# optimal amount of capacity and corresponding prices

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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#### Solution Summary

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