# Omniscient Wireless Limited (OWL) is planning to roll out a new nationwide, broadband, wireless…

Omniscient Wireless Limited (OWL) is planning to roll out
a new nationwide, broadband, wireless telephone service next month. The firm
has conducted market research indicating that its 10 million potential
consumers are in two segments, which they call the Light segment and the
Regular segment. Light users have less demand for wireless-phone service and in
particular they seem unlikely to have any value for more than 300 minutes of
calls per month. Regular users have more demand for mobile-phone service
generally and have high value for more than 300 minutes per month. OWL analysts
have determined that the best plans to offer to consumers entail 300 minutes
per month and 600 minutes per month, respectively. They estimate that 50% of
users are Light and 50% are Regular, and that each type has the following
willingness to pay for each type of service:

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OWL’s cost per additional minute of wireless service is
negligible, so the subscription cost to the company is \$10 per user, no matter
which plan the user chooses. Each potential customer calculates the net payoff
(benefit minus price) that she would get from each of the usage plans and buys
the plan that would give the higher net payoff, so long as this payoff is not
negative. If both plans give equal, nonnegative net payoffs for a buyer, she
goes for 600 minutes; if both plans have negative net payoffs for a buyer, she
does not purchase. OWL wants to maximize its expected profit per potential
customer.

(a) Suppose the firm were to offer only the 300-minute
plan, but not the 600-minute plan. What would be the optimal price to charge,
and what would be the average profit per potential customer?

(b) Suppose instead that the firm were to offer only the
600-minute plan. What would be the optimal price, and what would be the average
profit per potential customer?

(c) Suppose the firm wanted to offer both plans. Suppose
further that it wanted the Light users to purchase the 300-minute plan and the
Regular users to purchase the 600-minute plan. Write down the
incentive-compatibility constraint for the Light user.

(d) Similarly, write down the incentive-compatibility
constraint for the Regular user.

(e) Use the results from parts (c) and (d) to calculate
the optimal pair of prices to charge for the 300-minute and 600-minute
services, so that each user type will purchase its intended service plan. What
would be the average profit per potential customer?

(f) Consider the outcomes described in parts (a), (b),
and (e). For each of the three situations, describe whether it is a separating
outcome, a pooling outcome, or a semi separating outcome.