
In case when Deb has a lower MC of 5, we have the following situation
500 - Qd - 2Qc = 20 and 500 - 2Qd - Qc = 5
Qd + 2Qc = 480 and Qc + 2Qd = 495
Solve them to get Qc =155 and Qd = 170
Price P = 500 - 325 = 175
Profit to Deb = (175 - 5)*170 = $289
Profit to Carol = (175 - 20)*155 = $240.25