Question

1. HBO has MC=0 of giving someone access to their platform. Suppose there are two possible markets of people in the US, Movie Buffs and Movie Casuals. There are 50 of each. The demand of Movie Buffs for HBO is D(p)= 100 - 2p if p is greater than and equal to 25   and D(p)= 50 if p is less than 25. The demand of Movie Casuals for HBO is D(p)= 50- 2p
2. Calculate the market demand of both Movie Buffs and Movie Casuals for HBO. (It might help you to sketch the two demand curves separately and then sum them – but you don’t need to include that here.) D(P)=
3. 2. Suppose HBO faces the market demand curve you calculated in (a). Calculate HBO’s profit maximizing quantity and price,  and . (1pt)
   3. Calculate the profits of the monopolist (don’t worry about fixed costs). (1pt)
   4. A data gathering company “CMU Analytics” offers its service to HBO. Their algorithm can identify whether people fall into the Movie Buff category or the Movie Casual category.  This would allow them to sell to the two markets separately at different prices. What kind of price discrimination is this? (1pt)

Answer 1

a).

Suppose there are two possible markets of people in the US, and their respective demand functions are given in the question. The market demand of both types is the horizontal summation of them.

=> Q = D1+D2 = (100-2*P1)+0, for “P > = 25”, where “P1=P2=P”.

=> Q = 100 - 2*P, for “P > = 25”.

=> Q = D1+D2 = 50+(50-2*P2), for “P < 25”, where “P1=P2=P”.

=> Q = 100 - 2*P2, for “P < 25”.

So, the market demand of both movies is given by, => “Q = 100 – 2*P”. The following fig shows the individual demand and the market demand of movies.

In the above fig “D1” represent the demand for movie buff and “D2” represent the demand for movie casual. The right fig is the market demand which is the horizontal summation of D1 and D2.

b).

Here the market demand is “Q = 100 – 2*P”, => P = 50 – Q/2, => MR = 50 – Q. Now, the MC is zero. So, the profit maximizing condition is given below.

=> MR = MC = 0, => 50 – Q = 0, => Q = 50. Now, the market price is “P=50-Q/2 = 50-50/2 = 25”. So, the profit maximizing price and quantity are “P=25” and “Q=50”.

c).

The maximum profit of the monopolist is given below.

=> Profit = Total Revenue – Total Cost = P*Q – FC - MC*Q = 25*50 – 0 - 0*50 = $1,250, where fixed cost is zero.

=> Profit = $1,250.

d).

Let’s assume HBO charge different price according to the type of the consumer. The demand of movie casual is given by.

=> D2 = 50 – 2*P2, => P2 = 25-Q2/2, => MR2 = 25-Q2. At the optimum the MR2 is equal to the MC.

=> MR2=MC, => 25-Q2=0, => Q2=25, => P2 = 25-Q2/2 = 12.5, => P2=12.5.

Similarly, the demand of movie buff is given by.

=> D1 = 100 – 2*P1, => P1 = 50-Q1/2, => MR1 = 50-Q1. At the optimum the MR1 is equal to the MC.

=> MR1=MC, => 50-Q1=0, => Q1=50, => P1 = 50-Q1/2 = 25, => P1=25.

So, this types of price discrimination is called the 3rd degree price discrimination, under this type of price discrimination HBO will charge “P1=25” to the movie buff group and “P=12.5” to the movie casual group.