layout: true background-image: url(figs/tcb-logo.png) background-position: bottom right background-attachment: fixed; background-origin: content-box; background-size: 10% --- class: title-slide .row[ .col-7[ .title[ # Consumer Behavior ] .subtitle[ ## Rational Consumer Choice ] .author[ ### Dennis A.V. Dittrich ] .affiliation[ ] ] .col-5[ ] ] --- ### Consumer Behavior: The Economic Approach Consumer behavior is best understood in three distinct steps: .col-7[ 1. **Budget constraints** Consumers have limited incomes which restrict the quantities of goods they can buy. 2. **Consumer preferences** The first step is to find a practical way to describe the reasons people might prefer one good to another. 3. **Consumer choices** * Link preferences and budget constraints. * Which combination of goods will maximize the consumers’ satisfaction? ] --- # Budget Constraint .row[.col-4[ A __bundle:__ a particular combination of two or more goods in welldefined quantities. We assume that we can compare different bundles of goods and decide which one we prefer. ] .col-8[ ![](img02/Chapter030.png) ] ] --- ## The Budget Constraint --- Budget Line .row[ .col-4[ __Budget constraint:__ the set of all bundles that exactly exhaust the consumer’s income at given prices. Its slope is the negative of the price ratio of the two goods, it is known as the **Marginal Rate of Transformation (MRT)**. __Affordable set__, or feasible set: bundles on or below the budget constraint; bundles for which the required expenditure at given prices is less than or equal to the income available\. __Unaffordable set__, or unfeasible set: bundles that lie outside the budget constraint ] .col-8[ ![](img02/Chapter031.png) $$M = x_1p_1 +x_2p_2 = \sum_i^n p_i x_i $$ $$x_2 = \frac{M}{p_2} - \frac{p_1}{p_2}x_2 $$ ] ] --- ### Budget Shifts Due to Price and Income Changes .row[ .col-6[ If the price of ONLY one good changes… * The slope of the budget constraint changes. ] .col-6[ The Effect of a Rise in the Price of Shelter ![](img02/Chapter032.png) ]] .row[ .col-6[ If the price of both goods change by the same proportion… * The budget constraint shifts parallel to the original one. If income changes… * The budget constraint shifts parallel to the original one. ] .col-6[ The Effect of Cutting Income by Half ![](img02/Chapter033.png) ]] --- class: practice-slide # Exercise ![](img02/Chapter031.png) .col-8[ Show the effect on the budget constraint of a fall in the price of shelter from 5 Euro/sqm to 4 Euro/sqm. ] --- ## Budgets Involving More Than Two Goods .row[ .col-5[ When we have more than 3 goods, the budget constraint becomes a __hyperplane__, or __multidimensional plane__. ]] .row[ .col-5[ In this case, view the consumer’s choice as one between a good, _X_, and an amalgam of other goods, _Y_. This amalgam is called the __composite good__. * The amount of income left after buying good _X_ * The amount the consumer spends on goods other than good _X_ ] .col-7[ The Budget Constraints with the Composite Good ![](img02/Chapter034.png) ]] --- ## A Quantity Discount Gives Rise to a Nonlinear Budget Constraint ![](img02/Chapter035.png) --- ## Budget Constraints Following Theft of Gasoline, Loss of Cash ![](img02/Chapter036.png) --- # Comparing bundles: Preferences Comparing two bundles `\(x\)` and `\(y\)` from the set of all possible bundles of goods `\(\Gamma\)` .col-7[ **Strict preference**: `\(x \succ y\)` `\(x\)` is preferred to `\(y\)` **Weak preference**: `\(x \succeq y\)` `\(x\)` is at least as good as `\(y\)` **Indifference**: `\(x \succeq y ∧ y \succeq x\)` or `\(x \sim y\)` `\(x\)` is at least as good as `\(y\)` and `\(y\)` as least as good as `\(x\)` * Strict preference, weak preference and indifference are ordinal relations. * They only say something about the order of preference of the bundles of goods. * Nothing is said about how strong the differences are. ] --- # Preference Ordering .col-7[ __Preference ordering__: a ranking of all possible consumption bundles in order of preference. They Differ widely among consumers Properties of well behaved Preference Orderings: __Completeness:__ the consumer is able to rank all possible combinations of goods and services. __Reflexive:__ a bundle A is at least as good as itself. __Transitivity:__ for any three bundles A, B, and C, if he prefers A to B and prefers B to C, then he always prefers A to C. __More-Is-Better:__ other things equal, more of a good is preferred to less. __Convexity:__ mixtures of goods are preferable to extremes. ] --- class: reflection-slide # Food for thought .col-8[ If people prefer mixtures of goods to extremes, why do restaurants not sell ice cream topped pizza? ] --- ### Preference Ordering and Equally Preferred Bundles ![](img02/Chapter037.png) --- # Properties of Indifference Curves .row[ .col-5[ __Indifference curve:__ a set of bundles among which the consumer is indifferent. * Any bundle has an indifference curve passing through it. * Are Downward-sloping. * This comes from the “more-is-better” assumption. * Cannot cross. * Become less steep as we move downward and to the right along them. * This property is implied by the convexity property of preferences. ] .col-7[ An Indifference Curve ![](img02/Chapter038.png) ] ] --- # Part of an Indifference Map .row[ .col-5[ __Indifference map:__ a representative sample of the set of a consumer’s indifference curves, used as a graphical summary of her preference ordering. Each indifference curve in the map shows the bundles of goods among which the person is indifferent. The further away from the origin the indifference curves are, the higher the level of satisfaction they represent. ] .col-7[ ![](img02/Chapter039.png) ]] --- ## Why Two Indifference Curves Do Not Cross .row[ .col-7[ ![](img02/Chapter0310.png) ] .col-5[ From `$$D\sim F$$` `$$D\sim E$$` and transitivity follows `$$\rightarrow F\sim E.$$` But, `\(F\)` represents more shelter and more food than `\(E\)`: `$$F\succeq E$$` Contradiction! ]] --- # Trade-offs Between Goods .col-7[ __Marginal rate of substitution (MRS):__ the rate at which the consumer is willing to exchange the good measured along the vertical axis for the good measured along the horizontal axis. The MRS is equal to the absolute value of the slope of the indifference curve. ] ![](img02/Chapter0311.png) --- ## Diminishing Marginal Rate of Substitution .row[.col-7[ ![](img02/Chapter0312.png) ] .col-5[ Along their curve, indifference curves exhibit a dimishing marginal rate of substitution. Indifference curves are convex. * As more and more of one good is consumed, we can expect that a consumer will prefer to give up fewer and fewer units of a second good to get additional units of the first one. * Consumers generally prefer balanced bundles of goods ]] --- # People with Different Tastes ![](img02/Chapter0313.png) --- class: practice-slide # Exercise .col-8[ Gary likes food but dislikes cigarette smoke. The more food he has, the more he would be willing to give up to achieve a given reduction in cigarette smoke. If food and cigarette smoke are the only two goods, draw Gary's indifference curves. ] --- # The Best Feasible Bundle .row[ .col-4[ Consumer’s Goal: to choose the __best affordable bundle__. * The same as reaching the highest indifference curve she can, given her budget constraint. * For convex indifference curves the best bundle will always lie at the point of tangency. ] .col-8[ ![](img02/Chapter0314.png) ]] --- class: practice-slide # Exercise ![](img02/Chapter0314.png) .col-8[ Suppose the marginal rate of substitution at point A is 1. Show that this means the consumer will be better off if she purchases less food and more shelter than at A.] --- ## Corner solutions .row[ .col-6[ __Corner solution__: in a choice between two goods, a case in which the consumer does not consume one of the goods. ] .col-6[ ![](img02/Chapter0315.png) ]] .row[ .col-6[ Equilibrium with Perfect Substitutes ] .col-4[ ![](img02/Chapter0316.png) ]] --- class: practice-slide # Exercise .col-8[ Albert always uses exactly one pat of butter on each piece of toast. How do his indifference curves look like?. At what point on these indifference curves will he consume? ] --- # Cash or Food Stamps? .row[ .col-5[ Food Stamp Program * Objective - to alleviate hunger. * How does it work? * People whose incomes fall below a certain level are eligible to receive a specified quantity of food stamps. * Stamps cannot be used to purchase cigarettes, alcohol, and various other items. * The government gives food retailers cash for the stamps they accept. ] .col-7[ ![](img02/Chapter0317.png) ] ] --- ## Where Food Stamps and Cash Grants Yield Different Outcomes ![](img02/Chapter0318.png) --- class: reflection-slide # Food for Thought .col-8[ Why do people often give gifts in kind instead of cash? ] --- ## The Utility Function Approach to Consumer Choice .row[ .col-7[ Finding the highest attainable indifference curve on a budget constraint is just one way to analyze the consumer choice problem In this second approach, we represent the consumer’s preference not with an indifference map, but with a utility function. **Utility** Numerical value representing the satisfaction that a consumer gets from a bundle of goods. **Utility Function** Function that assigns a level of utility `\(U(x)\)` to each bundle of goods `\(x\)`. ] .col-5[ Preferences that are * Complete, * Reflexive (d.h. x ∼ x), * Transitive and * Continuous (i.e. small changes in the amount of one good cause small changes of in the level of utility) can be represented by utility functions. ] ] --- # Ordinal versus Cardinal Utility .row[.col-6[ ### Ordinal Utility Function Utility function that generates a ranking of bundles in order of most to least preferred. It does not indicate by how much one bundle is preferred to another. ] .col-6[ ### Cardinal Utility Function Utility function that generates a ranking of bundles in order of most to least preferred. Additionally, utility differences are meaningful; they describe by how much one bundle is preferred to another. ]] .row[.col-7[ The actual value is not important. An ordinal ranking classification is usually sufficient to explain how most individual decisions are made. ]] --- ### Indifference Curves for the Utility Function `\(U=FS\)` .row[.col-7[ ![](img02/Chapter0319.png) ] .col-5[ For a specific utlity `\(\bar{U}\)` we have: `$$\bar{U}=FS$$` Solving for `\(S\)` we get the equation for the indifference curve representing the utility level `\(\bar{U}\)`: `$$S=\frac{\bar{U}}{F}$$` Utility along an indifference curve remains constant ![](img02/Chapter0320.png) ] ] --- ## Indifference Curves for the Utility Function `\(U(X,Y)=(2/3)X + 2Y\)` .row[.col-7[ ![](img02/Chapter0323.png) ] .col-5[ For a specific utlity `\(\bar{U}\)` we have: `$$\bar{U}=(2/3)X + 2Y$$` Solving for `\(Y\)` we get the equation for the indifference curve representing the utility level `\(\bar{U}\)`: `$$Y=\frac{\bar{U}}{2}-\frac{X}{3}$$` ]] --- # Marginal rate of substitution The MRS is equal to the absolute value of the slope of the indifference curve. .row[.col-7[ ![](img02/Chapter0311.png)] .col-5[ ![](img02/Chapter0320.png) ]] .row[ .col-6[ $$0 = MU_S\Delta S + MU_F\Delta F $$ $$MU_S\Delta S = -MU_F\Delta F $$ $$\frac{MU_S}{MU_F} = -\frac{\Delta F}{\Delta S} $$ ] .col-6[ $$ \left| -\frac{\Delta F}{\Delta S} \right| = MRS$$ `$$\rightarrow MRS = \left|\frac{MU_S}{MU_F}\right|$$` ]] The MRS is equal to the absolute value of the ratio of the marginal utilities. --- ### The Optimal Bundle when `\(U=XY\)`, `\(P_x=4\)`, `\(P_y=2\)`, and `\(M=40\)` .row[.col-6[ ![](img02/Chapter0324.png) ] .col-6[ At the optimal bundle the slope of the indifference curve and the budget line are identical: MRS=MRT. At the optimal bundle the ratio of marginal utilities is equal to the price ratio: $$\frac{MU_X}{MU_Y} = \frac{P_x}{P_y} $$ $$\frac{y}{x}=\frac{4}{2} $$ `$$y=2x$$` Using the budget constraint: $$40=4x+2\times 2x=8x $$ `$$x=\frac{40}{8}=5\quad y=2\times 5= 10$$` ] ] --- ## Summary .row[.col-6[ * Rational consumer choice takes preferences as given and assumes consumer will try to satisfy them in the most efficient way * Budget constraints tell us what combinations of goods the consumer can afford to buy * The market exchanges goods according to their Marginal Rate of Transformation that is given by their price ratio * Preference orderings can be represented by indifference curves, usually exhibiting diminishing marginal rates of substitution ] .col-6[ * The consumer is willing to exchange goods according to their Marginal Rate of Substitution that is given by the ratio of their marginal utilities * Utility maximization is achieved when the budget is allocated so that the marginal utility per dollar of expenditure is the same for each good: `$$\frac{MU_X}{P_x}=\frac{MU_Y}{P_y}$$` ]] .grey.footnote[Figures curtesy of Frank (2015); Microeconomics and Behavior; McGraw-Hill.]