Principles of Microeconomics Lecture 8: Utility and Demand PDF

Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Principles of Microeconomics Economics 1021A Lecture 8: Utility and demand...

Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Principles of Microeconomics Economics 1021A Lecture 8: Utility and demand (Textbook Chapters 8 & 9) Fall 2024 1/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. One carat cut diamond sells for $3,000. Is nice and shiny. One liter of water can be found for $1. Need it to live. Classical philosophers and proto-economists: “What gives?” (paraphrased) 2/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The things which have the greatest value in use have frequently little or no value in exchange; on the con- trary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will pur- chase scarcely anything; scarcely anything can be had in exchange for it. A diamond, on the contrary, has scarcely any use-value; but a very great quantity of other goods may frequently be had in exchange for it. — Adam Smith 3/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value $2,295 $99 4/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value 5/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value 6/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. We could chalk this up to a inelastic supply, but that’s only half the story. Still need someone willing to buy a $3,000 diamond. Also need to explain why the same consumer won’t buy a $9 a bottle water. We need a better theory of consumer choice. 7/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Consumption choices Fundamental consumer model has two important components: 1 Preferences: Define your ideal choice. 2 Constraints (a.k.a. budget): Define your consumption possibilities, which is the set of options you can afford to buy given prices and income. Goal: predict quantities of each good that a rational consumer will choose given their preferences and constraints. 8/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Preferences Assume consumers choose based on preferences: Preferences are immutable, predetermined, and rational. Can be represented by utility: a quantitative measure of benefit or satisfaction from consuming. Prefer X to Y =⇒ X gives higher utility than Y. We focus on choices of “how much” to consume of each good, but the theory is more general and can apply to yes/no decisions, career choices, migration, etc. 9/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility theory Utility-based rational choice model assumes consumers make choices that maximize utility. Applies if people are rational and can rank outcomes: People act as if maximizing utility, enabling predictions. If utility from 1 apple is 25 and utility from 1 banana is 50, I prefer the banana. But, utility is unitless and only useful for ranking bundles. If utility from 12 apples is 60, and that’s all I know, it doesn’t mean very much. 10/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: direct approach Determine feasible choices: Lisa has $40 a month to spend The price of a movie is $8 and cola is $4 a case Rows of table show bundles that exhaust $40 11/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: direct approach Find utility for each bundle 1 movie =⇒ 50 utils 8 cases of cola =⇒ 248 Total utility is 298 12/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: direct approach Choose highest utility bundle 2 movies =⇒ 90 utils 6 cases of cola =⇒ 225 Total utility is 315 and falls from here 13/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects In-class question 1 The last example assumed that: Total Utility = Utility From Cola + Utility From Movies. This means that we can know the utility of having 2 colas without knowing the number of movies. When would this assumption fail? a) People eat popcorn at the movies, making them thirsty. b) Drinking cola during a movie means you’ll miss part of it while waiting in the restroom. c) People often drink cola while watching movies. d) People buy more cola in the summer. 14/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference curves Indifference curve is a line that shows combinations of goods among which a consumer is indifferent. Useful for representing preferences in marginal analysis. Distinguish substitutes and complements. Separates changes in demand from substitution and income effects. 15/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference curves 6 movies with 2 colas just as good as 2 movies with 6 colas: 16/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference curves Indifference curves represent pref- erences: Bundles on IC preferred to inside. Bundles outside of IC preferred to on IC. Moving up and right to pre- ferred bundles shifts the indiffer- ence curve and increases utility. 17/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference curves Properties of indifference curves: 1 Moving out from zero =⇒ higher utility. 2 An individual’s indifference curves never cross. 3 Indifference curves slope downward if both goods are useful. 18/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Substitutability The shape of indifference curves reveals the degree of substitutability between two goods: 19/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Budget constraint Assumptions about constraints consumers face: Prices and income/budget are taken as given (i.e. they are exogenous). Set at market level. Not affected by individual choices. Subset of income is divided between two goods to focus on tradeoffs. We can compartmentalize decisions (e.g. $200 grocery budget, $50 entertainment budget,...) Theory applies to many goods, we focus on two-good case. 20/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Budget constraint Consumption possibilities are limited by income and prices Budget line: defines limits of consumption possibilities in terms of spending at given prices | {z } = P1 × Q1 + P2 × Q2 +.... Income | {z } Budget Spending Focus on two good case, which I can draw in a graph (quantities on axes) by isolating quantity of good 1: Income P2 Q1 = − × Q2 P1 P1 21/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Consumption possibilities On a conceptual level, the bud- get line is a constraint on con- sumer choices Affordable: points on/inside budget line Unaffordable: points outside budget line Spend entire budget =⇒ on budget line 22/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price change Change price of good on x-axis af- fects x-intercept and slope Price ↑ =⇒ budget gets steeper and x-intercept moves in Price ↓ =⇒ budget gets less steep and x-intercept moves out 23/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price change Change price of good on x-axis af- fects x-intercept and slope Price ↑ =⇒ budget gets steeper and x-intercept moves in Price ↓ =⇒ budget gets less steep and x-intercept moves out Changing price of y-axis good af- fects y-intercept and slope 23/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Income change Change in available income causes parallel shift of budget line Income ↑ =⇒ shift out Income ↓ =⇒ shift in Relative prices unchanged =⇒ slope unchanged 24/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects In-class question 2 Someone made a bot that trawls the web buying paperclips and toothpicks with a $500 budget. The bot is dumb. It has no objective and randomly chooses points on its budget line. Assume that the price of paperclips doubles and all else is equal. On average, should we expect that the bot buys fewer paperclips? 25/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice Consumer equilibrium: choose bundle of goods that maximizes utility given prices and income. Use this framework to make predictions about rational decisions and individual demand. Use marginal thinking to “solve the consumer’s problem” and put the model to work. 26/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference and optimal choice Which affordable points are preferred D F to F? E A B C 27/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference and optimal choice Which affordable points are preferred D F to F? E Is D an optimal B A C choice? 27/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Indifference and optimal choice Which affordable points are preferred D F to F? E Is D an optimal B A C choice? How about C? 27/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution Optimal choice depends on the IC’s slope. There’s an insight here. Define the marginal rate of substitution (MRS) to measure willingness to make tradeoffs. Broad definition: rate at which a person is willing to trade goods while remaining indifferent. 28/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution Optimal choice depends on the IC’s slope. There’s an insight here. Define the marginal rate of substitution (MRS) to measure willingness to make tradeoffs. Broad definition: rate at which a person is willing to trade goods while remaining indifferent. Specific definition: marginal rate of substitution of x for y (MRSx ,y ) is the amount of y consumer trades for one unit of x without ending up better or worse off. 28/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution Optimal choice depends on the IC’s slope. There’s an insight here. Define the marginal rate of substitution (MRS) to measure willingness to make tradeoffs. Broad definition: rate at which a person is willing to trade goods while remaining indifferent. Specific definition: marginal rate of substitution of x for y (MRSx ,y ) is the amount of y consumer trades for one unit of x without ending up better or worse off. MRS equals the magnitude of indifference curve’s slope. 28/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution and optimal choice Collecting observations: 1 Optimal choice sets slopes of budget and IC equal. 2 Slope of budget = − Price ratio. 3 Slope of IC = − MRS. 29/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution and optimal choice Collecting observations: 1 Optimal choice sets slopes of budget and IC equal. 2 Slope of budget = − Price ratio. 3 Slope of IC = − MRS. Altogether, this means that: Px Optimal choice sets MRSx ,y = Py. 29/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution and optimal choice Px Optimal choice sets MRSx ,y = Py. This makes sense when we see that the marginal rate of substitution is a marginal utility ratio: MUx MRSx ,y = MUy Marginal utility (MUx ) of a good is change in utility from a small change in the quantity consumed. Closely related to marginal benefit and a central piece of our choice theory. 30/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal rate of substitution and optimal choice Px Optimal choice sets MRSx ,y = Py. This makes sense when we see that the marginal rate of substitution is a marginal utility ratio: MUx MRSx ,y = MUy Implication: Px MUx MUy MRSx ,y = ⇐⇒ = Py Px Py 30/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis MUx MUy Optimal choice sets Px = Py. Key tradeoff: MU per $ spent on each good. Example: MUM : marginal utility from movies. PM : price of movies. MUM /PM : marginal utility per dollar spent on movies (bang for buck from buying a movie). 31/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis MUx MUy Optimal choice sets Px = Py. Key tradeoff: MU per $ spent on each good. Example: MUM /PM : bang for buck from buying a movie. MUM How do we interpret PM ? The units are: Utils/Movie Util =. $/Movie $ This is the inverse price of getting a bit more utility from movies. 31/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis MUx MUy Optimal choice sets Px = Py. Key tradeoff: MU per $ spent on each good. MUM PM is the inverse price of getting a bit more utility from movies. So, rational decisions compare prices of each way to get a bit more utility. 31/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Wait... marginal utility changes? MUx MUy Optimal choice sets Px = Py. How do consumer choices change marginal utility? Diminishing marginal utility: as quantity consumed of a good increases, marginal utility from decreases. First apple is great, ninth apple is just ok. A common assumption about preferences. 32/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal utility example Lisa has $40 to spend, movie price is $8 a ticket, and cola is $4 a case. Rows show just-affordable bundles and we can see that utility is highest at QM = 2 and QC = 6. What is the MU of the 4th movie? 33/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Marginal utility example Assume Lisa chooses QM = 4 and QC = 2: 1 How much does utility fall if she has one less movie? 2 How much much money does that free up and how many more cola cases can she buy? 3 Does the utility gained from colas offset the loss from movies? 33/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis At QM = 1 and QC = 8: MUM /PM > MUC /PC This implies: Movies are a cheap way to get utility (at the margin). 34/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis Move $1 from cola to movies: Utility gain = MUM /PM. Utility lost = MUC /PC. Utility gain > utility lost. 34/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis Move $1 from cola to movies. With diminishing MU: MUM falls and MUC grows. So, marginal utilities per dollar approach each other. 34/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis At QM = 3 and QC = 4: MUM /PM < MUC /PC This implies: Colas are a cheap way to get utility (at the margin). 35/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis Move $1 from movies to cola: Utility gain = MUC /PC. Utility lost = MUM /PM. Utility gain > utility lost. 35/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Utility maximizing choice: marginal analysis MUM /PM = MUC /PC No gain from moving money across goods. No possible gain means the we’re maximizing utility. 36/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Summary: consumer choice Optimal choices satisfy the following two conditions: 1 Choose a point on the budget line. Ensures that we use all available resources. 2 Choose a point where the marginal rate of substitution between two goods equals their relative price. IC slope (MRS) = Budget slope (price ratio), ensuring that we are on the highest attainable indifference curve. Same as saying all goods give the same marginal utility per dollar, so no good deals are left on the table. 37/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. One carat cut diamond sells for $3,000. Is nice and shiny. One liter of water can be found for $1. Need it to live. This makes sense to a marginalist. 38/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. No paradox to a marginalist. Most people rarely buy diamonds. Low QD =⇒ high MUD. We have access to a lot of water. High QW =⇒ low MUW. 39/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. No paradox to a marginalist. Most people rarely buy diamonds. Low QD =⇒ high MUD. We have access to a lot of water. High QW =⇒ low MUW. MUW MUD So, need high PD and low PW to make PW = PD. 39/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Paradox of value The paradox of value: market prices don’t always reflect usefulness. No paradox to a marginalist. Most people rarely buy diamonds. Low QD =⇒ high MUD. We have access to a lot of water. High QW =⇒ low MUW. MUW MUD So, need high PD and low PW to make PW = PD. In other words: a utility maximizer buys one expensive diamond and lots of cheap water. 39/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Individual demand Now we’ll think about changing prices and income to show how utility theory underlies demand curves. Approach: Set up a utility maximizing consumer with a fixed budget constraint. Assume income/prices move exogenously. Study the behaviour of individual demand by examining how prices and income affect utility maximizing choices. 40/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price changes Movie price falls, optimal movie consumption grows: Starting from optimal choice, reducing PM increases marginal MUM utility per dollar PM at any given quantity. At old quantities and new prices MUM /PM > MUC /PC. How to find MUM /PM = MUC /PC at new prices? 41/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price changes Movie price falls, optimal movie consumption grows: Starting from optimal choice, reducing PM increases marginal MUM utility per dollar PM at any given quantity. At old quantities and new prices MUM /PM > MUC /PC. How to find MUM /PM = MUC /PC at new prices? Diminishing marginal utility means increasing Q movies will decrease MUM. Increase quantity of movies to find new optimal choice. Individual demand slopes down in own price 41/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price changes Movie price falls from $8 to $4: The budget line rotates out. Optimal movie consumption grows from 2 to 6 per month. This is a movement along the individual demand curve. 42/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price changes Movie price falls, optimal cola consumption changes: Assume cola and movies are not complements. At old quantities and new prices MUM /PM > MUC /PC. How to find MUM /PM = MUC /PC at new prices? 43/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Price changes Movie price falls, optimal cola consumption changes: Assume cola and movies are not complements. At old quantities and new prices MUM /PM > MUC /PC. How to find MUM /PM = MUC /PC at new prices? Diminishing marginal utility means decreasing Q colas will increase MUC. Decrease quantity of cola to find the new optimal choice. Consume less of any good that is not a complement. 43/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Income changes Income falls from $40 to $28: The budget line shifts in. Optimal movie consumption falls from 4 to 3 per month. This is a movement of the individual demand curve. Income shifts individual demand at every price. 44/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Substitution and income effects Price changes affect quantity demanded through two mechanisms: 1 Substitution effect: change relative price of good. Always negative (P grows, Q D falls). 2 Income effect: change purchasing power/real income. Normal good: negative (reinforce sub effect). Inferior good: positive (opposite of sub effect). 45/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Substitution and income effects Extreme examples highlight substitution and income effects: 1 Does increasing price reduce quantity demanded if there are thousands of similar goods, each taking only a very small budget share? 2 Does increasing price reduce quantity demanded if there is only one good that takes your entire budget? When and why does this distinction matter? 46/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Total price effect Movie price falls from $8 to $4: Budget line rotates out. Point J: new optimal bundle. Total price effect: move from C (2 movies) to J (6 movies). Decomposition: Price effect = Income effect + Substitution effect. 47/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Substitution effect Substitution effect: change in quantity bought if relative prices change but consumer utility does not change. Isolate with hypothetical budget cut after price change: reduce income until hypothetical optimum is on initial indifference curve. Move from C (2 movies) to K (4 movies). 48/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Substitution effect Substitution effect: change in quantity bought if relative prices change but consumer utility does not change. Always negative (opposite direction of price): Reducing a goods price makes it cheaper relative to other goods, always substitute towards that good away from goods. 49/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Income effect Income effect: change in quantity bought because new price affects purchasing power. Movie price falls from $8 to $4: IE is difference between total price effect and substitution effect. Move to new utility (IC2 ). Move from K (4 movies) to J (6 movies) meaning movies are a nor- mal good. 50/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Income effect Income effect: change in quantity bought because new price affects purchasing power. Movie price falls from $8 to $4: IE is difference between total price effect and substitution effect. Move to new utility (IC2 ). Move from K (4 movies) to J (6 movies) meaning movies are a nor- mal good. Price falls =⇒ feel richer =⇒ positive IE on all normal goods. 50/51 Intro Pref + Utility Indifference Constraints Choice Paradox of Val Demand Decomposing effects Inferior goods Inferior goods: quantity demanded grows when income falls. SE always negative, but counteracted by positive IE. SE bigger than IE makes demand slope downward. Conflict predicts relatively inelastic demand for inferior goods. 51/51