Utility Maximization Lecture 13 Dr. Jennifer P. Wissink ©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved. March 15, 2017

Announcements: micro Spring 2017 Please make sure you see the Bb message all about prelim 1. Good job on the whole! ALL questions about grading go to me(Wissink) and only to me. Wissink Office Hours (for the rest of this week) Wednesday 3/15 from 12-2pm Thursday 3/16 from 2-4pm Friday 3/17 from 2-4pm

ECON Week at Cornell Monday: Exploring Careers in Government, Public Policy, and Academia 4:30-5:30PM, 401 Physical Sciences Building Tuesday: Exploring Corporate, Finance, and Consulting Careers 4:30-5:30PM, 120 Physical Sciences Building Wednesday: Economics Department Meet & Greet. Food Provided. 4:30-5:30PM, 477 Uris Hall Thursday: Free Screening of The Big Short. Pizza Provided. 4:45PM, G01 Uris Hall

i>clicker question James Bond like his martinis with equal parts Clearheart gin and Prairie Organic vodka. Shaken not stirred. He considers gin and vodka to be perfect complements. Which indifference curve map below would most likely be James Bond’s? A B C D E

i>clicker question Cathy and Susan consume only X and Y. Suppose Susan’s indifference curve is the BLUE one and Cathy’s indifference curve is the RED one. Which one of the following is the best choice? Susan likes X relatively more than Cathy likes X. Susan likes Y relatively more that Cathy likes Y. Susan has more income than Cathy. Susan has less income than Cathy. Susan and Cathy are irrational consumers since their indifference curves cross.

From Preferences to Utility Utility is the way economists describe and measure preferences with a number. Between two bundles... the better bundle gets a higher utility number. the worse bundle gets a lower utility number. if you are indifferent between the two bundles, they get the same utility number. UtilityMaryclaire = u(B, C) This is a 3-dimensional function! The indifference curve map versus the utility function!

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

How to Find Maryclaire’s Best Bundle When I=$40, PC=$2 & PB=$4 20 B B 10

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

Maryclaire’s Best Bundle (B*, C*) When I=$40, PC=$2 & PB=$4 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 better off.  She is on the highest indifference curve possible while still on the budget line. (If Maryclaire is VERY nicely behaved…) She 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.  Maryclaire’s MRS = ERS at E* C* E* Indifference Curve Budget Line B B*

Historical Note: What’s a Util? 20th Century Ordinalists Sir John Hicks 19th Century Cardinalists Let U=u(B, C) be Maryclaire’s utility function from consuming beans and carrots measured in utils. Then MUB = 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. MUB = ∆U/ ∆B ceteris paribus And MUC = Maryclaire’s marginal utility of carrots. MUC = ∆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 MUi decreases. William Stanley Jevons

The Cardinalists and the “Bang per Buck” Story What’s the “bang per buck”? 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 only 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 PB=$2 and PS=$10. At this bundle Stan’s marginal utilities are MUB=10utils & MUS =20utils. The l.d.m.u. has already set in for Stan. Stan’s income is some value I can’t compute. $700 $150 $220 $30 Stan is successfully solving the consumer theory problem for himself. Yes. No. Maybe so. If Stan moves $10 from S to B his utility will increase by 30 utils. 20 utils. 3 utils. 5 utils. 2 utils. Stan should buy more S & less B. buy more B & less S. buy more of both. just buy more of S. quit tennis.

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

Now What? Use the Model to Bake the Cake From Scratch What’s the cake? The market demand curve for beans. 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, PC=$2 & PB Varies from $4 to $2 to $1

i>clicker question So… are demand curves always necessarily downward sloping? That is, MUST they always satisfy the “law of demand”? Yes! No. Robert Giffen A Giffen Good is a good that violates the law of demand. That means, when $Px increases, the consumer buys more X. Or when the $Px decreases the consumer buys less X!

Reacting To An Own-Price Change with Fixed Income: Suppose the PX increases; what happens to QDX INCOME EFFECT SUBSTITUTION EFFECT X now looks relatively more expensive You feel poorer – your dollars now buy less “X” normal “X” inferior QDX increases QDX decreases QDX decreases QDX might increase OR decrease QDX decreases

i>clicker questions Consider only “own price” changes for goods where the consumer has a fixed income. If “X” is a normal good then its demand curve might be downward or upward sloping. it will never satisfy the law of demand. it will always satisfy the law of demand. it can’t have a substitution effect. it must only have an income effect. Consider only “own price” changes for goods where the consumer has a fixed income. If “Y” is an inferior good then its demand curve might be downward or upward sloping. it will never satisfy the law of demand. it will always satisfy the law of demand. it can’t have a substitution effect. it must only have an income effect. Consider only “own price” changes for goods where the consumer has a fixed income. If “W” is a good that violates the law of demand then it must be normal. it must be inferior. it might be inferior. it’s stupid. it’s hard to tell.