Econ 100AMicroeconomic AnalysisLecture 2; Reading 3.1 & 3.2*

AnnouncementsFirst i-Clicker lecture is 9/15Register your i-Clicker at:http://www.iclicker.com/support/registeryourclicker/I will give out book codes after lecture todayCurve

Concepts to know from Lecture 1What is Microeconomics?What is a model?Positive vs. normative analysis/statement

Choice and RationalityTo get from individual choice to market demand, we first need to make a few assumptions about choiceEconomists assume that individuals face a choice setconstraint

RationalityThe most fundamental assumption in economics is the assumption of rationalityA consumer with rational preferences will act to maximize his/her well-being.The assumptions we make allow for mathematical representation of preferences and constraint, with (mostly) a single solution

PreferencesHelp consumers choose between different bundles of goods.Properties of Preferences:CompletenessTransitivityMore is better

Rationality is defined as a set of conditions on preferences*

Preferences NotationIf an individual chooses bundle A over bundle B then A is strictly preferred to BABIf an individual is indifferent between A or B thenA & B are equally preferredABIf A is at least as good as B thenA is weakly preferred to B AB

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CompletenessBundle ABundle B

1 latte2 lattes3 chocolate1 chocolateWhen presented with a choice, people can rank their preferences

Ask preferences*

TransitivityBundle ABundle BBundle C

2 Apples4 Apples1 Apple3 Bananas1 Banana 4 Banana

If A is preferred to B and B is preferred to C then:A must be preferred to C

No cyclical preferences!(Ranking does not change with order of choice)

More is BetterBundle ABundle BBundle C

2 M&M4 M&M5 M&M2 Snickers3 Snickers4 Snickers

Bundle C is preferred to B and Bundle B is preferred to A

Side note: This assumption implies that utility function is weakly positive

More is betterMore is better (monotonicity) is a simplifying assumption to allow for simpler graphical analysis Mostly trueWhen is it not true?

To summarizeEconomists do not say:Why do you have a specific set of preferencesWhether your preferences are good/badEconomists do say:If your preferences satisfy completeness, transitivity and more is better, we can model your choices by maximization of a utility function

Graphical Representation of PreferencesVisual intuition can help solve complex modelsBy presenting preferences and constraints visually, we can quickly find models solution and make predictions when things changeTo graphically represent preferences we are going to assume an individual consumes 2 goods

How many beverage offerings choice are in this choice set?

Graphical Representation of Preferences

TwixSnickers(a)2(b)55(c)2(d)7(e)1010(f)7

Graphical Representation

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Indifference CurvesLines connecting bundles, which the consumer equally prefers are called Indifference Curves.All bundles on a single indifference curve are equally preferredBundles on indifference curves further from the origin are preferred to those closer to the originThere is an indifference curve through each possible bundle

Properties of Indifference CurvesIndifference curves cannot be upward sloping

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Properties of Indifference CurvesIndifference curves cannot be thick

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Properties of Indifference CurvesIndifference curves cannot cross

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Properties of Indifference CurvesThese properties ensure that indifference curves reflect complete, transitive and more is better conditions

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Do it yourself

IC 1IC 2IC 3TSTSTS232332432316421524411516619586137166671181475810912.584.599.594

Do it Yourself

Slope of the indifference curveIn the example above, what is the slope of IC1 going from 4 to 5 twix? What does the slope represent?Why is it negative?Why is it convex?

Indifference CurvesHow would the indifference curve look like if you liked Twix much more than snickers?

Indifference CurvesWhat if you liked Snickers much more than Twix?

Indifference CurvesWhat if you were allergic to peanuts?

To summarizeA steeper I.C. means that the good on the x-axis is more preferredA flatter I.C. means that the good on the y-axis is more preferred

UTILITY

UtilityNumerical value reflecting relative satisfaction obtained from a bundle of goods.If Amir prefers bundle A to bundle B, then U(A) > U(B)If Amir is indifferent between A & B then U(A) = U(B)

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Utility FunctionsAssign a numerical (ordinal) value to a specific bundle

Examples: u(M,P) = sqrt(M*P)u(M,P) = M + 3PWe are all different! We can use different functions to reflect differences in utility across individuals

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Rationality and Utility functionsUtility functions assign a numerical value to each bundle of goods it mathematically represents the rank ordering of ones preferencesWhen preferences are rational they can be easily represented with a utility function

ExampleGiven the utility function: U = XYWhat is the utility for X = 2 and Y = 8?Find two more bundles of goods with the same level of utilityGraph the indifference curve

ExampleWhat is the equation of the indifference curve you found?

Utility & indifference curvesWe can use a three-axis space to graph utilityIndifference curves are slices through the utility graph

QuestionDan enjoys cereal and milk only if he can have 0.5 a cup of both. What will his indifference curves look like?

MABCCMCCM0.50.50.50.50.50.5

Types of goodsPerfect complements: ones well-being depends on having both goods in set quantitiesExamples:I.C. are L-shapedU(X,Y) = min(iX, jY)

Types of goodsPerfect Substitutes: one is indifferent between consuming one good or anotherExamples:I.C. are linearU(X,Y) = iX + jYFind the equation of the I.C.

Types of goodsImperfect substitutes: willing to trade some of one good to get more of the otherI.C. are convexExample: U = XY1-

Marginal Rate of Substitution (MRS): the slope (rise over run) of the indifference curve at each point. How much of one good a consumer is willing to give up for more of the other good.

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MRSRepresents the willingness to trade between two goodsFor imperfect substitutes:Varies along the I.C.For perfect substitutes:ConstantFor perfect complements:Either 0 or infinity

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To summarizeAssumption of rationalityCompleteness TransitivityMore is betterPreferencesIndifference CurvesUtilityMRS

More thoughtsAbout choice:http://www.ted.com/talks/lang/en/sheena_iyengar_on_the_art_of_choosing.html

About rationality:http://www.ted.com/talks/dan_ariely_asks_are_we_in_control_of_our_own_decisions.html

WednesdayBudget ConstraintOptimal Choice

Rationality is defined as a set of conditions on preferences*

*Ask preferences*

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