Problem set 3: Price discrimination

Numerical exercise (10 points)
Suppose that IBM has a monopoly position on the printer market. IBM has 100 potential consumers for its LaserPrinter. All consumers have a unit demand (i.e., the buy at most one printer) and have the following willingness to pay: 55 companies are willing to pay 100 € for one LaserPrinter; 45 individuals are willing to pay 50 € for one LaserPrinter.
The constant marginal cost of producing one LaserPrinter is equal to 10 €. (2 points) What is IBM’s optimal price for the LaserPrinter (supposing that a unique price has to be set, i.e., that IBM is not able to price discriminate)? Compute also IBM’s profit and quantity produced at the optimum.

Optimal price p* = 100
Optimal quantity q* = 55
Optimal profit π* = 4950
We are looking for a unique price which maximizes the firm’s profit. Optimal unique price If - 0 ≤ p ≤ 50 → q = 100 and the maximum profit is π(p=50) = (50 – 10).100 = 4000€ 50 < p ≤ 100 → q = 55 and the maximum profit is π(p=100) (100 – 10).55 = 4950€ p > 100 → q = 0 and the maximum profit for any price is zero.

We maximize the profit’s firm by putting a price equal to 100€. With this price we can pick up all the consumer surplus of the companies but we can’t serve the individuals which have a lower willingness to pay. If we look in term of losses, if we set a price equal to 50, we lose the surplus of the companies which is equal to (100-50)*55 = 2750. On the opposite, if we set a price equal to 100, the individuals are out of the market and we lose (50-0)*45 = 2250. So we can notice that we lose more in term of profit, when we set a price equal to 50 than when we set a price of 100. So IBM will choose to set a price equal to 100.

Suppose now that IBM wants to introduce a damaged version of its printer, the LaserPrinterE. This printer is almost identical to the original LaserPrinter, except that it includes a piece of