Consumer Theory Applications Lecture 14 Dr. Jennifer P. Wissink ©2016 John M. Abowd and Jennifer P. Wissink, all rights reserved. March 16, 2016

Prelim 1 Epilogue - Reminder u Scores are posted to CMS. See Blackboard for important messages about grades. u About any low scores: Stay calm and do NOT panic. Remember our grading rubric... you can bank on those MEL and i>clicker points, so try to relax. Go re-read the syllabus. Play with the Grand Score Calculator. u TAs will hand back exams in sections and during their office hours based on what you checked on the front of your exam paper. If you did not check anything, see the head TA at office hours or here in lecture. u Re-grades: Wissink and only Wissink deals with ANY re-grade issues. Even if the re-grade is simply adding points wrong, it goes via Wissink (so we can make sure the master spread sheet gets updated). Fill out the form (see Bb) and turn your exam and form into me ASAP. u REGRADE DEADLINE: Monday March 21 by end of Wissink Office Hours (that is, 2pm)

From Preferences to Utility u Utility is the way economists describe and measure preferences. u Between two bundles, the one with the higher utility is the preferred bundle. u If two bundles generate the same satisfaction then they have the same utility and we say that the consumer is indifferent between the two. u Utility Maryclaire = u(B, C) –This is a 3-dimensional function! u The indifference curve map versus the utility function!

The Consumer Theory Problem: Decisions, Decisions, Decisions! u So… for Maryclaire and Beans and Carrots, what bundle is best? –Ok, what bundle will she buy? u Let’s bring together what she is willing to do with what she is able to do! u The optimal amount of beans and carrots to consume is the amount that maximizes her utility subject to her budget set. u Maryclaire’s (the consumer’s) formal problem: Choose a bundle of (Beans, Carrots) to maximize Utility Maryclaire = u(B, C) subject to $P B B + $P C C ≤ $I

How to Find Maryclaire’s Best Bundle When I=$40, P C =$2 & P B =$4 C C B B

C B

Maryclaire’s Best Bundle When I=$40, P C =$2 & P B =$4 Budget Line Indifference Curve E* C B B* C* u 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. –So... You are on the highest indifference curve you can possibly be on, and still on the budget line. »(When the consumer is VERY nicely behaved…) The consumer is on an indifference curve that is tangent to her budget line. »At E* the slope of the indifference curve is equal to the slope of the budget constraint. »  MRS = ERS at E*

Historical Note: What’s a Util? u 19 th Century Cardinalists –Let U=u(B, C) be Maryclaire’s utility function from consuming beans and carrots measured in utils. –Then MU B = Maryclaire’s marginal utility of beans. »It measures the change in utility as we change bean consumption by an incremental unit while holding carrot consumption constant. »MU B = ∆U/ ∆B ceteris paribus –And MU C = Maryclaire’s marginal utility of carrots. »MU C = ∆U/ ∆C ceteris paribus –Now, the “law of diminishing marginal utility” would imply that, ceteris paribus, as good “i” increases in the bundle (holding everything else constant), eventually the MU i decreases. u 20 th Century Ordinalists William Stanley Jevons Sir John Hicks

The Cardinalists and the “Bang per Buck” Story u What’s the “bang per buck”? u So what’s true at an optimal bundle? –(1) Spend/Allocate all your income and –(2) Equate the “bang per buck” across all goods you consume.

i>clicker questions Stan gets utility from protein bars (B) and sports drinks (S). His utility is currently 147 utils. He is spending all his income. He is consuming B=100 bars and S=50 drinks. Prices are P B =$2 and P S =$10. At this bundle marginal utilities are MU B =10utils & MU S =20utils. The ldmu has already set in. Stan’s income is A.some value I can’t compute. B.$700 C.$150 D.$220 E.$30 Stan is successfully solving the consumer theory problem for himself. A.Yes. B.No. C.Maybe so. Stan should A.buy more S & less B. B.buy more B & less S. C.buy more of both. D.just buy more of S. E.quit tennis. If Stan moves $10 from S to B his utility will increase by A.30 utils. B.20 utils. C.3 utils. D.5 utils. E.2 utils.

Reconciling the “Bang per Buck” Story with the MRS=ERS Story u Recall: The ERS = $P B / $P C u Recognize (trust me): The MRS = MU B / MU C (when Beans are on the horizontal and Carrots on the vertical) u Recall for the ordinalist: At an optimal bundle E* –(1) You allocate all your money to beans and carrots & –(2) At E*, the MRS = ERS u Recall for the cardinalist: At an optimal bundle E* –(1) You allocate all your money to beans and carrots & –(2) At E*, you have MU B /$P B = MU C /$P C u Get same optimal bundle E* either way!

Now What? Use the Model to Bake the Cake From Scratch u What’s the cake? –The market demand curve for beans. u What’s the recipe to bake the cake? –Use the BL/IC diagram to get Maryclaire’s demand curve for beans.

How to Find Maryclaire’s Demand for Beans When I=$40, P C =$2 & P B Varies from $4 to $2 to $1 C $P B B B

Maryclaire’s Demand For Beans – Table Summary u The table shows the amount of beans that Maryclaire demands at each price. u These are the points of tangency from the indifference curve & budget line diagram.

Maryclaire’s Demand For Beans – Graphed (Nicely) u When the price of beans is $4/lb, Maryclaire demands 5.5 lbs of beans (A). u When the price of beans is $2/lb, Maryclaire demands 10 lbs of beans (B). u When the price of beans is $1/lb, Maryclaire demands 18 lbs of beans (C). u Her demand curve is shown at the right, again.