Question

As a manager of a chain of movie theaters that are monopolies in their respective markets, you have noticed much higher demand on weekends than during the week. You therefore conducted a study that has revealed two different demand curves at your movie theaters. On weekends, the inverse demand function is P = 20 – 0.001Q; on weekdays, it is P = 15 – 0.002Q. You acquire legal rights from movie producers to show their films at a cost of $25,000 per movie, plus a $2.50 “royalty” for each moviegoer entering your theaters (the average moviegoer in your market watches a movie only once). What type of pricing strategy should you consider in this case? What price should you charge on weekends? What price should you charge on weekdays?

Answer 1

ANSWER :

The weekend inverse-demand function is given by: P=20-0.001Q

The weekday inverse-demand function is given by: P=15-0.002Q

The cost incurred in acquiring legal rights from movie producers to show their films is given by: C(Q)=25000+2.5Q

The marginal cost of showing movie is given by: MC=2.5

The best pricing strategy would be to charge different per-unit price on weekends and weekdays using the condition MR=MC and following the price as followed from the respective inverse-demand function.

* Thus, on weekends, the equilibrium condition is given by:

P=20-0.001Q

   TR=20Q-0.001Q2

MR=20-0.002Q

    MR=MC

  20-0.002Q=2.5

Q=8750

* Thus, the optimal price to be charged on weekends is given by:

P= 20-0.001Q

=20-0.001*8750

P= 11.2

* On weekdays, the equilibrium condition is given by:

P= 15-0.002Q

TR =15Q-0.002Q2

MR =15-0.004Q

MR = MC

15-0.004Q=2.5

Q = 3125

* Thus, the optimal price to be charged on weekends is given by:

P= 15-0.002Q

=15-0.002 *3125

P= 8.7

Thus, the pricing strategy would be such that $11.25 would be charged per moviegoer on weekends and $8.7 would be charged per moviegoer on weekdays