Lecture 11 Utility

  • Utility
    • Conditions to define utility function:
      • mapping/function: \(\{ \text{Alternatives} \} \to \mathbf{R}\)
      • assign larger number to more preferred alternatives
    • Historically: "utility" means pleasure, happiness, satisfaction etc of receiving, owning or consuming
    • Utility = INDEX of measure of preference
    • If Rational preference relation, we can find a utility function to represent it if \(\{ \text{Alternatives} \}\) is finite.
    • For infinite, complication. Also, if a utility function represents preference relation then the preference relation is rational!
      • However, reverse implication is not true.
    • Given utility function \(u(\cdot)\), the following conditions hold
      • \(x \succ y \iff u(x) \gt u(y)\)
      • \(x \sim y \iff u(x) = u(y)\)
    • Utility functions are not unique. Here, we use ordinal utility: that just allows us to order things
      • The absolute numbers don't say anything. It is only the relationship that matters.
        • e.g. Lataji > Arijit Singh
      • Don't ascribe any significance to the ratios either
        • e.g. if \(u(\text{Lataji}) = 2u(\text{Arijit})\) it doesn't mean that I like Lataji "twice as much" as Arijit Singh (the scale is not scaling)
  • How do utilities relate to indifference curves?
    • \(u(\cdot)\) assigns one number to each IC
    • Two bundles on the same IC \(\implies\) same utility
    • \(u_{1} \lt u_{2} \lt u_{3}\)
  • How does utility relate to behavior?
    • Choosing the most preferred item corresponds to choosing the item with the highest utility.
    • You choose rationally insofar as you maximize utility. We thus, behave rationally.
  • Historical evolution of utility
    • Underlies the theory of consumer choice. We concern ourselves with riskless choice.
    • Jeremy Bentham, 1789: assumption that objective is EU maximization. (A fundamental concept of NM)
      • utility 'points out what we ought to do, as well as what we shall do'
      • Utility has a hedonic1 characteristic (noted by Kahneman (2000) as experienced utility)
    • Meaning has changed in favor of the concept: decision utility
      • Utility = "Weight assigned to the outcome of a decision", revealed by people's choices
      • Call it the "Revealed preference meaning" of utility, generally used on NM
      • Two obvious advantages
        • Easier to measure: can be inferred from choices and actions
        • No commitment to a hedonistic philosophy
      • Sen (1987): "maximization of expected utility is not always what people are trying to achieve"
  • Decision Utility
    • Easiest to measure in terms of revealed preference (usually discussed by economists)
    • Doesn't reflect attitude or judgements
    • Study by Tversky and Griffin (2000)
      • 66 undergrads
      • For the same role and experience
      • Mag A: 35000 (others make 38000)
      • Mag B: 33000 (others make 30000)
      • Half were asked: which they would choose
        • Decision utility
        • When asked to make a choice, they make arguments and justify their choice
      • Other half: which would make them happier
        • Hedonic or experienced utility
        • In this case, expected in future, people try to imagine how they would feel
      • Results:
        • 84% chose (A)
        • 62% thought (B) would make them happier
    • More recent Study: Comerford & Ubel (2013): Preference Choice for Effortful jobs
      • Express a preference for more effort
      • But choose jobs with less effort (lol)
      • In lab experiment
        • They set their own wages
        • Those whose wage demands got them effortless jobs: got lower enjoyment
      • Observation: Discrepancy between CHOICE and PREFERENCE
    • So, there is a discrepancy between
      • preference & choice
      • decision utility & experienced utility
      • choice & attitude (consideration of car may involve attributes of safety, fuel economy etc)
    • SDM approach involves two steps:
      • values for each attribute to some scale
      • weights for each attribute to compare them
      • e.g. loss of one mile to the gallon \(\sim\) two cubic feet of boot space
      • This procedure is more relevant in determining attitudes or judgements
    • For preference: most important attribute is weighed more heavily (maybe cause its a more convenient rationale for choice)
  • Prominence Effect
    • Explained by Somatic-Marker Hypothesis (SMH) proposed by neuroscientist, Damasio (1994)
    • Somatic-Marker is an unpleasant gut feeling, when a bad outcome connected to a response comes to mind
    • Automated alarm signal that forces attention to the negative outcome of a given actions "Behave: Danger ahead! If you choose this option".
  • The SMH
    • This auto signal makes you reject negative course of action and protects against future losses.... choose from fewer alternatives (better)
    • In context of prominence effect, Damasio observed... gut feeling can still lead to good and quick decisions
    • Visceral factors2... proposing that they can lead to better rather than worse decisions.
  • Cardinal & Ordinal utility
    • Early Economists:
      • "Utility can be quantitatively measured using utils", using a ratio scale with a zero point.
      • They can say, "Basket B yielded twice as much as utility as basket A"
      • Can even be considered interpersonally.
    • Disfavor cardinal utility for Ordinal (ranking system)
    • Interpersonal additions of utility is INVALID
    • Ordinal > Cardinal because:
      • fewer assumptions
      • Equilibrium conditions can be expressed in terms of ordinal utility
      • DMU Law can also be expressed
    • However NM uses cardinal, as it is more tractable mathematically.

  1. Hedonistic simply means there is a variance in the way it is interpreted/experienced by different people. 

  2. Powerful internal states that can affect our attention, motivation and behavior (order matters)... sometimes causing us to act against our rational, long-term interests.