This paper introduces a model of household consumption and savings in which household members have imperfectly aligned altruistic preferences. Specifically, member A values his own consumption more than member B values A's consumption. Each period, members individually choose the amount of household wealth to consume as Nash best responses. At each point in time, the household consumes a higher fraction of wealth than under the full commitment Pareto optimum. Ex-ante Pareto optimal household consumption plans are not subgame perfect because both members wish to deviate to increase their own consumption. As a result the household is willing to pay for a technology that commits them to an optimal lifetime consumption plan. Despite both members individually having time consistent exponential discount rates, equilibrium household consumption dynamics are captured by a single representative agent with hyperbolic time preferences.
Hertzberg, Andrew. "Exponential Individuals, Hyperbolic Households." Working paper, Columbia Business School, October 2010.
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