More On Elasticity Measures Lecture 11 Dr. Jennifer P. Wissink ©2017 John M. Abowd and Jennifer P. Wissink, all rights reserved. March 6, 2017

Example: Demand Function, Demand Curve & Own Price Elasticity of Demand Suppose you know the demand function for compact disc players (X) is: QDX = (T&P)(Pop) + 3I – 2PCD + 3PB – (5,145/T&P)PX Now… to go from the demand function to the demand curve, plug in values for everything BUT PX So suppose: T&P=7; Pop=1,000; I=5,000; PCD=9; PB=15 You get: Now find own price elasticity of demand at PX=$7

END OF MATERIAL FOR PRELIM 1 WHEW!! HINTS: DON’T pull an “all-nighter”. READ questions carefully. Highlight or underline each important piece of information. For the multiple choice: Cover up all the answers and “do” the problem based on the narrative first, then your work will lead you to the correct answer. For “work” problem: Draw graphs big enough and carefully enough to make it so they can “show” you the way. Always label BOTH axes right away, it helps remind you of what goes where and what you are doing. Label any items you put into the graph (like D for demand and S for supply). Use a contrasting color to help see things. TRY each problem – at least do something so there is some chance that you might get partial credit for what you did. Don’t spin your wheels too long on any one problem. Give it your best shot, then move on, then go back to it if there is time.

Three Other Elasticities Own Price Elasticity of Supply Cross Price Elasticity of Demand Income Elasticity of Demand

The Other Elasticities Extremely similar formulas are used: (Midpoint) Arc formula With discrete data points Point formula When you use the slope of the function Just need to substitute in… …carefully!

The Other Elasticities You Need to Know Cross Price Elasticity of Demand

The Other Elasticities You Need to Know Income Elasticity of Demand

The Other Elasticities You Need to Know Own Price Elasticity of Supply

The Four Elasticities You Need to Know Own Price Elasticity of Demand Cross Price Elasticity of Demand Income Elasticity of Demand Own Price Elasticity of Supply

Example: Midpoint Arc Calculation of Own Price Elasticity of Supply Approximate own price supply elasticity between B and A. At B: QS=9 and PS=5 At A: QS=12 and PS=6 So: % change in QS = (12-9)/((12+9)/2) = 0.286 So: % change in PS = (6-5)/((6+5)/2) = 0.182 So: Own price supply elasticity over the interval ≈ 0.286 / 0.182 = 1.57 Nonlinear Supply Curve 12 10 8 Price 6 B A 4 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Quantity

Example: Demand Function & Income Elasticity of Demand Suppose you know the demand function for compact disc players (X) is: QDX = (T&P)(Pop) + 3I – 2PCD + 3PB – (5,145/T&P)PX Now… plug in values for everything BUT Income (I). So suppose: T&P=7; Pop=1,000; PCD=9; PB=15; PX=$7 You get: Now find income elasticity of demand at I=5,000

Consumer Theory

Consumer Theory Study of how people use their limited means 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.

i>clicker question Prof. Wissink really thinks Saabs are cool cars and she prefers them to Hondas, yet she drives a Honda Fit. This is because she is not a good shopper. she does not know how to solve the consumer theory problem. she does not have enough money to buy a Saab. All of the above are correct None of the above are correct

Two Components of Consumer Demand Opportunities: What can the consumer afford? What are the consumption possibilities? Summarized by the budget constraint and budget line 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 Interesting NPR Piece on “habit formation”! How You Can Harness The Power Of Habit http://www.npr.org/2012/02/27/147296743/how-you-can-harness-the-power-of-habit

Consumer Theory Goal #1 Build the Market Demand We are going to study the demand for two goods (beans and carrots) using two different consumers (Maryclaire and Katie). For each good and each consumer, the theory produces a demand function: Demand function for beans: Bi = fB(PB, PC, I) i=Maryclaire, Katie Demand function for carrots: Ci = fC(PB, PC, I) i=Maryclaire, Katie where PB is the price of beans, PC is the price of carrots, 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 beans and one for carrots.

What is a Budget Set and a Budget Line? A budget set 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. A budget line is the boundary of the budget set.

Maryclaire’s Budget Line Suppose Maryclaire faces the following prices: Beans $4/lb Carrots $2/lb Suppose Maryclaire’s income is $40. The table shows the combinations of beans and carrots that Maryclaire can buy using up all her income. The mathematical expression for the budget line is: The absolute value of the slope of the budget line is the Economic Rate of Substitution (ERS) The ERS = 2 in this example (assuming Beans are the horizontal good and Carrots are the vertical good) .

Graph of Maryclaire’s Budget Set & Budget Line The graph to the right shows a picture of Maryclaire’s budget set & budget line. Recall the equation for the budget line: C = I/PC – (PB/PC)B The ERS equals the absolute value of the slope of the budget line  ERS=$PB/$PC = 2

i>clicker question How will Maryclaire’s budget line change if just her income increases? It will get steeper. It will shift in parallel to itself. It will get flatter. It will shift out parallel to itself. It will not change.

i>clicker question How will Maryclaire’s budget line change if just the PC increases? It will get steeper. It will shift in parallel to itself. It will get flatter. It will shift out parallel to itself. It will not change.