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Although rational consumers without bequest motives are better off investing exclusively with annuitized instruments in partial equilibrium, we demonstrate the welfare effect of annuitization is ambiguous in general equilibrium on account of pecuniary externalities. Absent institutional constraints like prices and budgets, the optimal consumption rule would have marginal utility increase at the preferential discount rate. In a rational competitive equilibrium where households fully annuitize, the growth rate of marginal utility will be the discount rate minus the interest rate, resulting in a consumption profile that is too flat. Accidental bequests transfer wealth from the old to the young, steepening the consumption profile and yielding a better equilibrium. If households are restricted to Keynesian consumption functions, the optimal irrational equilibrium with standard preferences can replicate observed consumption and macroeconomic behavior, and the equilibrium without annuities delivers higher utility than the equilibrium with annuities. Whereas preceding papers have merely hypothesized that households might engage in socially optimal, yet irrational behavior, the failure of households to annuitize is a real-world example of this. Policymakers should not take steps to encourage more annuitization by the public.