Clearvoice is a wireless telephone monopolist in a rural area. There are 100 con

Question

Clearvoice is a wireless telephone monopolist in a rural area. There are 100 consumers, each of whom has a monthly demand curve for wireless minutes of Qd = 100 –100P, where P is the per-minute price in dollars. The marginal cost of providing wireless service is 10 cents per minute. Suppose that Clearvoice charges 40 cents per minute. How large a fixed fee can Clearvoice charge and still persuade consumers to buy the service? What will be its profit from each consumer? [Hint: recall that the largest fixed fee is equal to the consumer surplus of each customer at the price of 40 cents/minute.]

Explanation / Answer

Price charged by clearvoice = 40 cents per minute or $0.40 per minute

Calculate quantity demanded by each consumer at $0.40 per minute -

Qd = 100 - 100P = 100 - 100($0.40) = 60 minutes

Each consumer demands 60 minutes of wireless telephone service in a month at $0.40 per minute.

Calculate price per minute when quantity demanded will be zero -

Qd = 100 - 100P

0 = 100 - 100P

P = $1

Calculate Consumer Surplus -

CS = 1/2 * (Price at which Qd = 0 - Current price charged) * Current quantity demanded

CS = 1/2 * ($1 - $0.40) * 60

CS = $18

The consumer surplus of each consumer at $0.40 per minute is $18.

As we know that largest fixed fee is equal to the consumer surplus of each consumer at price of $0.40 per minute.

Thus, the largest fixed fee that clearvoice can charge and still pursuade consumers to buy the service is $18 per month.

Calculate Total Revenue -

Total revenue = Fixed fee + variable fee = $18 + $0.40 * 60 = $18 + $24 = $42

Calculate Total Cost -

Total cost = Qd * MC = 60 * $0.10 = $6

Calculate profit of each consumer -

Profit = TR - TC = $42 - $6 = $36

The clearvoice's profit from each consumer will be $36.

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