1. 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
Type1 5min 4min 3min 2min 1min
Type2 4min 3min 2min 1min 0min
Type3 3min 2min 1min 0min 0min
Type4 2min 1min 0min 0min 0min
Type5 1min 0min 0min 0min 0min
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. (In a linear pricing scheme, every minute is priced the same.
b) Compute the profit -maximizing quantity -discount scheme. (HINT: Find what is the best price that you should charge for each minute.)
c) If the quantity-discount scheme yields higher profits than the linear scheme, why does it do so? If not, why not?