ajaz_eco204_2009_elasticity_review

# ajaz_eco204_2009_elasticity_review - University of Toronto...

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain Elasticity: a Quick Review Please help improve the course by sending me an e mail about typos or suggestions for improvements _____________________________________________________________________________________ In this note we will do a very quick review of an “elasticity”. In ECO 100, most of you have probably seen: “Price Elasticity” ሺ% ch “Income Elasticity” ሺ% ange in ܳ / % change in Priceሻ change in ܳ / % change in Incomeሻ “Cross Price Elasticity” ሺ% change in ܳ / % change in Price of Other Goodሻ However, in ECO 204 and upper level economics/finance courses, you will see other types of elasticities. As such, I am going to do a “general” discussion of elasticity. Let’s start by seeing why we use elasticities. Economics and finance models often state a relationship between two economic/financial variables. For example: A company’s sales depends on price A consumer’s consumption depends on income A company’s output depends on labor input In each case, a variable depends on (“is a function of”) another variable. We could describe such relationships in general terms by sayin riable ݕ is a function of the variable ݔ : g that a va ݕൌ ሺݔሻ ݂ Notice that as ݔ changes, it leads to changes in ݕ (if you’re in ECO 220, you may have seen that just because ݕ,ݔ are related doesn’t mean that ݔ causes changes in ݕ ). We will often want to know: how are changes in ݕ related to changes in ݔ ? One way to answer this question is to look at the elasticity of ݕ with respect to ݔ : ܧ ൌ Elasticity of ݕ with respect to ݔ ൌ % Δ ݕ % Δ ݔ 1 ECO 204 (Draft) Elasticity: a Quick Review

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University of Toronto, Department of Economics, ECO 204 2009 2010 S. Ajaz Hussain Notice that ܧ can be positive, zero or negative 1 . The sign simply tells us whether ݕ,ݔ are positively or negatively elated. r Example : Suppose the ݕ variable is a company’s sales ܳ and the ݔ variable is the price ܲ of its product. Then: ܳൌ݂ሺܲሻ ܧ ൌ Elasticity of ܳ with respect to ܲ ൌ % Δ ܳ % Δ ܲ For most products, higher prices lead to lower sales: thus, th ratio will be negative. is Remember that changes in ݔ are associated with changes in ݕ . As such, we’ll often want to know how sensitive changes in ݕ are to changes in ݔ . For example, if ݔ changes by 10%, will ݕ change by more than 10%? Exactly 10%? Or less than 10%? One way to answer this question is to see if the (absolute value of the) elasticity is larger than, equal to than 1. , or less Case 1: |ܧ|൐1 |ܧ| ൌ |Elasticity of ݕ with respect to ݔ|ൌฬ % Δ ݕ % Δ ݔ ฬ൐1 ௬௜௘௟ௗ௦ ሱۛۛۛሮ |% Δ ݕ| ൐ % Δ ݔ That is, if the elasticity is larger than 1, any percentage change in ݔ is associated with a larger percent ge in ݕ . In such cases, we say the elasticity is “elastic”. age chan Case 2: |ܧ|൏1 |ܧ| ൌ |Elasticity of ݕ with respect to ݔ|ൌฬ % Δ ݕ % Δ ݔ ฬ൏1 ௬௜௘௟ௗ௦ ሱۛۛۛሮ |% Δ ݕ| ൏ % Δ ݔ That is, if the elasticity is smaller than 1, any percentage change in ݔ
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ajaz_eco204_2009_elasticity_review - University of Toronto...

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