Suppose that Clear Vision, Inc., a cable television carrier, has the demand, mar

Question

Suppose that Clear Vision, Inc., a cable television carrier, has the demand, marginal revenue, total cost and marginal cost functions given below:

            P = 28 - 0.0008Q

            MR = 28 - 0.0016Q

            TC = 120,000 + 0.0006(Q^2)

            MC = 0.0012Q,                     

where Q = the number of cable subscribers and P = the price of basic monthly cable service. If you are a regulator trying to maximize social efficiency, what (if any) price ceiling would you impose on Clear Vision, Inc.?

Explanation / Answer

Social efficiency occurs where price = marginal cost.

Setting the demand curve equal to the marginal cost function gives

28 0.0008Q = 0.0012Q or

28 = 0.0020Q

so Q = 14,000.

To serve 14,000 subscribers, Clear Vission Inc. would have to charge 28 0.0008 × 14,000 = $16.80.

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