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Rotman Commerce

University of Toronto Rotman School of Management Finance D.J.S. Brean 21 September 2004 _______________________________________________________________________________ The 2-Period Model of Intertemporal Allocation of Consumption The 2-period model of intertemporal allocation of consumption, together with its extension to a simple model of investment, provides a useful framework for understanding several important relationships and decisions in finance. The 2-periods may be thought of as: now versus later, or today versus tomorrow, or the present generation versus future generations. The 2-period context captures the idea that one makes decisions today concerning consumption, savings and investment that have consequences for consumption tomorrow. The focus is on consumption. The idea is that money is used to consume things - food, clothing, housing, entertainment, et cetera. In our course in Finance, the reason for introducing the 2-period model is to provide a conceptual framework for understanding the economic function of capital markets and the behaviour of individuals with respect to that market. Among the concepts and issues addressed in the 2-period model are: Why people save Why people lend Why people invest Determinants of the interest rate The economic (allocative) role of the interest rate Present value Return on investment The opportunity cost of investment. Optimal investment criterion 1 Value maximization Dividend decision The relevance of finance Capital market - financial intermediaries A Quick Review of Consumer Theory There is a strong parallel between the analytic techniques applied in the problem of 2-period allocation of consumption and the techniques used in standard consumer theory. In consumer theory, individuals maximize utility defined over goods. The total amount of consumption is subject to a budget constraint. For example, consider the problem of buying apples and oranges with a given amount of money, say $10.00. Apples cost $0.50 each and oranges cost $1.00 each. Since the total amount of apples plus oranges that can be purchased is limited to $10.00, we know that: P aN a P .No= $o0 where: P a Price of an apple N a Number of apples purchased P o Price of an orange N = Number of oranges purchased o How many apples and how many oranges does a person buy? That depends on her preference for apples and oranges in light of the prices and her budget constraint ($10.00). In the jargon of consumer theory, a consumer maximizes utility - defined, in this case, over apples and oranges - subject to a budget constraint. The budget constraint is: P aN a P .No= o10 The consumers utility function represents her preferences, viz., Utility is a function of apples and oranges or 2
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