1. Suppose that a long-term-care facility (LTC) has private demand for beds equal to 1104p+2q, 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 120 beds at the LTC, and the facility will admit Medicaid patients to fill all beds not taken by private (non- Medicaid) patients. The LTC facility has total cost equal to q2. The Medicaid reimbursement rate (i.e. the Medicaid price) is fixed at r = 10 (thousand dollars per year).

private resident revenue= 110P-4P^2+2PQ

Medicaid resident revenue=100+40P-20Q

TR=private resident revenue+Medicaid resident revenue

Xc=120

TC=Q^2

Profit=TR-TC

a) Write an expression for the total revenue for the equations. b) Write an expression for the profit. c) Use calculus to find the first order condition with respect to p. Algebraically rearrange that F.O.C. so that p is by itself on the left hand side of your equation (solve for p as function of q). d) Use calculus to find the first order condition with respect to q. Algebraically rearrange that F.O.C. so that q is by itself on the left hand side of your equation (solve for q as function of p). 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.