Public Economics Lectures Part 1: Introduction

Rothschild-Stiglitz: First Best Solution
In first best, insurer can distinguish types (perfect information)
In this case, equilibrium is separating
Plugging in α 2 = 1−p i
p i
α 1 , each type solves
max(1 − p i )u(w − α 1 ) + p i u(w + 1 − p i
α 1 ).
α 1
p i
Solution
Set MRS 12 = 1−p i
p i
, i.e. u ′ (c 1 ) = u ′ (c 2 ), i.e. full insurance
Both types are perfectly insured: earn their expected income
(1 − p i )w regardless of the state.
Public Economics Lectures () Part 6: Social Insurance 15 / 207