 # The general model of demand and supply can be highly

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The general model of demand and supply can be highly useful in understandingdirectional changes in prices and quantities that result from shifts in one curve or theother. Often, though, we need to measure how sensitive quantity demanded or sup-plied is to changes in the independent variables that affect them. This is the conceptofelasticity of demandandelasticity of supply. Fundamentally, all elasticities arecalculated in the same way: They are ratios of percentage changes. Let us begin withthe sensitivity of quantity demanded to changes in the own price.1Following usual practice, we show linear demand curves intersecting the quantity axis at a price ofzero. Real-world demand functions may be non-linear in some or all parts of their domain. Thus, lineardemand functions in practical cases are approximations of the true demand function that are useful for arelevant range of values.© CFA Institute. For candidate use only. Not for distribution.
Demand Analysis: The Consumer92.2Own-Price Elasticity of DemandIn Equation 1, we expressed the quantity demanded of some good as a function ofseveral variables, one of which was the price of the good itself (the good’s “own-price”).In Equation 3, we introduced a hypothetical household demand function for gas-oline, assuming that the household’s income and the price of another good (automo-biles) were held constant. That function was given by the simple linear expressionQxd= 57 – 6.39Px. Using this expression, if we were asked how sensitive the quantity ofgasoline demanded is to changes in price, we might say that whenever price changesby one unit, quantity changes by 6.39 units in the opposite direction; for example, ifprice were to rise by €1, quantity demanded would fall by 6.39 liters per month. Thecoefficient on the price variable (–6.39) could be the measure of sensitivity we areseeking.There is a drawback associated with that measure, however. It is dependent onthe units in which we measuredQandP. When we want to describe the sensitivity ofdemand, we need to recall the specific units in whichQandPwere measured—litersper month and euros per liter—in our example. This relationship cannot readily beextrapolated to other units of measure—for example, gallons and dollars. Economists,therefore, prefer to use a gauge of sensitivity that does not depend on units of mea-sure. That metric is calledelasticity. Elasticity is a general measure of how sensitiveone variable is to any other variable, and it is expressed as the ratio of percentagechanges in each variable: %Δy/%Δx. In the case ofown-price elasticity of demand,that measure is illustrated in Equation 5:EQPpdxdxx=%%ΔΔThis equation expresses the sensitivity of the quantity demanded to a change inprice.Epdxis the good’s own-price elasticity and is equal to the percentage change inquantity demanded divided by the percentage change in price. This measure is inde-pendent of the units in which quantity and price are measured. If quantity demandedfalls by 8% when price rises by 10%, then the elasticity of demand is simply –0.8. Itdoes not matter whether we are measuring quantity in gallons per week or liters perday, and it does not matter whether we measure price in dollars per gallon or eurosper liter; 10% is 10%, and 8% is 8%. So the ratio of the first to the second is still –0.8.

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