Suppose that a monopolist has a patent for widgets and the demand curve is given by Q(P) = 12 – 0.02P. The monopolist’s total costs are TC(Q) = 25Q^2 + 500. You may assume that widgets are continuously divisible, like corn oil or sand. a: Find the quantity Q* that maximizes the monopolist’s profit by exploiting the marginal condition, necessary for profit maximization at an interior solution. Neatly show your work. b: Find the price P* that the monopolist charges. Neatly show your work. c: Neatly graph the marginal revenue and marginal cost curves, with Q on the horizontal axis. d: Label relevant areas on your graph using a, b, c, etc. and fill in the following chart.
Suppose that a monopolist has a patent for widgets and the
a: Find the quantity Q* that maximizes the monopolist’s profit by exploiting the marginal
condition, necessary for profit maximization at an interior solution. Neatly show your work.
b: Find the
c: Neatly graph the marginal revenue and marginal cost curves, with Q on the horizontal axis.
d: Label relevant areas on your graph using a, b, c, etc. and fill in the following chart.
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