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# ECON 3101 Lecture 3 Econ 3101

U of M

GPA 3.9

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This 4 page Class Notes was uploaded by Waverly Johnston on Thursday September 17, 2015. The Class Notes belongs to Econ 3101 at University of Minnesota taught by in Fall 2015. Since its upload, it has received 55 views. For similar materials see Applied Microeconomics: Consumers, Producers, and Markets in Economcs at University of Minnesota.

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Date Created: 09/17/15

Econ 3101 Lecture 3 91515 Today s lesson Consumer Theory preferences and axioms and Utility Preferences In order to study Consumer Theory we must understand three things Likes dislikes Why does the consumer like dislike certain things Opportunities constraints What limits the consumer Objectives of the agent What does the consumer agent want maximize leisure money general happiness It is also important to note that we will assume rationality is always there We will go forward with the belief that the agent makes decisions that are logically consistent Example 1 Looking at this graph which bundle would you prefer to have x0 yo giving you more candy and less popcorn or x1 y1 giving you more popcorn than candy popcorn Y y1 quotEA 3 2 B x1 x2 X candy It s hard to tell which is better right That s because we don t have any way to determine which bundle is preferable This is why we will need to define our two sets of axioms Axioms Think of them as a set of truths Remember rationality is held by these axioms 1 Completeness An individual cannot be indecisive He always makes up his mind about which option is more desirable He can be indifferent but not indecisive Notation A gt B 9 A is strictly preferred to B A lt B 9 B is strictly preferred to A A w B 9 The agent is indifferent between A and B A gt B 9 The agent weakly prefers A to B Special Note quotVquot means for allquot So VA E 96mm 3 E 3513 1 EitherA gt BA lt BorA m B But you can t have more than one of the above statements be true at the same time 2 Transitivity V bundles A B and C ifA gt B and B gt C A gt C same goes for quot Transitivity and Indifference Curves IC Just remember Indifference curves CANNOT cross In this example we consider the first Axiom completeness We know Y AB o A B gt Example But now we must consider the second Axiom transitivity We know If AB and A transitivity would give us B X However B and are on separate indifference curves so we know the above statement cannot be true If transitivity holds the CS cannot cross Utility Utility function A function that assigns a number to a bundle of goods Don t worry about the function he has on the slides You won t need to know that notation for this class Example ua b 2 1561 6193 If a 5 and b2 then u52 75 48 9123 The good news is we can directly relate utility to preferences if the utility we get from bundle a is the same from bundle b preferences tell us we are indifferent between the two bundles Example va a0 b0 a1 b1 then 610190 gt u 11191 69 610190 gt 1 I91 610 I90 quot 511 I91 69 a0 190 quot a1 191 What s the point of the utility function The utility function is helpful in ranking the bundles for the consumer It makes it easy to see which bundle is valued more and which is valued less Quick note we are thinking of utility as ordinal first second third not cardinal one two three AKA we care about order not size Linear utility Remember the formula y mx b This equation makes linear utility easy to understand Example ux y ax by The indifference curve passing through A x0 yo can be written in that linear equation y mx b ax by axo bxo axo bxo a b b Quick note With linear utility the IC through any bundle has the slope g This is always true CobbDouglas This is our last utility function for today uxy xayl39 Things to remember We will assume a E 01 CobbDouglas has diminishing marginal returns Marginal Utility MU MU tells us how much utility changes when there is a change in consumption of one of the goods M Ux x y Measures the change in utility when there is a unit change in x 0110631 MUxxrY x M Uy x y Measures the change in utility when there is a unity change in y 0149631 MUyxly y Notation If MUgt0 the consumer prefers more of the good If MUlt0 the consumer prefers less of the good If MU0 the consumer wants neither more nor less of the good Marginal Rate of Substitution MRS MRS tells us the rate at which we can exchange goods with the consumer while keeping the consumer indifferent to change keeping them on the same indifference curve Things to remember MRS at one certain point on an IC is the negative of the slope of the IC at that point MRS dxdy if we hold utility constant Practice remember MRS 1111quot Uy 1 Ux y 2 39 MUx 2 3y MUy 3x MRS yX

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