L03 Utility.

Slides:



Advertisements
Similar presentations
Chapter Five Choice. Economic Rationality u The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those.
Advertisements

Choice.
Chapter Four Utility. Preferences - A Reminder u x y: x is preferred strictly to y.  x  y: x and y are equally preferred. u x y: x is preferred at least.
Economic Rationality The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it. The.
Chapter Five Choice. Economic Rationality u The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those.
Chapter Four Utility. Utility Functions   A utility function U(x) represents a preference relation if and only if: x’ x” U(x’) > U(x”) x’ x” U(x’)
Utility.
Chapter Three Preferences.
Chapter Five Choice. Economic Rationality u The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those.
Utility Functions A utility function U(x) represents a preference relation if and only if: x’ x” U(x’) > U(x”) x’ x” U(x’) < U(x”) x’  x” U(x’) = U(x”).
Chapter Three Preferences. Rationality in Economics u Behavioral Postulate: A decisionmaker always chooses its most preferred alternative from its set.
Chapter Four Utility. Utility Functions u A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous.
Utility.
Chapter Five Choice.
Chapter Four Utility.
Utility. Utility Functions u Utility is a concept used by economists to describe consumer preferences. u Utility function is a function that assigns a.
Course: Microeconomics Text: Varian’s Intermediate Microeconomics 1.
Chapter Three Preferences. Rationality in Economics u Behavioral Postulate: An economic decisionmaker always chooses her most preferred alternative from.
Chapter Five Choice. Economic Rationality u The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those.
Chapter 5 Choice.
© 2010 W. W. Norton & Company, Inc. 4 Utility. © 2010 W. W. Norton & Company, Inc. 2 Preferences - A Reminder u x y: x is preferred strictly to y.  x.
Chapter 4 Utility.
© 2010 W. W. Norton & Company, Inc. 5 Choice. © 2010 W. W. Norton & Company, Inc. 2 Economic Rationality u The principal behavioral postulate is that.
Rational Choice. CHOICE 1. Scarcity (income constraint) 2. Tastes (indifference map/utility function)
1 Preferences Molly W. Dahl Georgetown University Econ 101 – Spring 2009.
© 2010 W. W. Norton & Company, Inc. 4 Utility. © 2010 W. W. Norton & Company, Inc. 2 Preferences - A Reminder u x y: x is preferred strictly to y.  x.
CDAE Class 4 Sept. 6 Last class: 1.Introduction 2.Preferences and choice Class exercise 1 Today: 2. Preferences and choice Next class: 2.Preferences.
L03 Utility. Big picture u Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. u Budget.
Chapter 4 UTILITY.
Chapter Four Utility 效用.
Budgetary and Other Constraints on Choice
L04 Choice. Big picture u Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. u Budget.
L02 Preferences. Rationality in Economics u Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives.
RL1 Review. u A decisionmaker chooses its most preferred alternative from the affordable ones. u Budget set u Preferences (Utility) u Choice (Demand)
L03 Utility. Quiz How much do you like microeconomics A: I love it (unconditionally) B: I cannot live without it C: I would die for it D: All of the above.
UTILITY. Chapter 11 What is Utility? A way of representing preferences Utility is not money (but it is a useful analogy) Typical relationship between.
Course: Microeconomics Text: Varian’s Intermediate Microeconomics
PREFERENCES. Rationality in Economics Behavioral Postulate: A decisionmaker always chooses its most preferred alternative from its set of available alternatives.
L02 Preferences.
Preferences and Utility
4 Utility.
L03 Utility.
Choice.
3 Preferences.
Chapter 4 Utility Key Concept: Utility, an indicator of a person’s overall well-being We only use its ordinal property in most cases. Marginal utility.
L04 Choice.
L04 Choice.
Chapter 5 Choice.
Chapter Three Preferences.
PREFERENCES.
Rational Choice.
L02 Preferences.
L09 Review.
L03 Utility.
L03 Utility.
L04 Choice.
RL1 Review.
L02 Preferences.
L04 Choice.
Choice.
Chapter 3 Preferences.
L03 Utility.
5 Choice.
Utility Functions f ~ p p
L02 Preferences.
L02 Preferences.
Molly W. Dahl Georgetown University Econ 101 – Spring 2009
L02 Preferences.
Economic Rationality The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it. The.
Presentation transcript:

L03 Utility

REEF Polling: iclicker Laptop/smartphone/iclicker Class Quiz REEF Polling: iclicker Laptop/smartphone/iclicker Q: How much do you like economics I love it I cannot live without it I would die for it All of the above

Big picture Behavioral Postulate: A decisionmaker chooses its most preferred alternative from the set of affordable alternatives. Budget set = affordable alternatives To model choice we must have decisionmaker’s preferences.

Preferences: A Reminder Rational agents rank consumption bundles from the best to the worst We call such ranking preferences Preferences satisfy Axioms: completeness and transitivity Geometric representation: Indifference Curves Analytical Representation: Utility Function ~ f

Indifference Curves x2 x1

Utility Functions Preferences satisfying Axioms (+) can be represented by a utility function. Utility function: formula that assigns a number (utility) for any bundle. Today: Geometric interpretation Utility function and Preferences Utility and Indifference curves Important examples

Utility function: Geometry x2 z All bundles in I1 are strictly preferred to all in I2. x1

Utility function: Geometry x2 z All bundles in I1 are strictly preferred to all in I2. x1

Utility function: Geometry x2 z All bundles in I1 are strictly preferred to all in I2. x1

Utility function: Geometry 5 x2 3 All bundles in I1 are strictly preferred to all in I2. z x1

Utility function: Geometry U(x1,x2) Utility 5 x2 3 All bundles in I1 are strictly preferred to all in I2. z x1

Utility Functions and Preferences A utility function U(x) represents preferences if x y U(x) ≥ U(y) x y x ~ y ~ f ~ f p

Usefulness of Utility Function Utility function U(x1,x2) = x1x2 (2,3), (4,1), (2,2) Quiz 1: U represents preferences A: B: C: D:

Utility Functions & Indiff. Curves An indifference curve contains equally preferred bundles. Indifference = the same utility level. Indifference curve Hikers: Topographic map with contour lines

Indifference Curves U(x1,x2) = x1x2 x2 x1

Ordinality of a Utility Function Utilitarians: utility = happiness = Problem! (cardinal utility) Nowadays: utility is ordinal (i.e. ordering) concept Utility function matters up to the preferences (indifference map) it induces Q: Are preferences represented by a unique utility function?

Utility Functions p U=6 U=4 U=4 U(x1,x2) = x1x2 (2,3) (4,1) ~ (2,2). Define V = 5U. V(x1,x2) = 5x1x2 (2,3) (4,1) ~ (2,2). V preserves the same order as U and so represents the same preferences. p V= V= V=

Monotone Transformation U(x1,x2) = x1x2 V= 5U x2 x1

Theorem (Monotonic Transformation) T: Suppose that U is a utility function that represents some preferences f(U) is a strictly increasing function then V = f(U) represents the same preferences

Preference representations Utility U(x1,x2) = x1x2 Quiz 2: U(x1,x2) = x1 +x2 A: V = ln(x1 +x2)+5 B: V=5x1 +7x2 C: V=-2(x1 +x2) D: All of the above

Three Examples Cobb-Douglas preferences (most goods) Perfect Substitutes (Pepsi and Coke) Perfect Complements (Shoes)

Example: Perfect substitutes Two goods that are substituted at the constant rate Example: Pepsi and Coke (I like soda but I cannot distinguish between the two kinds)

Perfect Substitutes (Soda) Pepsi U(x1,x2) = Coke

Perfect Substitutes (Proportions) x2 (1 can) U(x1,x2) = x1 (6 pack)

Perfect complements Two goods always consumed in the same proportion Example: Right and Left Shoes We like to have more of them but always in pairs

Perfect Complements (Shoes) U(x1,x2) = L

Perfect Complements (Proportions) Coffee 2:1 U(x1,x2) = Sugar