The Typical Competitive Problem. Consider a representative competitive insurer purchasing medical care from a competitive goods market selling at marginal cost, and providing insurance within the informational structure outlined above. The firm chooses a co-payment and premium that maximizes consumer utility, subject to a break-even constraint, and incentive compatibility for the consumer. The insurer knows the quantity of medical care demanded by consumer h , given the co-payment and income, according to q(W − I , m, h) . The firm’s optimization problem can be written as: max 1u(W − I − mq* , q* , h)dh I ,m≤ MC ∫ s.t. I + (m − MC)E(q* ) ≥ 0 and q* = q(W − I , m, h)
The Typical Competitive Problem. Consider a representative competitive insurer purchasing medical care from a competitive goods market selling at marginal cost, and providing insurance within the informational structure outlined above. The firm chooses a co-payment and premium that maximizes consumer utility, subject to a break-even constraint, and incentive compatibility for the consumer. The insurer knows the quantity of medical care demanded by consumer h , given the co-payment and income, according to q(W − I , m, h) . In this case of heterogeneous consumers, we adopt the simplifying convention that consumers either purchase one unit of the medical good, or none at all. That is, consumers vary along the extensive margin only. The firm’s optimization problem can be written as: max 1 u(W − I − mq* , q* , h)dh I ,m≤ MC ∫ s.t. I + (m − MC)E(q* ) ≥ 0 and q* = q(W − I , m, h)
