Consider the following insurance model with adverse selec- (a) Give a diagrammatic description of…
Consider the following insurance model with adverse selec-
(a) Give a diagrammatic description of the optimal (two-contract) menu for the insurance monopolist. In particular, draw the status-quo (no con-tract) point in the (W1,W2) space, and indifference curves corresponding to the two types for both the insuree and the insurer. Show that the binding IC constraint is that the high-risk insuree would not want to mimic the low-risk insuree, and that the high-risk insuree gets full insurance (W1 = W2). Argue informally that the high-risk insuree may or may not get a rent (depending on the probability p), and that he gcts a rent if some insurance is given to the low-risk insuree.
(b) Perform the same analysis as in question a, but use algebra. Hints: the question a to guess which constraints are binding (ignore the others and check them later); let r denote the inverse function of the insuree's von Neumann-Morgenstern utility function U. Describe a menu as (U1, U2), (U1,, U2), where U1 is the low type's number of utils in state I. etc. Notice that the monopoly's objective is concave in these utility levels and the constraints are linear. Solve the monopoly's program. (For the answer, see Stiglitz 1977.)
