A company is considering building a bridge across a river. The bridge would cost $3 million to build and nothing to maintain. The anticipated demand over the lifetime of the bridge is x = 800 - 100p, where x is the number of crossings (in thousands) given the price per crossing p.
a. If the company builds the bridge, what will be the profit-maximizing price?
b. Will that price lead to the ancient number of crossings? Why or why not?
c. What will be the company's profit or loss? Should it build the bridge?
d. If the government were to build the bridge, what price should it charge?
e. Should the government build the bridge? Why or why not?