Initially, the social benefit of surgeries is B =100s4 and that the social cost of surgeries is C =30s.

Assume that there are two types of medical innovations. Innovation 1 ( type 1) makes the benefits B=200s-s^2/4 and innovation 2 (type 2) makes the benefits B=100-s^2/10. For both innovations, the cost remains the same.

(A) What is the socially optimal number of surgeries for each type of innovation?

(B) Assume that individuals can buy insurance and insurance covers two-thirds of the cost of surgeries. How many surgeries would occur if insured individuals decided how many surgeries to get?

(C) Which type of innovation has a larger discrepancy between the social and private number of surgeries [no need to calculate mathematically]?