The market demand for medical checkups per day is Q_F = 25(198 + n_C /20,000 - p_F), where n_C is the number of patients per day who are at least 40 years old, and p_F is the price of a checkup. The market demand for the number of dental checkups per day, Q_T, is Q_T = 100(150 - p_T)/3, where p_T represents the price of a dental checkup. The long-run market supply of medical checkups is Q_F = 50p_F - 10p_T. The long-run market supply of dentists is Q_T = 50p_T - 10p_F. The supplies are linked because people decide on a medical and dental career based in part on relative earnings.

a. If n_C = 40,000, what is the equilibrium number of medical and dental checkups? What are the equilibrium prices? How would an increase in n_C affect the equilibrium prices? Determine dp_F /dn_C and dp_T /dn_C.

b. Suppose that, instead of determining the price of medical checkups by a market process, large health insurance companies set their reimbursement rates, effectively determining all medical prices. A medical doctor receives $35 per checkup from an insurance company, and a patient pays only $10. How many checkups do doctors offer collectively? What is the equilibrium quantity and price of dental checkups?

c. What is the effect of a shift from a competitive medical checkup market to insurance-company dictated medical-doctor payments on the equilibrium salaries of dentists?