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This paper introduces a utility function that nests three classes of utility functions: (1) time-separable utility functions; (2) "catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption; and (3) utility functions that display habit formation. Closed-form solutions for equilibrium asset prices are derived under the assumption that consumption growth is i.i.d. The equity premia under catching up with the Joneses and under habit formation are, for some parameter values, as large as the historically observed equity premium in the United States.
Andrew B. Abel (Thu,) studied this question.