Consider a cable TV company that has a fixed cost of $48 million and a marginal

Question

Consider a cable TV company that has a fixed cost of $48 million and a marginal cost of $5 per subscriber. The company is regulated with an average-cost pricing policy. The two columns of the following table show three points on the initial demand curve. For example, at a price of $15 the quantity demanded is six million subscribers. For each $2 reduction in price, the number of subscribers increases by one million. Fill in the blanks in the following table.


Price Subscribers (millions) Average Cost
$15 6
13 7
11 8

Explanation / Answer

Average cost pricing policy means that the cable company would price where their average total costs meets the market demand. Total cost = 48 + 5Q Average total cost is = 48/Q + 5 Demand(Q) = 13.5 - P/2 ( solve this for Q) (Q-13.5)*2 = -P, P = 27 - 2Q Set the equations equal then solve it: 27 - 2Q = 48/Q + 5 22 = 48/Q + 2Q 22Q = 48 + 2Q^2 2Q^2 - 22Q + 48 = 0 Q = 3 or 8 Price under each: 27-2Q = 21 or 11 Revenue: 3*21 = 63 8*11 = 88 so the firm would produce at price at $11 dollars

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