This paper shows how models of insurance markets with asymmetric information can be calibrated and solved to yield quantitative estimates of the consequences of government regulation. We estimate the impact of restricting gender-based pricing in the United Kingdom retirement annuity market, a market in which individuals are required to annuitize tax-preferred retirement savings but are allowed considerable choice over the annuity contract they purchase. After calibrating a lifecycle utility model and estimating a model of annuitant mortality that allows for unobserved heterogeneity, we solve for the range of equilibrium contract structures with and without gender-based pricing. Eliminating gender-based pricing is generally thought to redistribute resources from men to women, since women have longer life expectancies. We find that allowing insurers to offer a menu of contracts may reduce the amount of redistribution from men to women associated with gender-blind pricing requirements to half the level that would occur if insurers were required to sell a single pre-specified policy. The latter "one policy" scenario corresponds loosely to settings in which governments provide compulsory annuities as part of their Social Security program. Our findings suggest that recognizing the endogenous structure of insurance contracts is important for analyzing the economic effects of insurance market regulations. More generally, our results suggest that theoretical models of insurance market equilibrium can be used for quantitative policy analysis, not simply to derive qualitative findings.