Associate Professor Lisa Giddings Elasticity Part 1 Microeconomic Theory Associate Professor Lisa Giddings

Objectives Answers to last MiniQuiz A bit more practice and…. Elasticity! Note: Still Chapter 3 of Goolsbee

We are building up to LO #1! ECO308 LEARNING OUTCOMES 1. Students will be able to construct and use supply and demand models to determine the impact of a microeconomic policy on equilibrium price and output.

Last Powerpoint’s MiniQuiz Using the equations for processed pork, solve for the equilibrium price and quantity in terms of consumer income. How does equilibrium P & Q change with consumer income? Qd = 171 – 20p + 20pb + 3Pc + 2Y Qs = 178 + 40p – 60Ph Pb=4, Pc=3.33, Y=12.5 and ph = 1.50 What happens if income increases by 10% (an increase of 1.25 in thousands)?

Quick MiniQuiz to Finish Up our S&D Model Recall the following: Qd = 171 – 20P + 20Pb + 3Pc + 2Y Qs = Qs = 178 + 40p – 60Ph With typical values: Pb=4, Pc=3.33, Y=12.5 and ph = 1.50 What is the difference between the following two derivatives: DQd/DPc = 3 and DQ*/DPc = 2 Can you explain what each one means?

Question from Practice Problems The demand function for roses is Q = a – bP and the supply function is Q = c + eP + ft Where a, b, c, e, and f are positive constants and t is the average temperature in a month. Show how the equilibrium quantity and price vary with temperature.

The Shapes of the S & D Curves Ok, so now we know HOW exogenous variables affect equilibrium…. If income, for example, increases, then we expect the demand curve to shift out, and price and quantity to rise in equilibrium. We have explored this both graphically and algebraically. If we have a model that describes demand and supply explicitly, we can predict what will happen for ALL exogenous changes fairly EXACTLY… Now we are going to explore how the SHAPE of demand and supply curves matter.

Elasticity Elasticity is the most commonly used measure of the sensitivity of one variable, such as the quantity demanded, to another variable, such as the price. Elasticity is a percentage change in one variable in response to a given percentage change of another variable

Price Elasticity of Demand The percentage change in the quantity demanded, Q, in response to a given percentage change in the price, P ε = (∆Q/Q )/(∆P/P) Range of ε: 0 > ε < ∞ Note: Because demand curves slope downward, the elasticity of demand is a negative number. Realizing that, some economists ignore the negative sign when reporting a demand elasticity. Example: if the quantity demanded of a good falls by 10% in response to a 4% price increase, the good’s price elasticity of demand is ε = -10%/4% = -2.5. For this good, a 1% increase in price leads to a -2.5% change in quantity demanded.

Interpretation of ε If ε < 1: Inelastic (Steep Demand Curve) If ε = 1: Unitary Elastic If ε > 1: Elastic (Flat Demand Curve) If ε = ∞: Perfectly Elastic (Horizontal Demand Curve) If ε = 0: Perfectly Inelastic (Vertical Demand Curve) When demand is very price-sensitive, a small change in price will lead to large changes in quantities demanded. Examples: those markets where consumers have a lot of ability to substitute away from or toward the good in question. Markets with less price-responsive demand have elasticities that are small in magnitude. The market for candy at the circus.

Factors that Affect ε The availability of substitutes Glenn and Sara Ellison looked at the markets for different CPUs and memory chips on a price search ending Web site. This makes it very easy to compare multiple suppliers’ prices for certain products. Because the product is so standardized, little distinguishes one chip from another, so price is the determining factor for most consumers. Ellison and Ellison found that the price elasticity of demand for any single chip was about -25… If the supplier raises its price just 1% higher than that of its competitors it can expect sales to fall by 25%.

More Factors Affecting ε Time Horizons Short Run: limited ability to change consumption patterns Long Run Example: Gasoline

Elasticity and Linear Demand Curves Note that elasticity is not constant on a linear demand curve. At higher prices, demand is more elastic. Note that demand curves that are not linear can have constant elasticities! Q = Ap^ε where A is a positive constant and ε is a negative constant.

Elasticity is NOT Slope So, you can see that elasticity and slope are not the same. Let’s go back to our Tomato Market Qd = 1,000 – 200P The slope of this demand curve is found by looking at the inverse demand curve: P = 5 – 0.005Qd The coefficient on P (in the first equation - ∆Q/∆P) and on Qd (in the second equation ∆P/∆Q) tells us some things… Like The quantity demanded falls by 200 pounds for every dollar per pound increase in price. That coefficient is But there are problems with this: 1. slopes depend completely on the units of measurement we choose. Suppose we measured tomato prices P in cents per pound rather than in dollars. Now the demand curve would be Qd = 1,000 – 2P because the quantity of tomatoes demanded would fall by 2 pounds for every 1 cent increase in price. But the fact that the coefficient on P is now 2 instead of 200 doesn’t mean that consumers are 1/100 as price sensitive as before. Actually nothing has changed about price sensitivity. 2. You can’t compare the slopes across different products. Does the fact that consumers demand 100 fewer celery hearts for every 10 cent per celery heart increase in the price mean that consumers are more or less price elastic in the celery market than in the tomato market? Using Elasticities to express responsiveness avoids these tricky issues.

But… Elasticity is RELATED to Slope ε = (∆Q/Q )/(∆P/P) Now, let’s rearrange: (∆Q/Q )/(∆P/P) = (∆Q/Q )*(P/∆P) = (∆Q/ ∆P)*(P/Q) This equation should look a little more familiar. What is (∆Q/ ∆P)? Well this LOOKS like the inverse of slope. Remember a slope is just rise/run or ∆Y/ ∆X. In economics terms, we have ∆P/ ∆Q, So, ∆Q/P is just the inverse of this. ….. And isn’t that just what we have when we are given a demand curve in the form of the following: Q = a – bP So ∆Q/ ∆P is just b

So… For any given demand curve of the following form: Qd = a – bP ε = (∆Q/ ∆P)*(P/Q) For any given demand curve of the following form: Qd = a – bP Then, ε = -b(P/Q) Where P and Q are the price and quantity at equilibrium!

Example: Find the price elasticity of demand for Tomatoes in the following market: Qd = 1,000 – 200P Qs = 200P – 200 P* = 3 and Q* = 400 ε = (∆Q/ ∆P)*(P/Q) = -200(3/400) = 1.5 Are tomatoes elastic or inelastic? ε = -0.3

MiniQuiz Find the price elasticity of demand for pulled pork: Qd = 171 – 20p + 20pb + 3Pc + 2Y Qs = 178 + 40p – 60Ph Pb=4, Pc=3.33, Y=12.5 and ph = 1.50

ε and Expenditures and Revenue Interesting and Useful Relationship between Consumer expenditures and ε : Consumer expenditures rise with prices if demand is inelastic, but decrease with prices if demand is elastic. Why should we care? Total expenditure = Total Revenue = P * Q

ε and TR ε = %∆Q/%∆P TR = P * Q So… Check this out: ε > 1 ε < 1 ε < 1 Increase Price Large decrease in Qd so %∆Q > %∆P and TR falls Small decrease in Qd So %∆Q < %∆P and TR increases Decrease Price Large Increase in Qd So %∆Q > %∆P and TR increases Small increase in Qd So %∆Q < %∆P so TR falls

Revenues along a Linear Demand See graph on page 52

Test this The demand for movie tickets in a small town is given as: Qd = 1000 – 50P 1. Calculate the price elasticity of demand when the price of tickets is $5. 2. Calculate the price elasticity of demand when the price of tickets is $12. 3. At what price is the price elasticity of demand “unit elastic”? 4. What happens to the price elasticity of demand as you move down the demand curve? 5. What happens to the revenue as you move down the demand curve?

Other Elasticities Income Elasticity of Demand Ey = (%∆Qd/%∆Y) = ∆Qd/∆y * Y/Q The percentage change in quantity demanded associated with a 1% change in consumer income Inferior Goods: Goods that have an income elasticity that is negative, meaning consumers demand a lower quantity of the good when their income rises Normal Goods: goods with positive income elasticities (consumers’ quantity demanded rises with their income) Luxury Goods: the subcategory of normal goods with income elasticities above 1. Having an income elasticity greater than 1 means the quantity demanded of these products rises at a faster rate than income.

Cross-Price Elasticity of Demand Ex = (%∆Qd1/%∆P2) = ∆Qd1/∆P2 * Ps/Qd1 The percentage change in quantity demanded of one good associated with a 1% change in the price of another good Complement Goods: Goods that have a cross price elasticity that is negative, meaning consumers demand a lower quantity of the good when the price of the other good rises Substitute Goods: Goods that have a cross price elasticity that is positive, meaning consumers demand a lower quantity of the good when the price of the other good declines

Price Elasticity of Supply η = (∆Qs/Qs )/(∆P/P) How responsive is Quantity Supplied to changes in prices?

MiniQuiz Suppose that the price elasticity of demand for cereal is -0.75 and the cross-price elasticity of demand between cereal and the price of milk is -0.9. If the price of milk rises by 10%, what would have to happen to the price of cereal to exactly offset the rise in the price of milk and leave the quantity of cereal demanded unchanged?