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Elasticity If a seller needs to reduce the price of a product, how much should it be reduced? Reduce too little, and projected increase in sales will not meet desired goals. Reduce too much, and the projected profit target might not be achieved. The economic concept here is price elasticity of demand: how much quantity demanded changes in response to a change in price. The key question here is “how much” will the quantity change if the price changes?

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**Learning Objectives 20-01. Compute the price elasticity of demand.**

Know the relationships between price changes, price elasticity, and total revenue. Know what the cross-price elasticity of demand measures. Know what the income elasticity of demand tells us. Know what the elasticity of supply measures. We will use these objectives to summarize the chapter.

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Price Elasticity The law of demand states that quantity demanded will increase when the price is lowered, and vice versa. The critical question to be answered is how much quantity demanded will change due to a price change. Price elasticity of demand: the percentage change in quantity demanded divided by the percentage change in price. Introductory example: a furniture store is considering having a sale. If it drops its prices by a certain percentage, what will happen to its customer flow? (Increase) By how much will the customer flow increase? (A lot, because the good is price-elastic).

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**Price elasticity (E) = % change in quantity demanded**

Price elasticity of demand: the percentage change in quantity demanded divided by the percentage change in price. A 10% increase in quantity demanded in response to a 20% price decrease yields a price elasticity of 0.5. Price elasticity (E) = % change in quantity demanded % change in price Student get confused because we use the absolute value, ignoring the obvious negative number. The negative comes from the inverse relation between P and Q.

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**Computing Price Elasticity**

We use the average method of computation: Take the quantity before and the quantity after the price change and average them. Divide the average quantity into the change in quantity to get the percentage change in quantity. If quantity went from 2 to 4, then the average is 3. The change is 2, so the percentage change is 2/3 or We use the average method so that if we go from $10 to $20, the elasticity measurement we get is the same as if we go from $20 to $10. This is not intuitive to the student. Going from $10 to $20 is a 100% increase (20-10/10). Going from $20 to $10 is a 50% decrease (10-20/20). Doubling the price and a half-off sale don’t seem to be the same concept.

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**Computing Price Elasticity**

We do the same thing to get the percentage change in price: Take the price before and the price after and average them. Divide the average price into the change in price to get the percentage change in price. If price went from 45 to 40, then the average is The change is 5, so the percentage change is 5/42.5, or Stick to one method. The text uses the average method, so, to reduce student confusion, it might be best to stick with that method.

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**Computing Price Elasticity**

The % change in quantity is and the % change in price is We can now compute the price elasticity of demand: E = / = 5.65 A 1% change in price brings about a 5.65% change in quantity demanded. Price elasticity (E) = % change in quantity demanded % change in price Again, note that we use absolute values of E.

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**Interpreting Elasticity**

If E > 1, demand is elastic. Consumer response is large relative to the price change. If E < 1, demand is inelastic. Consumer response is small relative to the price change. If E = 1, demand is unitary elastic. % change in quantity demanded is exactly equal to % change in price. Once calculated, we can sort the price elasticity of a good into one of these three categories.

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Elasticity Extremes It might be useful to calculate the elasticity for each extreme. Perfectly inelastic, E = 0, since price doesn’t change for any quantity change. Perfectly elastic, E = infinity, since quantity doesn’t change for any price change.

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**Determinants of Elasticity**

Necessities vs. luxuries. Demand for necessities is relatively inelastic. Demand for luxuries is relatively elastic. Availability of substitutes. The greater the availability of substitutes, the more elastic is the product’s demand. No or few substitutes? Inelastic demand. This slide and the next one begin to categorize the answers to the previous question: Why are some goods more elastic in response than others? You could have the students sort out the differences between, say, necessities and luxuries, etc.

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**Determinants of Elasticity**

Relative price to income. Demand for low-priced goods is relatively inelastic. Demand for high-priced goods is relatively elastic. Time. The more time you have to adjust to a price change, the more elastic is your response. No time to adjust? Highly inelastic demand. Follow-on from the previous slide.

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**Price Elasticity and Total Revenue**

The goal of sales is to receive total revenue. If demand is inelastic (E<1), a price rise increases total revenue, and vice versa. If demand is elastic (E>1), a price rise decreases total revenue, and vice versa. If demand is unitary-elastic (E=1), a price change does not change total revenue. Total revenue = Price x Quantity sold You could set up some numbers on the board to reinforce this info. Set up an obvious elastic good (furniture?), have a sale, and calculate elasticity and total revenue change. Repeat with an obvious inelastic good (cigarettes?), and calculate elasticity and total revenue change.

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Income Elasticity A increase in demand for a good when income rises is true for a normal good. Most goods are normal goods. However, for some goods the demand decreases as income rises. They are inferior goods. Examples are used clothes and ramen noodles. As income increases, people upgrade to higher- quality substitutes for inferior goods. Not always more. True for normal goods. Not so for inferior goods. You could start a discussion on what happens when the primary breadwinner in a family gets laid off. How does the family modify their purchases?

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Income Elasticity As income increases, people have more money to spend. Demand for goods, in general, will shift rightward. For a particular good, how much of a demand increase will occur? Income elasticity of demand: % change in quantity demanded divided by % change in income. Your income rises by 10%. You go to the movies more and buy 20% more popcorn. Income elasticity of demand for popcorn is 20% / 10% or 2.0. Now we switch to the determinants of demand. Income is a principal one. Income increases and we buy more. How much more? Always more?

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**Cross-Price Elasticity**

Suppose the price of candy in the theater falls. How would this affect the sales of popcorn? Candy and popcorn are substitutes for each other. Lower-priced candy will see an increase in quantity demanded. Also, the demand for popcorn will decrease. But by how much? Cross-price elasticity of demand: the % change in quantity demanded of X divided by the % change in price of Y. This concept leads to the formal definition of substitute goods and complementary goods. An increase in the price of one good A changes the demand for the other good B. If B’s demand increases, the goods were substitutes. One can do the job of the other. Coke and Pepsi. If B’s demand decreases, the goods are complements. They are bought together. Big Mac and fries.

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**Cross-Price Elasticity**

Cross-price elasticity of demand: the % change in quantity demanded of X divided by the % change in price of Y. If popcorn sales declined 20% when the candy price dropped 10%, the cross-price elasticity of demand for popcorn is -20 / -10 or Ex = +2.0, a relatively elastic response. Note that the sign is significant. When goods are substitutes, cross-price elasticity is positive. We ignored the sign in price elasticity of demand. Now it becomes important.

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**Cross-Price Elasticity**

Cross-price elasticity of demand: the % change in quantity demanded of X divided by the % change in price of Y. If popcorn sales declined 20% when the movie admission price increased 10%, the cross-price elasticity of popcorn is -2.0, a relatively elastic response. Again the sign is significant. When goods are complements, cross-price elasticity is negative. Emphasize the sign difference.

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**Cross-Price Elasticity**

Substitute goods: goods that can replace each other; when the price of good X rises, the demand for good Y increases, and vice versa, ceteris paribus. Complementary goods: goods frequently consumed in combination; when the price of good X rises, the demand for good Y decreases, and vice versa, ceteris paribus. Here are the formal definitions. Ask the students to come up with substitute goods and complementary goods.

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Elasticity of Supply The law of supply states that an increase in price causes an increase in quantity supplied. But how much more will be produced as the price rises? Elasticity of supply: the % change in quantity supplied divided by the % change in price. If it is highly elastic, producers are very responsive to a price change. If it is highly inelastic, producers do not have much of a response to a price change. Sellers are people too and they react to price changes. The discussion here can parallel that of price elasticity of demand.

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