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Question 2 (32 pts.) A regulator has received an application for a vertical merger between the monopolist of an intermediate good, a lab test, and the monopolist of a final good, medical diagnosis. The intermediate good and the final goods are used in one-to-one fixed proportions. The cost of converting each lab test into a medical diagnosis is S 5. The Ministry of Health provides a universal copayment plan for each medical diagnosis that covers the cost of each lab test. The Ministry of Health objects to the proposal of a vertical merger on the grounds of expost moral hazard that will drive up the number of medical diagnoses, Qd. The Ministry of Health has estimated that for a competitive industry: - Access to a copayment plan results in 95 medical diagnoses, i.e., Q; = 95 sold at Pd = 5, - In the absence of a copayment plan, Qd = 90 and Pd = 10. a) (2 pts.) Calculate the demand function for the final good, medical diagnosis. b) (2 pts.) Calculate the average cost of a lab test. c) (2 pts.) Write down the optimization problem of the upstream firm. d) (2 pts.) Calculate the first-order condition yielding the MR = MC rule for the upstream firm. e) (2 pts.) Calculate the derived demand for lab tests. f) (4 pts.) Calculate that the quantity of lab tests is Q; = 15 and the corresponding price Pl. Do NOT skip steps