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A model of optimal consumption and portfolio choice that captures the notions of local substitution and irreversible purchases of durable goods is studied. Necessary and sufficient conditions for a consumption and portfolio policy to be optimal are provided. A closed-form solution of the optimal consumption and portfolio policy is given. The optimal consumption policy consists of a possible initial "gulp" of consumption, or a period of no consumption, followed.by a process of accumulated consumption with singular sample paths. The equilibrium risk premium in a representative investor economy with a single physical production technology is computed.
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Hindy et al. (1993) studied this question.
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