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Ch 6 Intertemporal Consumption

Ch 6 Intertemporal Consumption - University of Toronto...

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ C HAPTER 6: Modeling Inter-temporal Consumption 1 Updated: 1/18/2013 Fixed typos are shaded yellow 1. Introduction The Utility Maximization Problem (UMP) developed in previous chapters modeled a consumer ’s choice of the quantities of commodities (goods) to be consumed in a time period. For example, if a price taking consumer’s monthly income is then we can model her monthly consumption of (say) two goods by solving the UMP: ( ) Here ( ) is a utility function in terms of the amounts of goods 1 and 2 (for example ( ) ). This “basic UMP models the consumption of goods over a time period but not consumption over several time periods (“inter - temporal consumption”). As such, the basic UMP model can’t model how economics agents save over time. In this chapter we develop an inter-temporal UMP model which allows us to model consumption over several periods allowing for the possibility that the consumer may sacrifice consumption in one period in order to consume more in another period. For example, a consumer could save (reduce consumption) today in order to consume more tomorrow; alternatively, a consumer could borrow (increase consumption) today by consuming less tomorrow (after all, the loan must be paid back). 2. Inter-temporal Consumption Model: Assumptions Consider an economy where all agents are assumed to live for exactly two periods: at the individual is “young” and at the individual is “old” 2 . We will often refer to as “today” and as “tomorrow”. In contrast to the “basic UMP model” in which there are several goods, the inter-temporal UMP model has exactly one good: corn . 1 Thanks: Asad Priyo, Adam Michael Lavecchi, Inna Bershtadt. For feedback, comments and typos please e-mail [email protected] 2 Later in this chapter we will relax this assumption and model agents who live for more than 2 periods. Note to self: in next version of ECO 204 and the chapters extend this model to an overlapping generations model (see Blanchard and Fischer).
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 6: Inter-temporal Consumption (this version 2012-2013) Since corn is the only good and all agents live for two periods, the only decision agents have to make is how much corn to consume at and at Amount of corn consumed by an agent at (i.e. when the agent is young) Amount of corn consumed by an agent at (i.e. when the agent is old) As with consumer theory we have to specify what combinations of are physically available for consumption. The inter- temporal corny consumption set (sorry, couldn’t resist) is: {( ) } ( This consumption set shows all bundles of corn available for consumption over an agent’s lifetime. Next, as with consumer theory, we assume the agent has rational preferences which in ECO 204 are assumed to be representable by a utility function. For example, does the agent perceive consumption today and tomorrow as substitutes in the sense that
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