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An economy with agents having constant yet heterogeneous degrees of relative risk aversion prices assets as though there were a single decreasing relative risk aversion "pricing representative" agent. The pricing kernel has fat tails and option prices do not conform to the Black-Scholes formula. Implied volatility exhibits a "smile." Heterogeneous beliefs about distribution parameters also implies non-lognormal pricing kernels with fatter tails and "overpricing" of out-of-the-money options. Heterogeneity as the source of non-stationary pricing fits Rubinstein's (1994) interpretation of the "over-pricing" as an indication of "crash-ophobia". Rubinstein's term suggests that those who hold out-of-the-money put options have relatively high risk aversion or relatively high subjective probability assessments of low market outcomes. The essence of this explanation is heterogeneity in investor attitudes towards risks and probability beliefs.

This paper explores how private and social incentives for fertility may have combined to produce the complex fertility pattern observed in Israel in the past half‐century. Fertility has declined within some ethnic‐religious groups, moderately increased in others, and parts of the ultra‐Orthodox Jewish population have experienced a reverse fertility transition, in which childbearing has increased rapidly and substantially. We present a theoretical analysis of the social dynamics of fertility that shows how private preferences, preferences for conformity to social norms in childbearing, and piecewise linear child allowances could have combined to yield such a complex fertility pattern. We then explain the identification problem that makes it so difficult to infer the actual Israeli fertility process from data on completed fertility. (JEL: J13, Z13, H53)