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Consider a situation where a city is considering services from one cable provider in a given area. Given the demand and total cost functions of

P = 28 - 0.0008Q
TC = 120,000 + 0.0006Q2

Where Q is number of cable subscribers and P price in dollars of monthly cable service.

1. How many cable subscribers would be expected if cable firm was allowed to operate completely unregulated
2. How many cable subscribers would be expected if company acted like a perfect competitor
3. How many cable subscribers would be expected if city did not allow the firm to charge more than $18 price
4. What is profit if company was allowed to operate completely unregulated
5. What would be deadweight loss if company acted like a perfect competitor
6. What would be gain in social welfare if company was forced to act like a perfect competitor instead of an unregulated monopoly

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This posting determines gain in social welfare.

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1. How many cable subscribers would be expected if cable firm was allowed to operate completely unregulated
When the firm is unregulated, it can play as a monopoly and maximize it profit by first order condition, MR = MC.
The firm faces the demand P = 28 - 0.0008Q
Then the total revenue is TR = P*Q =28 - 0.0008Q2
Marginal revenue is MR = dTR / dQ = 28 - 0.0016Q
Its marginal cost is MC = dTC / dQ = 0.0012Q
So the first order condition, MR = MC is:
28 - 0.0016Q = ...

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