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{"ops":[{"insert":"There are an infinite number of firms that can engage in research and development at a cost of $5 cach. The R&D is risky and may or may not be successful. If successful, a new product will be developed with a demand curve ofQ(p) 200 10p and a cost of production equal to C(q) = 10q in each period of time. The discount factor is 8.5. If n firms engage in R&D, the probability of atleast one success is p(n) = 1-e with a = 0,2031.a. Suppose that once the product is developed all firms will be able to freely enter the industry and copy the product. How many firms will engage in R&D?b. Suppose that the government offers research grants to pay the cost of research in this product. How many such grants should the goverment offer?c. Suppose that the government offers a prize for the first firm to develop this product. Each firm doing R&D thinks it is equally likely to be first. That is, the probability of winning the prize is How large of a prize should the government offer? \n"}]}

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