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**The Income Effect, Substitution Effect, and Elasticity**

Module 10 Micro: Econ: 46 The Income Effect, Substitution Effect, and Elasticity KRUGMAN'S MICROECONOMICS for AP* Margaret Ray and David Anderson

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**What you will learn in this Module:**

How the income and substitution effects explain the law of demand The definition of elasticity, a measure of responsiveness to changes in prices or incomes The importance of the price elasticity of demand, which measures the responsiveness of the quantity demanded to changes in price How to calculate the price elasticity of demand The purpose of this module is to get “behind the scenes” of the demand curve to explain why it is downward sloping and why some demand curves are more responsive to a price change than others. In order to do this, we develop the concepts of income and substitution effects, and price elasticity.

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**The Law of Demand The substitution effect The income effect I**

Explaining the Law of Demand The law of demand is very intuitive: when the price of jellybeans rises, all else equal, people buy fewer jellybeans. But why? A. The Substitution Effect Consumers have many items from which to choose. Suppose Eli can buy jellybeans ($1 each) or gummy worms ($2 each) with his $6 of weekly income. Currently, Eli is buying 4 packages of jellybeans and 1 package of gummy worms. If Eli buys one package of gummy worms, he must give up buying two packages of jellybeans. In other words, the opportunity cost of gummy worms is two jellybeans. Suppose the price of gummy worms falls to $1, while income and the price of jellybeans remains unchanged. Now a package of gummy worms only requires the sacrifice of one package of jellybeans. So relative to jellybeans, gummy worms are now less expensive, and we predict that Eli will substitute and consume fewer jellybeans and more gummy worms. B. The Income Effect Revisit the previous example before the price of gummy worms fell. If Eli spent all of his income on jellybeans, he could buy 6 packages. If Eli spent all of his income on gummy worms, he could buy 3 packages. Now the price of gummy worms has fallen to $1 each. If Eli spent all of his income on gummy worms, he could buy 6 packages. So Eli’s income hasn’t increased, but his purchasing power, has increased and more purchasing power will likely cause Eli to buy more gummy worms.

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**Defining Elasticity Definition of elasticity Law of demand Example**

Elasticity measures the responsiveness of one variable to changes in another. We start with the price elasticity of demand, but elasticity is a general concept that can be applied to any two related variables. And we cover several other elasticity measures in later modules, so learning elasticity as a general concept is useful. Price elasticity of demand, for example, measures the responsiveness of quantity demanded to changes in price. We KNOW that when price increases, Qd decreases (this is the law of demand). The question here is, decreases by how much? This will be very important, for example to firms when they decide whether or not to raise their price. Ask the students how their consumption of gasoline would be affected if the price of gasoline doubled. Then compare this response to how they would respond if the price of ballpoint pens doubled. Use this example to help them understand that elasticity measures the responsiveness of 1 variable to changes in another (in this case price and Qd).

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**Calculating Elasticity**

Elasticity measures the responsiveness of one variable to changes in another. We start with the price elasticity of demand, but elasticity is a general concept that can be applied to any two related variables. And we cover several other elasticity measures in later modules, so learning elasticity as a general concept is useful. Help students see the connection between the concept of elasticity and the elasticity formula. Use words, then symbols. Price elasticity of demand, for example, measures the responsiveness of quantity demanded to changes in price. We KNOW that when price increases, Qd decreases (this is the law of demand). The question here is, decreases by how much? Ask the students how their consumption of gasoline would be affected if the price of gasoline doubled. Then compare this response to how they would respond if the price of ballpoint pens doubled. Use this example to help them understand that elasticity measures the responsiveness of 1 variable to changes in another. Ed = %ΔQd/ΔP will often be the starting point when working with elasticity. Calculating elasticity Elasticity is the % change in the dependent variable divided by the % change in the independent variable In symbols, elasticity is %∆dep/%∆ind Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in the price. In symbols: Ed = %ΔQd/ΔP note: we drop the negative sign for Ed only.

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**The Midpoint Formula The problem with calculating percentage changes**

The solution: Use the Midpoint formula! %ΔQd = 100*(New Quantity – Old Quantity)/Average Quantity %ΔP = 100*(New Price – Old Price)/Average Price Ed = %ΔQd/ΔP Example Elasticity computations change if the starting and ending prices (or quantities) are reversed. That’s why we use the midpoint formula. Example: If a variable goes from a value of 100 to a value of 110, it is a 10% increase. If the variable were to go from a value of 110 to a value of 100, it is a 9.1% decrease. Because of this, the value of the price elasticity will change, depending upon whether the price is rising or falling. To address this issue, we use the average price and average quantity between two points on a demand curve. This method is called the midpoint method. %ΔP = 100*(New Price – Old Price)/Average Price Likewise with %ΔQd = 100*(New Quantity – Old Quantity)/Average Quantity Example: The price of a college’s tuition increases from $20,000 to $24,000 per year. The college discovers that he entering class of first-year students declined from 500 to 450. %ΔP = 100*(New Price – Old Price)/Average Price = 100*($2000)/$21,000 = 9.5% %ΔQd = 100*(New Quantity – Old Quantity)/Average Quantity = 100*(-50)/475 = % Ed = 9.5%/10.5% = .90 or an inelastic response between these two points on the demand curve.

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