204_summer_2009_lecture_4

204_summer_2009_lecture_4 - University of Toronto...

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Unformatted text preview: University of Toronto Department of Economics ECO 204 Summer 2009 Sayed Ajaz Hussain Lecture 4 1 Ajaz Hussain. Department of Economics Last Time ¡ Some interesting utility functions ¢ Cobb ‐ Douglas ¢ Complements ¢ Perfect substitutes ¡ Graphing indifference curves ¡ Marginal rate of substitution ¢ Interpretation and application ¡ Monotonic transformations ¡ Non ‐ convex preferences Ajaz Hussain. Department of Economics 2 Today ¡ Modeling some preferences ¡ Utility maximization problem (UMP) ¢ Optimal choice & Sensitivity analysis ¢ Cobb ‐ Douglas utility function ¢ Complements utility function ¢ Perfect substitutes utility function ¢ Some interesting utility functions ¡ A perceptions based explanation for perfect competition ¡ 3 mini case studies 3 Ajaz Hussain. Department of Economics Modeling Some Preferences Ajaz Hussain. Department of Economics 4 Cocaine Ecstasy Else Food Addiction Subsistence Subsistence level Optimal Choice ¡ Consumers make optimal choices by maximizing utility given budget (UMP) ¡ Ahead: ¢ Assumptions ¢ Setting up UMP ¢ Solving UMP ¢ Optimal choice ¢ Sensitivity analysis ¢ Demand function (“curve”) Ajaz Hussain. Department of Economics 5 Assumptions ¡ Consumer: ¢ has consumption set (consisting, say, of N goods) ¢ preferences given and represented by utility function ¢ has (real) income Y ¢ is price taker ¡ Prices: ¢ Real (i.e. not nominal) ¢ Uniform or non ‐ uniform ¢ Uniform prices do not vary with quantity purchased o Example? ¢ Non ‐ uniform prices do vary with quantity purchased o Example? ¢ Typical to assume prices uniform Ajaz Hussain. Department of Economics 6 UMP ¡ Consumer must decide how much of each good to consume ¡ Seeks to maximize utility ensuring that expenditure ≤ income ¡ Formally: ¢ Choose Q 1 , Q 2 , .. , Q N to max U(Q 1 , .., Q N ) subject to: P 1 Q 1 + P 2 Q 2 + .. + P N Q N ≤ Y ¡ What are the variables? Parameters? ¡ Let’s assume N = 2 ¢ You should think about N > 2 cases – see HWs, practice Qs Ajaz Hussain. Department of Economics 7 Setting up UMP ¡ Choose Q 1 , Q 2 , .. , Q N to max U(Q 1 , .., Q N ) subject to: P 1 Q 1 + P 2 Q 2 + .. + P N Q N ≤ Y Ajaz Hussain. Department of Economics 8 P 1 Q 1 + P 2 Q 2 + .. + P N Q N = Y Can be solved by Lagrangian method • See Math Review Assume monotone preferences: why?...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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204_summer_2009_lecture_4 - University of Toronto...

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