Modeling Preferences and Utility

rewrite these notes and explain: 2. Preferences and Utility Functions Where do supply and demand curves come from? Demand Curve How consumers make choices Supply Curve How firms make production choices Utility Maximization Consumer Preferences Budget Constraint Maximize people’s happiness with their budget constraint Yields demand curve 3 steps Step one preferences How we model peoples tastes Step two how it is mapped to utility preferences Step three how budget constraints apply First without concern for budget How do you think about what you want Start with preference assumptions Models rely on assumptions Are they realistic Three preference assumptions Completeness There are preferences over any set Can’t say I don’t know Transitivity If a to b and b to c then a to c Non-satiation More is better Gives models power Graphical representation of preferences Indifference curves Graphical maps of preferences Pizza or Cookies 2 p 1 c, 1 p 2 c, 2 p 2 c Out of the three choices the third is preferred One indifference curve between the first two Includes all combinations in which you are indifferent 4 properties Consumers prefer higher indifference curves More is better Indifference curves are downward-sloping From principle of non-satiation Indifference curves never cross Violates transitivity Only one indifference curve through every bundle I care about school location and economic school quality If you are indifferent between a place with good location and bad quality versus a place with good quality and bad location but there is a third option that is in between quality and location but in combination it is better than your preference for the first two you would choose that one. Utility functions Represented mathematically Every individual has a stable mathematical mapping of preferences How do you mathematically represent preferences What is utility Not a cardinal concept, only ordinal Can be ranked Margin utility Marginal decision making What is the preference for the next decision Step wise decision making Diminishing margin utility Margin utility falls as you consume more What is your happiness for an increment of consumption You always want more Margin utility is always positive Slope of indifference curve is marginal rate of substitution Rate at which you are willing to substitute one thing for another Diminishing marginal utility Marginal rate of substitution is always diminishing How MRS relates to utiltiy function MRS how relative marginal utility evolves as you move down indifference curve The more you have of a good the less you want it Indifference curves are not convex to origin Diminishing market utility Soda costing less for larger sizes Explain how this works mathematically Like how Costco is not necessarily a good deal

### 2. Preferences and Utility Functions #### Origins of Supply and Demand Curves **Demand Curve:** - Derived from consumer choice behavior. **Supply Curve:** - Derived from firm production decisions. #### Utility Maximization - **Consumer Preferences**: The basis of understanding how consumers make choices. - **Budget Constraint**: Limits on consumer spending based on income and prices. - **Goal**: Maximize consumer satisfaction within their budget constraints, which generates the demand curve. ### Steps to Understand Consumer Choices 1. **Modeling Preferences**: - Understand and model consumer tastes. 2. **Mapping Preferences to Utility**: - Translate tastes into utility functions. 3. **Applying Budget Constraints**: - Consider how spending limits affect choices. ### Modeling Preferences - **Initial Consideration**: Ignore budget constraints to focus on desired choices. - **Preference Assumptions**: - **Completeness**: Consumers have preferences for any given set of options. - **Transitivity**: If a consumer prefers option A over B, and B over C, then they prefer A over C. - **Non-satiation**: More of a good is always better. #### Graphical Representation of Preferences: Indifference Curves - **Indifference Curves**: Graphs showing combinations of goods between which a consumer is indifferent. - Example: Preferences between pizza and cookies. - **Properties of Indifference Curves**: 1. Higher curves are preferred (more is better). 2. Downward-sloping (reflects non-satiation). 3. Never cross (maintains transitivity). 4. One unique curve through every combination of goods. #### Utility Functions - **Mathematical Representation**: Each person has a stable utility function representing their preferences. - **Utility**: Measures satisfaction (ordinal ranking, not cardinal). - **Marginal Utility**: Additional satisfaction from consuming one more unit of a good. #### Diminishing Marginal Utility - **Principle**: Marginal utility decreases as consumption increases. - **Implication**: Consumers experience less additional happiness with each extra unit consumed. - **Graphical Representation**: Slope of the indifference curve, or marginal rate of substitution (MRS). #### Marginal Rate of Substitution (MRS) - **Definition**: The rate at which a consumer is willing to trade one good for another. - **Diminishing MRS**: MRS decreases as more of one good is consumed, reflecting diminishing marginal utility. ### Practical Examples - **Diminishing Marginal Utility**: Illustrates why larger quantities (like bulk purchases at Costco) might seem less advantageous. - **Indifference Curves**: Demonstrate how different combinations of goods provide the same level of satisfaction. By understanding these concepts, we can better comprehend how consumers make choices and how these choices shape market demand curves.