# Solved Assignments [Requires calculus] In Figure 8-3 the demand facing your firm is Q = 12 – P, and total cost is C…

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[Requires calculus] In Figure 8-3 the demand facing your firm is Q = 12 − P, and total cost is C = 4Q. Q is your annual output, and P is its price. Show that your profit-maximizing output is 4 units, priced at \$8 each, and that your economic profit is \$16. a. Now assume that raising marginal cost to \$5 raises the demand curve by \$2 at all outputs. Show that you now maximize profits by producing 4.5 units, which you sell at \$9.50 each. What is the largest increase in marginal cost you will tolerate to shift the demand curve upward by \$2? Explain in commonsense terms why it is less than \$2. b. Start again from the original demand and marginal cost, and assume that you can invest in advertising to inform buyers about a new use for your product. With probability 0.5 it raises the demand curve by \$4 at all outputs, and with probability 0.5 it has no effect. Before considering the campaign’s cost, by how much per year does expected profit increase if you undertake it? Figure 8-3

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