Question

The local movie theater industry has a demand curve of P=26-.2Q for a movie showing (please note the decimal in front of the 2). It has a supply curve (MC curve) of $2, because the theater figures for each customer there will be a cleanup cost afterwards. In reality, a theater might sell food and drinks for extra profits, but this one does not.

1. What is allocative efficiency? What is the price of a ticket and number of patrons (quantity) that will result in allocative efficiency? Why is this price not practical?
2. If the theater, the only one in town, wishes to price as a monopoly, what would the price of a ticket and quantity (number of patrons) be?
3. If this theater would like to price discriminate by charging some $20 and letting them sit in the front rows, regular customers the monopoly price, and senior citizens who do not sit in the front $5, by how much would the $20 price increase profits over a regular monopoly price? By how much would the $5 price increase profits over the regular monopoly price? By having three prices instead of one, how much would profit increase by? Explain your answers and demonstrate with a graph.
4. Assume another theater opens so there are two theaters in town. The marginal cost and demand curve remain the same for the industry, but there are now two firms instead of one. Use the Cournot model of duopoly to determine the new movie theater ticket price with two theaters instead of one. Explain your answer and include a graph.
5. What would be the Lerner Index for these two theaters? What does this number measure?

Answer 1

a).

allocative efficiency is a state of an economy, when there is an optimum distribution of resources. Now, more specifically it represents a situation when price is equal to marginal cost, where the total surplus is maximum.

Here the marginal cost of movie is $2 movie showing, => the price of a ticket and the quantity that will result in allocative efficiency is “P=2”, => Q=(26-2)/2 = 12”.

This not practical because a producer charge price exactly equal to MC, where MC is constant then the economic profit of the producer will be zero. Here a producer will try to maximize its profit by charging more than MC and supplying less than the allocative level of output.

B).

Here the market demand schedule is “P = 26 – 2*Q”, => MR = 26 – 4*Q”. Now, at the optimum the MR must be equal to MC. So, at the optimum.

=> MR = MC, => 26 – 4*Q = 2, => Q = 24/4 = 6, => Q=6, and P=14. So, the profit maximizing price and the quantity are “P=$14” and “Q=6”.

C).

Consider the following fig.

Here the monopoly price and the quantity are “P2=14” and “Q2=6” respectively, => the profit is the area P2C2C1A2. So, the monopoly profit is given by, => P2C2C1A2 = (14-2)*6 = $72.

If this theater charges “P1=$20” for the front row sit, => “Q1=3” people will buy the tickets, => the addition profit is given by the area “P1A1B1P2 = (20-14)*3 = $18.

If this theater charges “P3=$5” for the senior citizen, => “Q3-Q2=10.5-6 = 4.5” people will buy the tickets, => the addition profit is given by the area “B2C1B3A3 = (5-2)*4.5 = $13.5.

If three prices instead of one charge then the total profit will increases by “$18+$13.5 = $31.5”.

D).

Let’s assume another theater open having same MC and the market demand schedule, => P = 26 – 2*Q. So, the profit function of theator1 is given below.

=> A1 = P*Q1 – MC1*Q1 = (26-2*Q1-2*Q2)*Q1 – 2*Q1 = 26*Q1 - 2*Q1^2 - 2*Q2*Q1 – 2*Q1.

=> A1 = 24*Q1 - 2*Q1^2 - 2*Q2*Q1, => FOC for profit maximization require dA1/dQ1 = 0.

=> 24 - 2*2*Q1 - 2*Q2 = 0, => Q1 = 6 – Q2/2, be the best respond function of theater1.

Now, the profit function of theator2 is given below.

=> A2 = P*Q2 – MC2*Q2 = (26-2*Q1-2*Q2)*Q2 – 2*Q2 = 26*Q2 - 2*Q2^2 - 2*Q2*Q1 – 2*Q2.

=> A2 = 24*Q2 - 2*Q2^2 - 2*Q2*Q1, => FOC for profit maximization require dA2/dQ2 = 0.

=> 24 - 2*2*Q2 - 2*Q1 = 0, => Q2 = 6 – Q1/2, be the best respond function of theater2.

Now, by simultaneously solving the above two equation we got “Q1=Q2=4”, => total output supplied by both the firms are “Q=8”, => the market price is “P=10”.

Consider the following fig.

Here “P2” and “Q2” the price and quantity under the monopoly market and “P3=10” and “Q3=8” are the same under the Cournot duopoly market model. So, under the second case the price is lower but the total output supplied is more.