Utility Maximization

1
Utility Maximization

• POL 433Y
• Go to
• http//ccnet.utoronto.ca/20049/pol433y1y/

2
Preferences

• Assume rational actors can make comparisons
  across all pairs of consequences.
• Completeness
• Transitivity
• Fixed
• Allows us to assume ordinal preferences and allow
  for possibility or cardinal utilities.

3
Predict Actions

• Choose among acts
• States of the world exhaustive set of situations
• Event is a subset
• Consequences/Outcomes One for each pair of act
  and states.
• Preference Ordering over consequences

4
Preferences-gtUtility

• If one preferences one outcome (x) to another
  outcome (y), ones utility for x is higher than
  y.
• Important preferences -gt utility (not
  vice-versa).
• Rational choosers chose the outcome with the
  highest expected utility
• Expected utility is calculated from utility from
  consequence likelihood of it occurring.

5
Likelihood

• Likelihood affected by
• Opponents strategy
• Mixed strategy, as in Dating Game.
• Chance of mistakes by you and opponent
• Possibility of state occurring
• Risk
• Uncertainty

6
Risk and Uncertainty

• Risk- each state has known probability of
  occurring.
• Uncertainty unknown probability of state
  occurring
• Risk Averse people prefer gamble with a smaller
  variance in outcomes functions are concave
  downward.
• Risk Acceptant people prefer gamble with high
  variance in outcomes functions are concave
  upward.
• Prefer some gambles with greater risk and lower
  expectations

7
Nixons Xmas Bombing
8
Calculate

• If we assume that there is a 0.7 chance the
  Vietnamese are bluffing, and that more
  concessions is worth 0.3 to Nixon, one can
  calculate the expected utility for the Nixon
  administration.
• What should Nixon do?
• What if chance Vietnamese are bluffing is only
  0.2?
• What if utility for more concessions is 0.8?

9
Becker

• What does he explain?
• Discrimination
• Crime
• Workforce
• Family formation and dissolution
• Child Care

10
How?

• How does he explain these patterns?
• What assumptions does he make?
• Too restrictive? Not restrictive enough?
• Do they capture how people make decisions?
• Do they need to?
• Human Capital
• Do people carefully weigh their options to become
  educated get medical care by carefully weighing
  benefits and costs?
• Do firms perform the same decision-making
  processes?

11
Is love dead?

• Cost-benefits of getting married.
• Does this explain why richer couples stay married
  more often than poor ones?
• What are the public policy implications?
• Tax marriage penalty
• No fault divorce
• Should great old-age homes occur in communities
  with great schools?

12
Voting Cycles

• Individual people with complete and transitive
  preferences should not prefer Apples to Bananas
  to Cherries but prefer Cherries to Apples.
• What about groups?
• 3 people
• Jack A gt B gt C
• Kelly C gt A gt B
• Lauren B gt C gt A

13
Single Peaked Prefs

• Two alternatives, y and z, on the same side of x,
  individual votes for y if and only if y x lt
  z - x.
• This is a spatial preference, as alternatives
  closer to ideal are rated higher than
  alternatives further away.
• Creates an order to the alternatives.
• If preferences are single peaked, median option
  wins in one-dimensional conflict.

14
No single peaked prefs (Hinich and Munger, Ch. 2)

• UN in Bosnia
• Stay Out Oppose foreign intervention
• No involvement gt Limited peacekeeping gt Invasion
• New World Order Keep conflict from escalating
  and spreading
• Limited peacekeeping gt Invasion gt No involvement
• Blame Serbia Punish aggressors/instigators.
• Invasion gt No involvement (no limits on Bosnian
  response) gt Limited peacekeeping
• Do not have single-peaked preferences.