University:
Washington State University
Course:
ECONS 305 | Intermediate Microeconomics without Calculus
Academic year:

2019
Views:

9

Pages:

20
Author:

Athena Harrison

EconS 305 - Elasticities - Part 2 Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 1 / 20 Introduction Today, we will …nish our discussion on elasticities with two more types. Cross-Price Elasticity Elasticity of Supply Recall from last time that elasticities (when associated with demand) measure how sensitive quantity demanded is to a given factor. We looked at price elasticity of demand, which measures quantity demanded’s sensitivity to price. We also looked at the income elasticity, which measures quantity demanded’s sensitivity to income. Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 2 / 20 Cross-Price Elasticity We can also calculate elasticities for the price of other goods, known as the cross-price elasticity. These measure how sensitive quantity demanded is to changes in the price of a di¤erent good. Just like price elasticity of demand and income elasticity, it follows a similar formula εt = ∆q pt ∆pt q where pt is the price of the other good. Like our other elasticities, we ∆q can substitute for ∆p in a linear demand function. Consider the t function qD = a bp + cY + dpt We have that d is the slope coe¢ cient for the price of the other ∆q good, so ∆p = d. We can substitue that value into the cross-price t elasticity formula for simple calculations. EconS 305 - Lecture 7 September 9, 2015 3 / 20 Cross-Price Elasticity The sign of εt is also the most important part If εt > 0, then as the price for good t goes up, the demand for our good will also rise. This means that as the price for good t increases, people substitute away from that good and into our good. We then refer to good t as a substitute for our good. Examples: Coke and Pepsi. Co¤ee and Tea. If ε < 0, then as the price for good t goes up, the demand for our good will fall. This means that as the price of good t increases, people buy less of both our good and good t. We refer to good t as a complement for our good. Examples: Peanut Butter and Jelly. Hot dogs and buns. Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 4 / 20 Example The market for motels in Pullman faces the following linear demand function qD = 100 2p 0.5Y 0.25pg where p is the price for motels in Pullman, Y is the average income of tourists visiting Pullman, and pg is the price of gasoline. Are motels a normal or inferior good? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 5 / 20 Example qD = 100 2p | {z 0.5} Y 0.25pg ∆q ∆Y ∆q We know that ∆Y = 0.5 in this case. Plugging that value into our income elasticity gives ξ= 0.5 Y <0 q Thus, the income elasticity is negative and motels are an inferior good. Why would motels be an inferior good? Is gasoline a substitute or a complement for motels? EconS 305 - Lecture 7 September 9, 2015 6 / 20 Example qD = 100 2p 0.5Y | 0.25 {z } pg ∆q ∆p g ∆q We know that ∆p = 0.25 in this case. We can plug this into the g cross-price elasticity to obtain εg = 0.25 pg <0 q And since the cross-price elasticity is negative, gasoline and motels are complements. Does this make economic sense? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 7 / 20 Application: Coke vs. Pepsi Let’s look at some more real world data. Below are estimated elasticities for both Coke and Pepsi. Price Elasticity of Demand Income Elasticity Cross-Price Elasticity Coke 1.74 0.58 0.52 Pepsi 1.55 1.38 0.64 What do these numbers tell us about the relationship between these two goods? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 8 / 20 Application: Coke vs. Pepsi Price Elasticity of Demand Coke 1.74 Pepsi 1.55 Let’s start with the price elasticity of demand. If the price of Coke increases by 1%, we can expect a 1.74% decrease in the amount of Coke sold. Coke is an elastic good. If the price of Pepsi increases by 1%, we can expect a 1.55% decrease in the amount of Pepsi sold. Pepsi is an elastic good. Coke is slightly more elastic than Pepsi. Why? Does this make economic sense? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 9 / 20 Application: Coke vs. Pepsi Income Elasticity Coke 0.58 Pepsi 1.38 Now, let’s look at the income elasticities. If the income of consumers increases by 1%, we can expect a 0.58% increase in the amount of Coke sold. Coke is a normal good. If the income of consumers increases by 1%, we can expect a 1.38% increase in the amount of Pepsi sold. Pepsi is a normal good. Does this make economic sense? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 10 / 20 Application: Coke vs. Pepsi Cross-Price Elasticity Coke 0.52 Pepsi 0.64 Finally, let’s look a the cross-price elasticities (the most interesting one). If the price of Coke increases by 1%, we can expect a 0.64% increase in the amount of Pepsi sold. If the price of Pepsi increases by 1%, we can expect a 0.52% increase in the amount of Coke sold. Coke and Pepsi are substitutues. Does this make economic sense? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 11 / 20 Application: Coke vs. Pepsi Firms use elasticities when planning sale data. For example, what if Coke decided to have a temporary sale where they reduced their price by 10%. They could expect (approximately) a 17.4% increase in their quantity sold. This is approximate since it is doubtful that the elasticity is constant along the line. At the same time, they could expect Pepsi’s quantity sold to decrease by approximately 6.4%. It is a great method for arguing how to allocate shelf space at a grocery store. EconS 305 - Lecture 7 September 9, 2015 12 / 20 Elasticity of Supply We have one last type of elasticity to look at, the elasticity of supply. This measures how sensitive the quantity supplied is to changes in the price. For the most part, we interpret this measurement the same way we interpret the price elasticity of demand. In fact, its formula is almost identical εS = where ∆q S ∆p ∆qS p ∆p qS is simply the slope of the supply function. Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 13 / 20 Elasticity of Supply Like price elasticity of demand, we are interested in the magnitude of the elasticity of supply, rather than the sign. Why? The elasticity of supply should always be positive, based on the law of supply. Supply curves are always upward sloping! Again, when εS > 1, we would say that the elasticity of supply is "elastic." If εS < 1, the elasticity of supply is "inelastic," with εS = 1 being "unit elastic." Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 14 / 20 Elasticity of Supply Consider the following supply function qS = 1 1+ p 2 What is the elasticity of supply when p = 4? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 15 / 20 Elasticity of Supply Just like with the last lecture, we want to start with the elasticity of supply formula, ∆qS p εS = ∆p qS ∆q S S and substitute out for the ∆q ∆p term. Recall that ∆p is the same thing as the slope of a line, or more importantly, the slope of our supply function 1 qS = 1 + p 2 |{z} = ∆q S ∆p Thus, we can substitute this value into our supply function yielding εS = Eric Dunaway (WSU) 1 p 2 qS EconS 305 - Lecture 7 September 9, 2015 16 / 20 Elasticity of Supply Next, we need to …nd our quantity supplied to match the p = 4 given to us. This is done by just plugging the price into our supply function qS = 1 1+ p = 2 1 1 + (4) = 1 2 Finally, we just insert all of the numbers into our elasticity formula and obtain our solution εS = 1 p 14 = =2 2 qS 21 As we can see, since εS = 2 > 1, the quantity supplied is elastic at this point. A 1% increase in price would yield a 2% increase in the quantity supplied. We would need a demand function to see what this would do to revenue. Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 17 / 20 Summary Elasticities are great tools. We can use them to obtain a unitless measure for how things react to changes in other things. Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 18 / 20 Preview for Friday Taxes! What kinds do we have? Who pays them? Who likes them? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 19 / 20 Assignment 1 & 2 (1 of 1) 1. Consider the market for football tickets. It faces the following supply and demand functions qS qD = 2 + 2p = 8 3p + 2Y + pB where p is the price for football tickets, Y is average income in 10,000’s and pB is the price of basketball tickets. Let Y = 4 and pB = 2. a. Plot both the supply and demand curve. b. Find the market equilibrium price and quantity. c. Calculate the price elasticity of demand, income elasticity, and cross-price elasticity at the equilibrium price and quantity that you found in part (b). d. Explain your results. Do they make economic sense? Eric Dunaway (WSU) EconS 305 - Lecture 7 September 9, 2015 20 / 20

Elasticities Part 2

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