Lecture 3: Consumer Choice
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1 Lecture 3: Consumer Choice September 15, 2015
2 Overview Course Administration Ripped from the Headlines Quantity Regulations Consumer Preferences and Utility Indifference Curves Income and the Budget Constraint Making a Choice with Utility and the Budget Constraint
3 Course Administration 1. Return problem sets 2. Problem set answers may be updated until problem sets are returned 3. Problem set and RFH grades are posted on Blackboard presentation is graded, mostly on success in relating to the themes of the previous lecture article finding is pass/fail 4. Any questions or outstanding issues?
4 How What You re Learning is Policy-Relevant Ripped from Headlines presentation(s) As a reminder, next week Afternoon Finder Presenter Erica Harvey Yihan Cheng Ben Goebel Caroline DeCelles Evening Finder Presenter Alex Severn Katie Deeter McKenna Saady Anna Chukhno
5 Two Types of Quantity Regulations We just looked at regulations on price. Now we consider regulations on quantity. 1. Quota a regulated (almost always limited) quantity of a good or service provided 2. Government provision of a good or service (skip for time reasons)
6 Analyzing Quotas What s the impact of a quota on price? Give an example of a market with quotas
7 Quotas in Pictures Market Equilibrium: How Does Supply Change with a Quota? P S P* Q * D Q
8 Quotas in Pictures Supply with a Quota: What Happens to Price? P S S P* Q new Q * D Q
9 Quotas in Pictures Supply with a Quota: What Happens to CS and PS? P S S quota price P* Q new Q * D Q
10 Quotas in Pictures Supply with a Quota: What Happens to CS and PS? P S S CS new quota price P* PS new Q new Q * D Q
11 Quotas in Pictures Figuring Out the Differences P P* A B D S C E S quota price Q new Q * D Q
12 Figuring Out the Difference, Details Before CS = P P* A B D S C E S quota price Q new Q * D Q
13 Figuring Out the Difference, Details Before CS = A + B + C PS = P P* A B D S C E S quota price Q new Q * D Q
14 Figuring Out the Difference, Details Before CS = A + B + C PS = D + E P P* A B D S C E S quota price Q new Q * D Q
15 P S Figuring Out the Difference, Details S Before CS = A + B + C PS = D + E After CS = P* A B D C E quota price Q new Q * D Q
16 P S Figuring Out the Difference, Details S Before CS = A + B + C PS = D + E After CS = A PS = P* A B D C E quota price Q new Q * D Q
17 P S Figuring Out the Difference, Details S Before CS = A + B + C PS = D + E After CS = A PS = B + D P* A B D C E quota price Q new Q * D Q
18 P P* A B D S C E Q new Q * Figuring Out the Difference, Details D S quota price Q Before CS = A + B + C PS = D + E After CS = A PS = B + D Difference CS = A (A+B +C) = (B + C) < 0 PS = (B+D) (D+E) = B E, sign ambiguous transfer from
19 P P* A B D S C E Q new Q * Figuring Out the Difference, Details D S quota price Q Before CS = A + B + C PS = D + E After CS = A PS = B + D Difference CS = A (A+B +C) = (B + C) < 0 PS = (B+D) (D+E) = B E, sign ambiguous transfer from consumers to producers is
20 P P* A B D S C E Q new Q * Figuring Out the Difference, Details D S quota price Q Before CS = A + B + C PS = D + E After CS = A PS = B + D Difference CS = A (A+B +C) = (B + C) < 0 PS = (B+D) (D+E) = B E, sign ambiguous transfer from consumers to producers is B Note that nobody gets C or E after trades that don t take place DWL = C + E
21 Why Do We Study the Consumer s Problem? Build up to the demand curve from first principles Understand consumer choices Clearly illuminate areas where policy can act Illustrate welfare consequences of policy choices
22 Assumptions about Consumer Preferences 1. Completeness and Rankability You can compare all your consumption choices For two bundles A and B, you always either prefer A to B prefer B to A are indifferent between A and B 2. More is better at least no worse than less 3. Transitivity If A is preferred to B, and B to C, then A > C 4. The more you have of a particular good, the less of something else you are willing to give up to get more of that good
23 What is Utility? Overall satisfaction or happiness
24 What is Utility? Overall satisfaction or happiness Measured in utils! This framework allows us to describe what consumption or habits make you happier than other consumptions or habits It s not a tool for comparing across people
25 Some Example Utility Functions Most general U = U(X, Y ).
26 Some Example Utility Functions Most general U = U(X, Y ). They can take many forms U = U(X, Y ) = XY U = U(X, Y ) = X + Y U = U(X, Y ) = X 0.7 Y 0.3
27 Marginal Utility Marginal utility additional utility consumer receives from an additional unit of a good or service MU X = U(X, Y ) ( = U ) X X MU Y = U(X, Y ) ( = U ) Y Y
28 Marginal Utility Marginal utility additional utility consumer receives from an additional unit of a good or service MU X = U(X, Y ) ( = U ) X X MU Y = U(X, Y ) ( = U ) Y Y What is true about marginal utility of X as consumption of X increases?
29 Utility and Comparisons Ordinal: we can rank bundles from best to worst Not cardinal: we cannot say how much one bundle is preferred to another in fixed units We cannot make interpersonal comparisons No other assumptions on utility apart from the four preference assumptions.
30 Describing Your Utility A consumer is indifferent between two bundles (X 1, Y 1 ) and (X 2, Y 2 ) when U(X 1, Y 1 ) = U(X 2, Y 2 ) An indifference curve is a line where utility is constant: a combination of all consumption bundles that give the same utility
31 Working Up to an Indifference Curve Give me two items
32 Working Up to an Indifference Curve Give me two items Each axis is a quantity of those items Give me some points where you are equally happy
33 Working Up to an Indifference Curve Give me two items Each axis is a quantity of those items Give me some points where you are equally happy Give me a point where you are less happy
34 Working Up to an Indifference Curve Give me two items Each axis is a quantity of those items Give me some points where you are equally happy Give me a point where you are less happy Give me some points where you are equally less happy
35 Why Can We Draw Indifference Curves? Because of the assumptions we made at the beginning about preferences: completeness and rankability All bundles have a utility level and we can rank them
36 Indifference Curves Level and Slope What does more is better tell us?
37 Indifference Curves Level and Slope What does more is better tell us? That higher indifference curves give more utility Curve must have a negative slope Suppose that you increase your consumption of X More is better you are happier To be equally happy as before, you should give up some Y
38 More Utility on Curves Farther From Origin
39 Indifference Curve Shape Curves never cross it would violate transitivity Curves are U-like (convex) with respect to the origin Comes from assumption about diminishing marginal utility Your willingness to trade off differs along the curve
40 Steepness of the Indifference Curve We know that you are equally happy anywhere along the indifference curve So what changes as you move along the curve?
41 Steepness of the Indifference Curve We know that you are equally happy anywhere along the indifference curve So what changes as you move along the curve? you are trading off X and Y the rate at which you trade them off tells us how much you value them
42 When the curve is steep, what are you willing to give up more of? Q Y Q X
43 When the curve is steep, what are you willing to give up more of? Q Y Q X
44 When the curve is steep, what are you willing to give up more of? Q Y ΔQ Y ΔQ X Q X
45 When the curve is flat, what are you willing to give up more of? Q Y Q X
46 When the curve is flat, what are you willing to give up more of? Q Y Q X
47 When the curve is flat, what are you willing to give up more of? Q Y ΔQ Y ΔQ X Q X
48 Quantifying the Trade-off in the Indifference Curve How much of X are you willing to give up for Y? We call the Marginal Rate of Substitution the trade-off between these two Define MRS XY = MU X MU Y = slope of indifference curve
49 Quantifying the Trade-off in the Indifference Curve How much of X are you willing to give up for Y? We call the Marginal Rate of Substitution the trade-off between these two Define MRS XY = MU X MU Y = slope of indifference curve We can rewrite as MRS XY = MU X MU Y = Y X ( = ) U X U Y It s a rate of change along the indifference curve Is it the same everywhere on the curve?
50 Quantifying the Trade-off in the Indifference Curve How much of X are you willing to give up for Y? We call the Marginal Rate of Substitution the trade-off between these two Define MRS XY = MU X MU Y = slope of indifference curve We can rewrite as MRS XY = MU X MU Y = Y X ( = ) U X U Y It s a rate of change along the indifference curve Is it the same everywhere on the curve? Not necessarily. If you want a derivation, see the textbook!
51 Curves for Perfect Complements Work with your neighbor! Suppose we have two goods that are perfect complements X and Y being perfect complements means each is useless without the other What do the indifference curves look like? We write this utility as U = min{ax, by } Q Y Q X
52 Curves for Perfect Complements Work with your neighbor! Suppose we have two goods that are perfect complements X and Y being perfect complements means each is useless without the other What do the indifference curves look like? We write this utility as U = min{ax, by } Q Y Q X
53 Curves for Substitutes Work with your neighbor! Q Y Suppose we have two goods that are perfect substitutes What do the indifference curves look like? Q X
54 Curves for Substitutes Work with your neighbor! Q Y Suppose we have two goods that are perfect substitutes What do the indifference curves look like? Write as U = ax + by A A Q X
55 Budget Constraint Assumptions 1. Each good has a fixed price and infinite supply 2. Each consumer has a fixed amount of income to spend 3. The consumer cannot save or borrow
56 Defining the Budget Constraint Budget constraint: I = P X Q X + P Y Q Y feasible bundle combinations of X and Y that the consumer can purchase with his income infeasible bundle all the combinations the consumer is just too poor to get
57 Drawing the Budget Constraint What if you spend all your money on X or Y? Q Y Q X
58 Drawing the Budget Constraint Q Y I/P Y I/P X Q X
59 Drawing the Budget Constraint Q Y I/P Y I/P X Q X
60 Drawing the Budget Constraint Q Y I/P Y Feasible set: Things you can buy I/P X Q X
61 Drawing the Budget Constraint Q Y I/P Y Infeasible set: Things you cannot afford! Feasible set: Things you can buy I/P X Q X
62 Slope of the Budget Constraint Algebra of the slope I = P X Q X + P Y Q Y
63 Slope of the Budget Constraint Algebra of the slope I = P X Q X + P Y Q Y P Y Q Y = I P X Q X Q Y = I P X Q X P Y P Y
64 Slope of the Budget Constraint Algebra of the slope I = P X Q X + P Y Q Y P Y Q Y = I P X Q X Q Y = I P X Q X P Y P Y Q Y = P X P Y Q X + I P Y So an additional unit of Q X requires you to give up P X P Y of Q Y
65 What Affects the Position of the Budget Constraint? Things that shift the slope
66 What Affects the Position of the Budget Constraint? Things that shift the slope Change in prices, P X or P Y And how do they change things? Things that don t change the slope, but move the line in and out
67 What Affects the Position of the Budget Constraint? Things that shift the slope Change in prices, P X or P Y And how do they change things? Things that don t change the slope, but move the line in and out Change in income How does this change the picture?
68 What Affects the Position of the Budget Constraint?
69 How to Be As Happy as Possible Maximize your utility given your budget constraint How do you do it?
70 How to Be As Happy as Possible Maximize your utility given your budget constraint How do you do it?
71 Algebra of Utility Maximization Utility is maximized, given the budget constraint, when the slope of the indifference curve is tangent to the budget constraint tangency equality MRS XY = P X P Y
72 Algebra of Utility Maximization Utility is maximized, given the budget constraint, when the slope of the indifference curve is tangent to the budget constraint tangency equality MRS XY = P X P Y MU X MU Y = P X P Y
73 Algebra of Utility Maximization Utility is maximized, given the budget constraint, when the slope of the indifference curve is tangent to the budget constraint tangency equality MRS XY = P X P Y MU X = P X MU Y P Y MU X = MU Y P X P Y
74 In-Class Problem Sarah gets utility from soda (S) and hotdogs (H). Her utility function is U = S 0.5 H 0.5, MU S = 0.5 H0.5, and MU S 0.5 H = 0.5 S0.5. H 0.5 Sarah s income is $12, and the prices of soda and hotdogs are $2 and $3, respectively. 1. Draw Sarah s budget constraint 2. What amount of sodas and hotdogs makes Sarah happiest, given her budget constraint? (Recall that you have two equations and two unknowns.)
75 What We Did This Class 1. Quotas 2. Preferences and utility 3. Indifference curves 4. Budget constraint 5. Optimization
76 Next Class Turn in Problem Set 3 Elasticity: GLS, Section 2.5 and read about avocados Paper assignment handout
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