Consider the model of Gaynor & Town (2012) in which hospitals choose quality with a fixed price. Recall that the model begins with a demand specification, qj = sj (zj , z\j ) × D(¯p, zj , z\j ), where the hospital’s market share sj is a function of its own quality zj and the quality of other hospitals z\j , and where total market demand is similarly determined by quality as well as the administratively set price ¯p. Hospital costs are reflected by the function, cj = c(qj , zj ) + F, where F denotes fixed costs, and hospital profits are denoted πj = ¯pqj − cj .
(a) Assuming hospitals are profit maximizing, derive the optimal level of quality as a function of share and demand elasticities. Show all of your steps.
(b) Using your equation from part 1, discuss how hospital quality will change if the hospital becomes an exclusive provider in a given insurer network (in other words, the hospital’s market share is constant with regard to quality changes).