Question

Suppose school has figured out a way to deliver the lectures all around the world in a way that creates a demand for their lectures because in some way they're better than the lectures that you could get from other universities. They evaluate the demand in Korea and demand in Germany. The demands are as follows: PK = 5,000 – 0.5QK PG = 3,000 – 0.5QG where PK and PG are the prices per course (per student) in Korea and Germany, respectively, and QK and QG are the number of students in Korea and Germany willing to enroll at those prices, respectively. The cost of online delivery is C = 1,800Q, where Q is the total number of students enrolled (i.e., Q = QK + QG). If school has decided to charge the same (uniform) tuition (price) to their online students everywhere around the world,

1. What price would they charge?

2. What would be their total online enrollment?

3. What would be their enrollment in Germany?

4. What would be their enrollment in Korea?

5. What would be the combined surplus in all the markets? I.e., what is the sum of the consumer surplus in Korea, consumer surplus in Germany, and school’s producer surplus from selling the instruction in both countries?

Answer 1

In this question, School acts as a monopolist who can engage in a third degree price discrimination by charging different prices for the online course in the Korean and German markets. However, it charges a uniform price in all the markets, and we first derive the aggregate demand curve at each price, which is nothing but horizontal summation of the two demand curves given.

Refer to the image below for the solution:

Now, school maximizes its profits by equating MR to its MC. MR has been derived in the graph above. For the solution to the remaining parts, refer to the images below: