A consumer’s demand for a medical service is Q=100−P_P where P_P is the out-of-pocket price she actually faces. She is considering four different insurance options: uninsurance, full insurance, a 50% coinsurance plan, and a copayment plan with a $25 copay.

a. Assume this service has a list price of P_L =$70. Calculate Q under each insurance plan.

b. Calculate the amount of social loss under each insurance plan.

c. Derive a general expression for social loss as a function of x and P_L, where x is the copay amount under a copayment plan. For simplicity’s sake, assume x < P_L.

d. Derive a general expression for social loss as a function of y and P_L, where y is the coinsurance rate.