Question

In: Economics

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

Clearvoice is a wireless telephone monopolist in a rural area. There are 100 consumers in the market, 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. If Clearvoice charges 40 cents per minute, how large a fixed fee can it charge and still persuade consumers to buy? What is it’s profit from each consumer? It’s total profit? What if the firm charges 10,20,30 cents per minute?

Solutions

Expert Solution

Each consumer's demand curve: Qd=100-100P

If P = $0.40 per minute,

Qd = 100 - 100 x (0.40)

Qd = 60 minutes

Flat fee = 60 x 0.40 = $24 per month

Even if a monthly fee of $24 is charged, consumers will buy.

Profit from each consumer = (P - MC) x Q

= (0.40 - 0.10) x 60

Profit = $18 per consumer

Total profit = 18 x 100 = $1800

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If the firm charges 10 cents per minute:

If P = $0.10 per minute,

Qd = 100 - 100 x (0.10)

Qd = 90 minutes

Flat fee = 90 x 0.10 = $9 per month

Even if a monthly fee of $9 is charged, consumers will buy.

Profit from each consumer = (P - MC) x Q

= (0.10 - 0.10) x 90

Profit = $0 per consumer

(Profit is zero, as P = MC)

Total profit = $0

---

If the firm charges 20 cents per minute:

If P = $0.20 per minute,

Qd = 100 - 100 x (0.20)

Qd = 80 minutes

Flat fee = 80 x 0.20 = $16 per month

Even if a monthly fee of $16 is charged, consumers will buy.

Profit from each consumer = (P - MC) x Q

= (0.20 - 0.10) x 80

Profit = $8 per consumer

Total profit = 8 x 100 = $800

---

If the firm charges 30 cents per minute:

If P = $0.30 per minute,

Qd = 100 - 100 x (0.30)

Qd = 70 minutes

Flat fee = 70 x 0.30 = $21 per month

Even if a monthly fee of $21 is charged, consumers will buy.

Profit from each consumer = (P - MC) x Q

= (0.30 - 0.10) x 70

Profit = $14 per consumer

Total profit = 14 x 100 = $1400

Rahul Sunny answered 1 year ago

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