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Unformatted text preview: Chapter 5: Demand Tuesday, June 29 UTILITY ― Utility ‖ is a fancy word for happiness. The basic assumptions in economic theory are that consumers make choices to maximize their utility, and that firms make choices to maximize their profit. Consumer choice is often modeled using utility functions (which give a level of ‗happiness‘, dependent on different variables, e.g. consumption of different goods. Consumers maximize these subject to the constraints imposed by their personal budgets, etc. For example, a utility function over goods X and Y could be something like U(X,Y) = X 2/3 Y 1/2 UTILITY Utility is measured in ― utils ‖, but no one really knows what a util is, or how many utils anyone has. Utility is not necessarily measured in dollar amounts. That is, a ―util‖ is not necessarily the amount of happiness that you would get from an extra dollar of spending. Models of utility can be constructed in this way, but the concept itself is more general. QUASILINEAR UTILITY (bonus slide, not required ) In econ 1, we will basically be assuming something called ‗quasilinear utility‘, i.e. a utility function that takes the form U = V(X) + Y total benefit from good X (This is the ‗total benefit function‘ that we often use in this class.) total utility, from X and Y. (This takes into account both the happiness gained from consuming good X, and the happiness from consuming other goods.) QUASILINEAR UTILITY (bonus slide, not required ) In econ 1, we will basically be assuming something called ‗quasilinear utility‘, i.e. a utility function that takes the form U = V(X) + Y Consumers maximize this function, subject to the constraint that P X X + P Y Y = I , or simply PX + Y = I , which implies that Y = I – PX . Thus, consumers are effectively maximizing the value of the function U = V(X) + I – PX. Setting the derivative with respect to X equal to zero, we get the condition V'(X) = P , that is, marginal benefit equals price . OTHER EXMPLES OF UTILITY FUNCTIONS (also not required) CobbDouglas utility: U = X α Y β Perfect complements utility: U = min{ α X, β Y} Perfect substitutes utility: U = α X + β Y MARGINAL UTILITY The marginal utility of good X is the amount of extra happiness (measured in utils, not necessarily in dollar amounts) that you get from one extra unit of good X. Equivalently, it is the rate of change in utility as more of good X is consumed, ΔU/ΔX . Bonus information : With quasilinear utility U = V(X) + Y, the marginal utility of good X is V'(X), or , and the marginal utility of good Y (the ‗numeraire‘) is 1....
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This note was uploaded on 08/03/2010 for the course ECON 1 taught by Professor Bergstrom during the Summer '07 term at UCSB.
 Summer '07
 Bergstrom
 Utility

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