Phone companies used to sell minutes of phone calls at the same price no matter how many phone calls a customer made. (We will abstract away from the fact that they charged different prices at different times of the day and week.) More recently, phone companies, particularly cell phone companies, have become more creative in their pricing.
A:
On a graph with “minutes of phone calls per month” on the horizontal axis and “dollars of other consumption” on the vertical, draw a budget constraint assuming the price per minute of phone calls is p and assuming the consumer has a monthly income I .
(a) Now suppose a new option is introduced: You can pay $Px to buy into a phone plan that offers you x minutes of free calls per month, with any calls beyond x costing p per minute. Illustrate how this changes your budget constraint and assume that Px is sufficiently low such that the new budget contains some bundles that were previously unavailable to our consumer.
(b) Suppose it actually costs phone companies close to p per minute to provide a minute of phone service so that, in order to stay profitable, a phone company must on average get about p per minute of phone call. If all consumers were able to choose calling plans such that they always use exactly x minutes per month, would it be possible for phone companies to set Px sufficiently low such that new bundles become available to consumers?
(c) If some fraction of consumers in any given month buy into a calling plan but make fewer than x calls, how does this enable phone companies to set Px such that new bundles become available in consumer choice sets?
B:
Suppose a phone company has 100,000 customers who currently buy phone minutes under the old system that charges p per minute. Suppose it costs the company c to provide one additional minute of phone service but the company also has fixed costs FC (that don’t vary with how many minutes are sold) of an amount that is sufficiently high to result in zero profit. Suppose a second identical phone company has 100,000 customers that have bought into a calling plan that charges Px = kpx and gives customers x free minutes before charging p for minutes above x.
(a) If people on average use half their “free minutes” per month, what is k (as a functions of FC, p,c and x) if the second company also makes zero profit?
(b) If there were no fixed costs (i.e. FC = 0) but everything else was still as stated above, what does c have to be equal to in order for the first company to make zero profit? What is k in that case?