Question

1. The movie distributor charges a movie theatre $4 per ticket to rent a movie. Suppose the theatre can seat a maximum of 200 people. The demand for the movie is different for the afternoon showing and for the evening showing. Based on the demand function P = 10 – Q/10 for the afternoon showing and P = 20 – Q/10 for the evening showing, the marginal-revenue function for the afternoon is MR = 10 – Q/5 and for the evening is MR = 20 – Q/5.

a. Calculate the profit-maximizing price in the evening and the afternoon; also calculate how many tickets will be sold for each show.

b. Suppose that the movie distributor now charges a flat fee of $1000 to show the movie regardless of the number of tickets sold. Will the movie theatre owner prefer this arrangement?

2. Assume that a monopolist decides to maximize revenue rather than profit. How does this operating objective change the size of the deadweight loss? If you are a “benevolent” manager of a monopoly firm and are interested in reducing the deadweight loss of monopoly, should you maximize profits or maximize revenue? Explain.

3. Suppose that you are a producer of anti-aging cream in a monopolistically competitive industry. This industry is monopolistically competitive because each producer uses a unique formula and protects it as a top secret; further, each product has its own brand name. The demand for your brand of cream is described by equation P = 200 - 2Q and the marginal revenue function is MR = 200 - 4Q. Assume the marginal cost of producing each unit of output is $4, and fixed costs are $1,000. In the short run, how many bottles of cream should you produce to maximize profits? What price should you charge? Calculate economic profits.

Answer 1

a).

So, here the demand for afternoon show and the demand for movie for evening show are given by, “Pa = 10 – Qa/10”, => MRa = 10 – Qa/5 and “Pe = 20 –Qe/10, => MRe = 20 – Qe/5”.

So, here the MC=4, => the equilibrium condition is given below.

=> MRa = MRe = MC = 4, => MRa = 10 – Qa/5 = 4, => Qa/5 = 6, => Qa = 30. Now, “MRe = MC = 4”, => 20 – Qe/5 = 4, => Qe/5 = 16, => Qe = 80, => Qa + Qe = 110.

=> Pa = 10 – Qa/10 = Pa = 10 – Qa/10 = 7, => Pa = 7 and Pe = 20 –Qe/10 = Pe = 20 –80/10 = 12, => Pe = 12.

So, the profit maximizing price are given by, “Pa = 7 and Pe = 12” and total numbers of tickets sold are “110”.

b).

Now, if the movie distributor charges a flat fee of “$1000”, => MC = 0.

=> the equilibrium condition is given by, MRa = MRe = MC = 0.

=> MRa = 10 – Qa/5 = 0, => Qa = 10*5, => Qa = 50 and MRe = 20 – Qe/5 = 0, => Qe = 20*5 = 100, => Qe = 100, => total ticket sold is “50+100 = 150”.

So, under this case the price are, “Pa = 10 – Qa/10 = 5” and “Pe = 20 – Qe/10 = 10, => Pa=5 and Pe=10”.

=> profit under this situation is “Pa*Qa + Pe*Qe – 1000 = 5*50 + 10*100 – 1000 = 250.

Now, profit under the initial situation is given by, “Pa*Qa + Pe*Qe – 4*(Qa+Qe)”.

=> 7*30 + 12*80 – 4*110 = 730 > 250.

So, the movie theatre will not prefer this arrangement.

2).

Here the deadweight loss under “revenue” maximization is less compare to the case of profit maximization. Since for profit maximization we use the condition “MR = MC = c > 0” and under revenue maximization we use the condition “MR = 0 < c, => the price under profit maximization is more than under revenue maximization, => the deadweight loss under profit maximization is more compared to the revenue maximization.

Consider the following fig.

So, here “Pm” and “Qm” be the monopoly price output combination and “Pr” and “Qr” be the price and output combination under revenue maximization. So, under monopoly choice the corresponding deadweight loss is “MEA” and the deadweight loss under revenue maximization is “RBA” and the former is more than the latter one, => the deadweight loss under monopoly is more than the under revenue maximization.