Ch 2 consumer theory basics

# next consider a consumer with the cobb douglas

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Unformatted text preview: any bundle in is always so that the consumer gets the same utility by giving up 2/3 units of good 2 in exchange for another unit of good 1 (or alternatively, giving up 3/2 units of good 1 in exchange for another unit of good 2). Put another way, she perceives the two goods as “substitutes” and since the rate of substitution is constant (and equal to ) we say that she perceives the two goods as “perfect substitutes” (“perfect” = constant rate of substitution). 32 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. As such, the linear utility model models a consumer who perceives goods as perfect substitutes in the sense that units of good 2 are the “same” as units of good 2. For example, if a consumer perceives two good to be literally perfect substitutes in the sense that a unit of good 1 is the same as a unit of good 2 then we can back out her utility function as any of these (why?): ⏟ { {( Next, consider a consumer with the Cobb-Douglas utility function defined over the consumption set ) }: ⏟ Pick any bundle in the consumption set: by definition, this bundle is on an indifference curve. How many units of good 2 will the consumer give up for an additional unit of good 1 and still have the same utility as before (i.e. be on the same indifference curve?). Once again the slope gives us the answer: ⏟ For example, suppose ⏟ [ (⏟ ) ⏟ then: ⏟ ⏟ Notice that unlike the linear utility model, the slope of Cobb-Douglas indifference curves change from bundle to bundle: 33 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. plot u=(q1^0.5)(q2^0.5) from q1=0,20 q2=0,10 In this example, the slope is negative which means that she perceives the two goods as “substitutes” and since the rate of substitution is variable we say that she perceives the two goods as “imperfect substitutes” (“imperfect” = variable rate of substit...
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