1) Patents and Trade Secrets [30] A firm can invent a new product. That firm is the only entity in that world that can invent the product. Doing so leads to a research cost of r, to be paid once in the first period. The monopoly price for this new product is 6$ per unit and the firm can produce this good, if research have been done, at a cost of $ where q is the quantity of good produced. Time is discrete and the firm faces the same price and cost function every period. Without a patent, other firms enter the market and those firms can produce the product more efficiently, therefore without a patent the firm makes 0 profit. a) What is the value for the firm of a patent of infinite duration? Assume a discount factor 8 = 0.9. b) Suppose that there is no possibility for the firm of keeping a trade secret. The research cost for that good is 30$. The government can create a patent for the good before the firm has to make a research decision. The terms of the patent cannot be changed after its creation. What is the duration of the patent that the government should pick? c) Suppose now that the firm must choose between a 20 year patent and a trade secret that cost 1$ per year to keep. Should the firm request a patent or should it keep a trade secret? d) If keeping a trade secret is possible, does your answer for part b) changes? Why or why not