A physical therapist is considering how to price his/her services. There are two types of patients denoted by i = 1, 2. Their demand curves are given in the figure below (The red one is for type 1 patients; the black one is for type 2 patients). Note that type 1 patients have positive willingness-to-pay for only two therapy sessions per week; he/she is willing to pay $40 for the first session, and $30 for the second session. The interpretation for the demand curve of type 2 consumers is similar. Assume that each therapy session costs the therapist $35 to provide (i.e., the marginal cost is $35), and there is no fixed costs to operate the business. Assume that there are 10 patients for each type. Price 70 50 40 30 20 10 0 1 2 3 Quantity (a) Suppose that the therapist can practice the first-degree price discrimination. What prices will he/she charge to type 1 and type 2 patients to maximize profits? How much profit margin per patient can the therapist make from each patient type? (5 points) 1 (b) Now suppose that the therapist only knows the demand curves shown in the figure. But the therapist cannot tell the patients' type. Hence, if the therapist chooses to do price discrimination, he/she can only use 2nd degree price discrimination. The therapist can offer up to two different price-quantity packages and let patients self- select. Describe the price-quantity package(s) that will maximize the therapist's profits. How much profit margin per patient the therapist make from each patient type? What is the total profits? Explain your answer in detail. (10 points) Notes: (1) An example of price-quantity package: buy 2 sessions for $50. If a consumer is indifferent between two packages, assume that he/she will choose the one that will give the therapist more profits. For each package, a patient can buy multiple units. (Suppose package one is: buy 2 sessions for $50. Type 2 patients can buy multiple package one.) A physical therapist is considering how to price his/her services. There are two types of patients denoted by i = 1, 2. Their demand curves are given in the figure below (The red one is for type 1 patients; the black one is for type 2 patients). Note that type 1 patients have positive willingness-to-pay for only two therapy sessions per week; he/she is willing to pay $40 for the first session, and $30 for the second session. The interpretation for the demand curve of type 2 consumers is similar. Assume that each therapy session costs the therapist $35 to provide (i.e., the marginal cost is $35), and there is no fixed costs to operate the business. Assume that there are 10 patients for each type. Price 70 50 40 30 20 10 0 1 2 3 Quantity (a) Suppose that the therapist can practice the first-degree price discrimination. What prices will he/she charge to type 1 and type 2 patients to maximize profits? How much profit margin per patient can the therapist make from each patient type? (5 points) 1 (b) Now suppose that the therapist only knows the demand curves shown in the figure. But the therapist cannot tell the patients' type. Hence, if the therapist chooses to do price discrimination, he/she can only use 2nd degree price discrimination. The therapist can offer up to two different price-quantity packages and let patients self- select. Describe the price-quantity package(s) that will maximize the therapist's profits. How much profit margin per patient the therapist make from each patient type? What is the total profits? Explain your answer in detail. (10 points) Notes: (1) An example of price-quantity package: buy 2 sessions for $50. If a consumer is indifferent between two packages, assume that he/she will choose the one that will give the therapist more profits. For each package, a patient can buy multiple units. (Suppose package one is: buy 2 sessions for $50. Type 2 patients can buy multiple package one.)
