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Optimal Pricing

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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 price should you charge on weekends?

Instruction: Round your answer to two decimal places.


What price should you charge on weekdays?

Instruction: Round your answer to two decimal places.


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Solution Summary

This solution helps to find out optimal price to charge customers on weekends and weekdays using inverse demand function, marginal revenue and marginal cost with step-by-step calculations.

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Economics of internet

Suppose that it is possible to provide internet backbone capacity at a constant marginal capital investment of $5 per megabit per second (mb/s). There are no marginal costs. There are two time periods during the day (for simplicity each will be 12 hours): day and night. During the peak period (daytime) of 250 business days per year, the demand for capacity during daytime for one day is given by
Peak Demand: P = a- bQ
Where P is the price for capacity during the period. During the off-peak period of those 250 days, demand is one-half that of the peak period for each possible price,
Off peak Demand: P = a- 2bQ
On other days, demand is zero. Assume that the interest rate is 10 percent and the facilities do not depreciate.

a. If a = $16, b = 0.08 and existing capacity is 120 mb/s, what would be the socially optimal prices during the two periods? (assume no capacity expansion)

b. What is the optimal amount of capacity and what are the corresponding prices? (assume can expand capacity)

c. The above is called a firm peak case with peak demanders paying all capital costs. Now suppose that the capital cost is $10 and there is no pre-existing capacity. If peak demanders pay all capital costs, what quantity is demanded by peak demanders? If off-peak price is zero, what is off-peak quantity? (fractions are okay). This is the shifting peak case.

d. For the demand curves in c., find the optimal amount of capacity and corresponding prices.

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