Fig. 3.

Efficient annuities when savings are observable and contractible. This figure plots the pair of annuity contracts solving Eq. (5) when savings is observable and contractible and when V̄^H (high-risk types’ minimum utility) is equal to the utility high-risk types get from their full insurance actuarially fair contract. The annuity curves plot the size of the life-contingent annuity payments as a function of the age of annuitant. “Desired consumption (bond-holding) of ‘deviating’ high-risk types” refers to the hypothetical optimal consumption (bond-holding) pattern for high-risk types who are given the low-risk types’ equilibrium annuity and can freely save.