... andefficiency (1/εh) considerations. The implication of ( 13. 14) for the optimum pricing of annuities depends on the welfare function, W, and on the joint distribution of incomes, (y1, ,yH), and ... Pricing of Annuities •1 13 13. 3 Second-best Optimum Pricing of Annuities Governments do not engage, for well-known reasons, in unconstrainedlump-sum redistributions of incomes. In contrast, most annuities are ... above,also raises the population growth rate. By (12 .3) , the first effect raises h,while the second decreases it. Since∞0dh(z,α,g)dαdz = 0,(12.12) the crucial question is which of these effects...