Lecture 6 Consumer Theory Sources: http://www.arts.cornell.edu/econ/wissink/econ1110jpw/ http://www.investopedia.com/university/economics  http://ingrimayne.com/econ/ Case, Fair, Oster, Introduction to Microeconomics Case, Fair, Principles of Microeconomics

Consumer Theory Study of how people use their limited means(resources) to make purposeful choices. Assumes that consumers understand their choices (preferences) and the prices (opportunity costs) associated with each choice. Assumes that consumers consider the alternatives and choose to maximize their objective subject to their constraints.

Why Don’t We Just Use the Demand Curve by Itself? The “Market Demand Function & Curve” for a single good aggregates and summarizes all market consumers’ intended purchases. “Consumer Theory” allows us to build a model from scratch to: Build the market demand from its core “ingredients.” Use the consumer theory model to address issues not adequately explained via reference to the summarized and aggregated model.

Two Components of Consumer Demand Opportunities: What can the consumer afford? What are the consumption possibilities? Summarized by the budget constraint Preferences: What does the consumer like? How much does a consumer like a good? How would a consumer willingly trade off one good for another? Summarized by preferences, indifference curve maps and the utility function

Ultimate Goal We are going to study the demand for two goods (hamburger and candy bar) using two different consumers (Mustafa and Hülya). For each good and each consumer, the theory produces a demand function: Demand function for hamburgers: Hi = fh(Ph, PC, I) , i=Mustafa, Hülya Demand function for candy bar: Ci = fC(Ph, PC, I) , i=Mustafa, Hülya where Ph is the price of hamburgers, PC is the price of candy bars, and I is the consumer i’s income. When we properly aggregate the two consumers’ demand equations we get the market demand equations, one for hamburgers and one for candy bars.

What Is A Budget Constraint? A budget constraint shows the consumer’s purchase opportunities as every combination of two goods that can be bought at given prices using up a given amount of income.

Mustafa’s Budget Constraint Suppose Mustafa faces the following prices: Hamburger $4/per unit. Candy bar $2/per unit. Suppose Mustafa’s income is $40. Hamburger Candy Bars The table shows the combinations of hamburgers and candy bars that Mustafa can buy using up all her income.

Mustafa’s Budget Constraint The mathematical expression for the budget constraint is: Income = Price Hamburgers x Hamburgers + Price Candy bars x Candy bars In symbols: I = Ph H + PC C

Points on Mustafa’s Budget Constraint when Ph=$4, PC=$2, I=$40 So, all the points on Mustafa’s budget constraint satisfy the equation: 40 = 4H + 2C Which can be re-written: C = (40 - 4 H)/2  C = 20 – 2H Slope of the budget constraint: -2 I = PhH + PCC  C = I/PC – (Ph / PC)H The absolute value of the slope of the budget line is the ERS ≡ Economic Rate of Substitution (= 2 in this example).

Graph of Mustafa’s Budget Constraint The graph to the right shows a picture of Mustafa’s budget constraint. Mustafa’s Candy bars The slope is equal to -2, as shown on the last slide (ERS = 2). Hamburgers

Mustafa’s Income Goes Up When Mustafa’s income goes up to $80, he is able to buy more candy bars and more hamburgers. Mustafa’s Candy bars The purple squares show his new budget constraint. Notice that the slope doesn’t change (ERS = 2, still). Hamburgers

Mustafa Faces New Prices Now, suppose that the price of hamburgers falls to $2/unit. and the price of candy remains $2/unit. and I=$40. Mustafa’s Candy bars The purple squares show the new budget constraint. Notice that the slope is now -2/2 = -1 (ERS = 1). Hamburgers

Mustafa Faces New Prices Now, suppose that the price of hamburgers remains at $4/lb and I=$40 and the price of candy falls from $2/lb. to $1/lb. Mustafa’s The purple squares show the new budget constraint. Notice that the slope is now -4/1 = -4 (ERS = 4). Hamburgers

Mustafa Faces New Prices and Income Now, suppose that: Income = 2 x $40 = $80. PB = 2 x $4/lb = $8/lb. PC = 2 x $2/lb = $4/lb. Mustafa’s Candy bars The purple squares show the new budget constraint. Mustafa is right back where he started – nothing real has changed. Hamburgers

Application #1: From Individual to Market Demand Market demand is simply the sum of all individual demands in the economy. If there are two consumers of hamburgers: Mustafa and Hülya, then the market demand is the sum of the quantities demanded by Mustafa and Hülya at each market price.

Application #1: From Individual to Market Demand Hülya Mustafa H0,h H1,h H0,m H1,m H0,market H1,market H0,h + H0,m = H0, market at P0 H1,h + H1,m = H1, market at P1

Preferences: Definitions A bundle of goods, B, specifies exact quantities of all the possible goods and services a consumer cares about. ASSUME: our consumer has preferences over all the possible bundles that could be assembled. How can we define these preferences? Let R = “at least as good as” B0 R B1 means: B0 is at least as good as B1 . Let IN = “indifferent to” B0 IN B1 means: B0 is indifferent to B1 . Let SP = “strictly preferred to” B0 SP B1 means: B0 is strictly preferred to B1 .

Preferences: Assumptions on R More is better than less: If B1 has more of at least one good than B0 (and no less of any other good), then B1 R B0 If B1 has more of ALL goods, then let’s agree that we will say B1 is actually better. Transitivity: If B0 R B1 and B1 R B2, then B0 R B2 Average bundles are at least as good as extreme bundles: If B0 IN B1 and B2 is an “average” of B0 and B1, then B2 R B0 and B2 R B1

Preferences: Assumptions on R “at least as good as” More is better than less: If B1 has more of at least one good than B0 (and no less of any other good), then B1 R B0 If B1 has more of ALL goods, then let’s agree that we will say B1 is actually better. Transitivity: If B0 R B1 and B1 R B2, then B0 R B2 Average bundles are at least as good as extreme bundles: If B0 IN B1 and B2 is an “average” of B0 and B1, then B2 R B0 and B2 R B1

Indifference Curve Maps Preferences that are described by the “at least as good as” operator can be represented by indifference curve maps. Recall assumptions on R: “more is better, or at least no worse” “rational” “averages are at least as good as extremes” A particular indifference curve connects all of the bundles that a consumer likes equally. that is all bundles for which B0 IN B1. An indifference curve map is ALL the indifference curves.

isoutility (iso is Greek and means "the same" or "equal") line or, more commonly, an indifference curve. Indifference curve maps and their 5 properties. Every bundle lives on some indifference curve – the indifference curve “map” is like a dense forest of indifference curves. Indifference Curves never slope “up”. Better bundles are on indifference curves to the “north-east”. Indifference Curves never cross each other. Indifference Curves never “bow-out”, they are either linear or “bowed-in”

Proving IC Map Properties Indifference Curves never slope “up” Better bundles are on indifference curves to the “north-east”

Proving IC Map Properties Indifference Curves never cross each other. BUT So… violates either more is better or transitivity. Indifference Curves never “bow-out”, they are linear or “bowed-in”

Mustafa’s Preferences Represented via Indifference Curves These 3 indifference curves describe a part of Mustafa’s preferences. Mustafa’s Points on I2 are preferred to points on I1. Points on I1 are preferred to points on I0. Candy bars Hamburgers

The Marginal Rate of Substitution At any given the bundle, the Marginal Rate of Substitution (MRS) tells us how much of one good Mustafa would willingly trade for an extra unit of the other good and remain indifferent. The MRS equals the absolute value of the slope of the indifference curve at a bundle of hamburgers and candy bars. The MRS declines (or stays constant) as we move down an indifference curve – it never gets larger. Mustafa’s Candy bars Hamburgers

From Preferences to Utility Utility is the way economists describe and sometimes measure preferences. Among two bundles, the one with the higher utility is the preferred bundle. If two bundles generate the same satisfaction then they have the same utility and we say that the consumer is indifferent between the two bundles.

Historical Note: What’s a Util? 19th Century Cardinalists William Stanley Jevons in 1859, he published General Mathematical Theory of Political Economy in 1862, outlining the marginal utility theory of value. For Jevons, the utility or value to a consumer of an additional unit of a product is inversely related to the number of units of that product he already owns, at least beyond some critical quantity. 20th Century Ordinalists Sir John Hicks was a British economist and one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his statement of consumer demand theory in microeconomics, and the IS/LM model (1937), which summarised a Keynesian view of macroeconomics.

Cardinalist approach says that utility can be measured in monetary units. Some economists even coined the word 'utils' for measurement units. Ordinalist approach says the consumer need not know in specific units the utility, but it is enough if he can rank the various 'baskets of goods' to determine order of preference. Ordinalist approach can be further divided into "indifference curves”.

What’s a Utility Utility is an abstract concept rather than a concrete, observable quantity. Total utility is the aggregate sum of satisfaction or benefit that an individual gains from consuming a given amount of goods or services in an economy. The amount of a person's total utility corresponds to the person's level of consumption. Usually, the more the person consumes, the larger his or her total utility will be.  Marginal utility is the additional satisfaction, or amount of utility, gained from each extra unit of consumption. Although total utility usually increases as more of a good is consumed, marginal utility usually decreases with each additional increase in the consumption of a good. This decrease demonstrates the law of diminishing marginal utility. Because there is a certain threshold of satisfaction, the consumer will no longer receive the same pleasure from consumption once that threshold is crossed. In other words, total utility will increase at a slower pace as an individual increases the quantity consumed.

What’s a Utility Take, for example, a chocolate bar. Let's say that after eating one chocolate bar your sweet tooth has been satisfied. Your marginal utility (and total utility) after eating one chocolate bar will be quite high. But if you eat more chocolate bars, the pleasure of each additional chocolate bar will be less than the pleasure you received from eating the one before - probably because you are starting to feel full or you have had too many sweets for one day.

many sweets for one day. This table shows that total utility will increase at a much slower rate as marginal utility diminishes with each additional bar. Notice how the first chocolate bar gives a total utility of 70 but the next three chocolate bars together increase total utility by only 18 additional units. The law of diminishing marginal utility helps economists understand the law of demand and the negative sloping demand curve.

The Consumer Theory Problem: What Bundle of Hamburgers and Candy bars? The optimal amount of hamburgers and candy bars to consume is the amount that maximizes utility subject to the budget constraint. The formal problem: Choose a bundle of (Hamburgers, Candy bars) to maximize u = u(Hamburgers, Candy bars) subject to $PhH + $PCC ≤ $I

How to Find the Best Bundle Utility is at a maximum when: all income is allocated to the goods you derive utility from AND… there is no way to transfer income from one good to another and make yourself any better off. you are on the highest indifference curve you can possibly be on, and still on the budget line. the slope of the indifference curve is equal to the slope of the budget constraint  MRS = ERS

How to Find Mustafa’s Best Bundle When I=$40, PC=$2 & PH=$4 20 Indifference Curves Budget Line 10 H H Can Do Willing to Do

How to Find Mustafa’s Best Bundle When I=$40, PC=$2 & PB=$4

Mustafa’s Best Bundle When I=$40, PC=$2 & PB=$4

Interpretation: Let MUh = Mustafa’s marginal utility of hamburgers. It measures the change in utility as we change hamburger consumption by an extra unit while holding candy consumption constant. Let MUC = Mustafa’s marginal utility of candy bars. It measures the change in utility as we change candy consumption by an extra unit while holding hamburger consumption constant. The “law of diminishing marginal utility” would imply that, ceteris paribus, as Good “i” increases, the MUi decreases, ceteris paribus as Good “i” decreases, MUi increases, ceteris paribus NOTE: If hamburgers are on the horizontal and carrots on the vertical, then the MRS = MUh /MUC Recall: the MRS declines (or stays constant) as we move along an indifference curve

So, the MRS = MUh/ MUc So, the ERS = Ph/ PC At an optimal bundle: You spend/allocate all your money AND MRS = ERS Rewritten we have: MUh / MUC = Ph/ PC now rearrange to get… MUh/Ph= MUC/PC Get same optimal bundle either way!

Mustafa’s Best Bundle When I=$40, PC=$2 & PB=$4 At an optimal bundle On the budget line The indifference curve is tangent to the budget line ΙslopeI of indifference curve = MRS ΙslopeI of budget line = ERS = Ph/ PC MRS = ERS MRS = Ph/ PC Indifference Curve Budget Line H

Mustafa’s Best Bundle When I=$40, PC=$2 & PB=$4 Units of Y Units of X 30 100 140 200