Econ501aL4

# Econ501aL4 - Utility Maximization Given the consumer's...

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Utility Maximization Given the consumer's income, M , and prices, p x and p y , the consumer's problem is to choose the a®ordable bundle that maximizes her utility. The feasible set (budget set) : total expenditure can- not exceed income, so we have p x x + p y y · M: (1) Since more is better, inequality (1) must hold with equality at the solution to the consumer's problem. 0 1 2 3 4 5 y 2468 1 0 x The Feasible Set, p x =1 ;p y =5 ;M =10

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The budget line, p x x + p y y = M ,h a sas l o p eo f ¡ p x =p y , an x-intercept of M=p x , and a y-intercept of y . From the diagram, we see that utility maximization over the feasible set occurs at the point of tangency between an indi®erence curve and the budget line. (Notice that we need axiom 6 for the tangency to be a utility maximum.) 0 1 2 3 4 5 y 2468 1 0 x
The slope of the indi®erence curve is ¡ MRS yx and thes lopeo fthebudgetl ineis ¡ p x =p y : The optimal bundle is the point on the budget line where we have = p x =p y : (2) Equation (2) has an economic interpretation: the in- ternal rate of trade should equal the external or market rate of trade. Otherwise, there are further gains from trade between the consumer and the market. For ex- ample, if =1 = 4and p x ;p y =5 ,then the consumer could increase her utility by choosing 1

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## This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Spring '08 term at Ohio State.

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Econ501aL4 - Utility Maximization Given the consumer's...

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