The market demand for medical checkups per day is QF = 25(198 + nC /20,000 - pF), where nC is the number of patients per day who are at least 40 years old, and pF is the price of a checkup. The market demand for the number of dental checkups per day, QT, is QT = 100(150 - pT)/3, where pT represents the price of a dental checkup. The long-run market supply of medical checkups is QF = 50pF - 10pT. The long-run market supply of dentists is QT = 50pT - 10pF. The supplies are linked because people decide on a medical and dental career based in part on relative earnings.
a. If nC = 40,000, what is the equilibrium number of medical and dental checkups? What are the equilibrium prices? How would an increase in nC affect the equilibrium prices? Determine dpF /dnC and dpT /dnC.
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?