Suppose the inverse demand curve for a new product is given by () = 250 2, marginal revenue is () = 250 4, and marginal production cost is = 50. (a) Assuming that the firm received a patent that gives it exclusive rights to sell the product, calculate its optimal output, price, and operating profit. Suppose that the fixed cost of developing the new product is = 5000. (b) Will it invest in developing the product if your answer from (a) holds? (c) Calculate social welfare in the presence of the patent, equal to the sum of consumer surplus and net profit. Does society benefit from the patent (suppose the market would not exist without inventing product)? What if = 10,000