A monopolist is a manufacturer who can manipulate the price of a commodity and usually does so with an eye toward maximizing profit. When the government taxes output, the tax effectively becomes an additional cost item, and the monopolist is forced to decide how much of the tax to absorb and how much to pass on to the consumer. Suppose a particular monopolist estimates that when x units are produced, the total cost will be

dollars and the market price of the commodity will be p(x) = 15 − 3/8x dollars per unit. Further assume that the government imposes a tax of t dollars on each unit produced.

a. Show that profit is maximized when

b. Suppose the government assumes that the monopolist will always act so as to maximize total profit. What value of t should be chosen to guarantee maximum total tax revenue?

c. If the government chooses the optimum rate of taxation found in part (b), how much of this tax will be absorbed by the monopolist and how much will be passed on to the consumer?

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C(x) 7 x + 5r + 100 || Too 8