In Box City, Clear Vision, Inc. has a monopoly as the only cable television carrier in the city. (Assume for purposes of this question that Clear Vision is not regulated.) Suppose that demand for cable service is given by P = 28 - 0.0008Q , where Q is total market quantity of units of service and P is price per unit of service. Assume that Clear Vision's short-run total cost function is given by TC = 120,000 + 0.0006Q2, and that Clear Vision's corresponding marginal cost function is given by MC = 0.0012Q .
(a) Find Clear Vision's profit-maximizing output and price. Determine the resulting profit for Clear Vision.
(b) Suppose that Box City imposes a (specific) tax of t = $1 per unit of service. Find Clear Vision's new profit-maximizing output, price, and profit. (Recall that in class we went over how a tax of this sort alters the total cost function and marginal cost function.)