Ch 6 Intertemporal Consumption

For example does the agent perceive consumption today

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Unformatted text preview: be representable by a utility function. For example, does the agent perceive consumption today and tomorrow as substitutes in the sense that she’s willing to eat less corn today in order to eat more tomorrow? Or does she perceive consumption today and tomorrow as complements in the sense that for each unit of corn consumed today she will consume (say) 2 units of corn tomorrow? Or does she have some type of preferences? Whatever the case, we assume that there’s a utility function representing her preferences. For example, the agent could have: Cobb-Douglas Preferences {( } ) defined over The consumer perceives consumption at and as imperfect substitutes and the consumer must consume positive amounts of corn at . One of features of this utility function is that the consumer is willing to substitute consumption across periods (for example, eat less today and eat more tomorrow, or vice versa) 2 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( The consumer perceives consumption at Complements Preferences {( } ) defined over ) and as complements such that for each unit of corn consumed at she must consume units of corn at (can you show this?). Unlike a consumer with Cobb-Douglas preferences, a consumer with complements preferences will not substitute consumption between periods – if she consumes more today, then she must consume more tomorrow. In the “basic UMP model” the consumer receives an income of each period. Because there are two periods in the inter-temporal UMP model, agents receive individual-specific income in each period where this income is not in units of corn: units of corn “income” at the beginning of units of corn “income” at the beginning of Since these corn incomes are exogenously given, we say that the consumer is “endowed” (gifted) with corn incomes and . Corn incomes are uncorrelated across individuals and/or over time -- that is, just because you have a high corn income at doesn’t mean that you will have a high corn income at and if your neighbor has a large endowment, it doesn’t mean that you will have a large endowment. Given preferences over and corn incomes the optimal amounts of corn to consume at agents will solve an inter-temporal UMP (done below) and choose . At there are two possibilities: ❶ The agent partially or fully consumes her income, i.e. ❷ The agent consumes more than her income, i.e. That is, at That is, at the agent “saves” corn. the agent “borrows” corn. Where do savers save corn and where do borrowers borrow corn from? Naturally, from the Royal Bank of Corn (RBC)! An agent who saves when she’s young will at (old age) withdraw her savings (principal plus interest) and be able to eat more than her old age corn income, i.e. . On the other hand, an agent who borrows when she’s young will have to pay back the loan at (old age) and because of this she will have to consume less than her old age corn income, i.e. : 3 ECO 204 Chapter 6: Inter-temporal Co...
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