Ch 2 consumer theory basics

It turns out there is a short cut for deriving the

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Unformatted text preview: ution). Notice that when the consumer is consuming large amounts of good 2 and small amounts of good 1 (i.e. when is a large number) the Cobb-Douglas indifference curves are steep: the consumer will give up lots of good 2 to have another unit of good 1 (this is intuitive because she craves good 1). However, when the consumer is consuming small amounts of good 2 and large amounts of good 1 (i.e. when is a small number) the Cobb-Douglas indifference curves are flatter: now the consumer will give up smaller amounts of good 2 to have another unit of good 1 (this is intuitive because she now craves good 2). These two examples illustrate how the slope of an indifference curve gives us information about the consumer’s preferences. In the examples above (and additional ones below) we calculate(d) the slopes by deriving the equation of an indifference curve and then differentiating with respect to good 1: ⏟ ⏟ ⏟ ⏟ ⏟ [ ⏟ ⏟ (⏟ ) [ ⏟ ⏟ These aren’t exactly easy calculations: we have to first derive the equation of an indifference curve and then differentiate with respect to good 1. It turns out there is a short cut for deriving the slope of an indifference curve where we bypass calculating the equation of an indifference curve altogether! This short cut is known as the Marginal Rate of Substitution ( ), literally a different title for the slope of an indifference curve: 34 ECO 204 CHAPTER 2 Modeling Consumer Choice and Behavior: Preferences and Budget Constraints (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) Here are some examples – notice we get the same answers without having to derive the equation of an indifference curve: ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ I like it. __________________________________________________________________________________________________ Optional Proof: Consider an arbitrary utility function: ( Consider an infinitesimally small change in and { ) so that: ( ) } { ( ) } Along an indifference curve { ⏟ ( ) } { ⏟ ( ) } | The left hand side is the change in good 2 over good 1 such that utility is constant. This is, by definition, the slope at a bundle on an indifference curve which we label the Marginal Rate of Substitution ( ): 35 ECO 204 CHAPTER 2 Modeling Consumer Choice and Behavior: Preferences and Budget Constraints (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do n...
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