# Ch 3 UMP - University of Toronto Department of...

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 C HAPTER 3 Utility Maximization Problems (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ C HAPTER 3: Utility Maximization Problem 1 Updated: 10/16/2012 Fixed typos are shaded yellow 1. Introduction This chapter shows the “ mechanics ” of solving differentiable utility maximization problems (UMP) and we will examine the economics of various utility models in chapter 4. First, you should review these topics covered in chapter 2 where we laid the foundation for modeling consumer choice: 1 Thanks: Asad Priyo and Adam Michael Lavecchi. For feedback, comments and typos please e-mail [email protected] Universe of Choices Set of Commodities Consumer Price Taker Exogenous Income Consumption Set Rational Preferences Utility Function(s) 𝑼(𝒒 𝟏 , . . , 𝒒 𝑵 )

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 C HAPTER 3 Utility Maximization Problems (this version 2012-2013) The standard intermediate-level microeconomics model for understanding, explaining, and predicting consumer choice of the amounts of commodities is the Utility Maximization Problem (UMP) where the consumer chooses quantities of goods 1 and 2 to maximize their utility from their consumption subject to the constraints that the bundle is affordable and physically available for consumption. The commodities with uniform prices general UMP is (can you write down the UMP for say commodities): , ( , ) . . , , Notice: We’re assuming tha t the consumption set is {( , ) } ). Of course, as we saw in chapter 2, it’s possible to have other kinds of consumption sets. For example, if we are modeling food consumption we could make food and all other goods and assuming that you need ( say) 1,500 calories a day to “live” (or not be cranky like me) the consumption set could be { , , } ). We’re assuming {( , ) } for convenience. ● We’re assuming that consumers maximize their own individual utility function and not some “group”/“clan”/“social”/“collective” utility function. This means that in ECO 204 we ’re not modeling situations where individuals act to “serve a higher goal” (for example, “religious behavior”). ● We’re assuming that a consumer’s individual utility function depends on her consumption levels and not on anyone else’s level of consumption. T his isn’ t always true in real life: sometimes our consumption level depends on what others consume. For example, in pop music there is a “bandwagon effect” where you (not me!) consume music by Justin Bieber because everyone is listening to and buying his music (he’s “popular” ). In this case, the individual utility function becomes a function of yours and others’ consumpt ion levels: ( ( ), ) Here the amount of good 1 you consume depends on total amount of good 1 that others consume where in a bandwagon effect this relationship is positive 2 . On the other hand, you may be a “snob” and w on’t consume Justin Bieber music precisely
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