You are a vice president at a company that sells industrial bottling machines. After doing some market research, you estimate that the annual demand curve your company faces for its machines can be described by the equation Q = 5,000 - 0.5P (or P = 10,000 - 2Q ). Your firm's marginal costs include the cost of production and the cost of compensating your salespeople, who receive a commission on each sale they make. Altogether, the marginal cost of producing and selling a machine is $2,000. Your annual fixed costs are $2,000,000 per year.

(a) You need to set a price for your machine. This is the price that you will sell at to all customers. What price should you set? How much profit will you make?

(b) The CEO of the company is pushing you on why the company can't sell more. You try to explain demand curves, and tell her that in order to sell more units you'll have to lower the price. She scoffs and says, "That's silly. Just get the sales team to work harder!" She proposes increasing their commission rate, saying, "if they get paid more for each sale they make, they'll make more sales. That's basic economics!"

You calculate that increasing the commission rate would raise your marginal cost from $2,000 to $2,500 per unit. Increasing commissions would also increase sales. Specifically, annual sales would increase by 200 units above what would have previously been sold at any price.

Is increasing the commission rate a good economic decision? Briefly explain.