The Clear Line Communications Corporation currently has the following linear structure of prices for long–distance calls between Durham and India: $2.00 for each minute of calls. Market research indicates that there are five types of consumers in the market (equal numbers of each type) demanding the following numbers of minutes/day at various prices/minute. $1 $2 $3 $4 $5
Type 1 5 min 4 min 3 min 2 min 1 min
Type 2 4 min 3 min 2 min 1 min 0 min
Type 3 3 min 2 min 1 min 0 min 0 min
Type 4 2 min 1 min 0 min 0 min 0 min
Type 5 1 min 0 min 0 min 0 min 0 min
According to this table, Type 1 customer will buy 1 minute at $5, an additional 1 minute at $4, another incremental one minute at $3, yet another minute at $2, and finally one more minute at $1. Thus the Type 1 consumer would buy a total of 5 minutes per day at the price of $1 / minute, whereas only 1 minute per day at the high price of $5/minute. Assume zero marginal and fixed costs.
A) Compute the profit–maximizing linear pricing scheme.
B) Compute the profit–maximizing quantity–discount scheme.
C) If the quantity–discount scheme yields higher profits than the linear scheme, why does it do so? If not, why not?