1. Suppose that a long-term-care facility (LTC) has private demand for beds equal to 100-5p+3q, where p is the private price (in thousands of dollars per year) and q is the quality level at the LTC. There are a total of 100 beds at the LTC, and the facility will admit Medicaid patients to fill all beds not taken by private (non- Medicaid) patients. So the number of Medicaid patients admitted equals 100 - (100-5p+3q). The LTC facility has total cost equal to q2. The Medicaid reimbursement rate (i.e. the Medicaid price) is fixed at r (thousand dollars per year). a) Write an expression for the total revenue for the LTC facility. b) Suppose that r equals 10. Write an expression for the LTC facility's profit. c) Use calculus to find the first order condition with respect to p. d) Use calculus to find the first order condition with respect to q. e) Your answers from parts c and d provide you with two equations and two variables (p and q are the variables). Solve for the numerical solutions for p and q. f) Now rewrite your profit function with r as a parameter (no longer equal to any particular numerical value). That is, write the Medicaid revenue as r[100 - (100-5p+3q)]. Re-do part d and obtain an equation for optimal quality. g) Given your answer in part f, take the derivative of optimal quality with respect to r. What is the intuition