Firm 1 is a monopoly due to a patent on a newly discovered driverless vehicle technology. The firm faces the market demand given by the following inverse demand function: P = 2500 2Q. The total cost of production is TC = 100,000 + 0.5Q 2 and the marginal cost is MC = Q.

a. What is Firm 1's profit maximizing quantity? What price will they charge per unit? Compute the profit.

b. Now suppose that the patent expires and other firms enter resulting in a monopolistic competitive market with each firm distinguishing their product and establishing a brand name. There are no barriers to entry, however, a fixed cost of $100,000 is required to purchase equipment and lease workspace. So the cost of production is same as when the firm was a monopoly TC1 = 100,000 + 0.5Q1 2 . Given the entry of other firms, Firm 1 faces a demand of P1 = 1000 2Q1. Compute the firm's profit.

c. Firm 1 decides to engage in a major advertising campaign so as to increase the brand value and convince consumers their product is superior to others. Analysis shows that the advertising campaign will boost demand for Firm 1's product to P1 = 1500 2Q1. The advertising agency has asked for $200,000 to be paid up front. Should Firm 1 go with this advertising strategy?

d. For what range of advertising cost does it make sense for Firm 1 to engage in advertising?