Question: [Requires calculus] In Figure 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?
