Price Elasticity of DemandAn important aspect of a products demand curve is how much the quantitydemanded changes when the price changes. The economic measure of thisresponse is the price elasticity of demand.Price elasticity of demand is calculated by dividing the proportionate changein quantity demanded by the proportionate change in price. Proportionate (orpercentage) changes are used so that the elasticity is a unit-less value anddoes not depend on the types of measures used (e.g. kilograms, pounds, etc).As an example, if a 2% increase in price resulted in a 1% decrease inquantity demanded, the price elasticity of demand would be equal toapproximately 0.5. It is not exactly 0.5 because of the specific definition forelasticity uses the average of the initial and final values when calculatingpercentage change. When the elasticity is calculated over a certain arc orsection of the demand curve, it is referred to as the arc elasticity and isdefined as the magnitude (absolute value) of the following: Q2 - Q1 ( Q1 + Q2 ) / 2 P2 - P1 ( P1 + P2 ) / 2where Q1 = Initial quantity Q2 = Final quantity P1 = Initial price P2 = Final priceThe average values for quantity and price are used so that the elasticity willbe the same whether calculated going from lower price to higher price orfrom higher price to lower price. For example, going from $8 to $10 is a25% increase in price, but going from $10 to $8 is only a 20% decrease inprice. This asymmetry is eliminated by using the average price as the basisfor the percentage change in both cases.For slightly easier calculations, the formula for arc elasticity can be rewrittenas:
( Q2 - Q1 ) ( P2 + P1 ) ( Q2 + Q1 ) ( P2 - P1 )To better understand the price elasticity of demand, it is worthwhile toconsider different ranges of values.Elasticity > 1In this case, the change in quantity demanded is proportionately larger thanthe change in price. This means that an increase in price would result in adecrease in revenue, and a decrease in price would result in an increase inrevenue. In the extreme case of near infinite elasticity, the demand curvewould be nearly horizontal, meaning than the quantity demanded isextremely sensitive to changes in price. The case of infinite elasticity isdescribed as being perfectly elastic and is illustrated below: Perfectly Elastic Demand CurveFrom this demand curve it is easy to visualize how an extremely smallchange in price would result in an infinitely large shift in quantitydemanded.Elasticity < 1In this case, the change in quantity demanded is proportionately smaller thanthe change in price. An increase in price would result in an increase inrevenue, and a decrease in price would result in a decrease in revenue. In the
extreme case of elasticity near 0, the demand curve would be nearly vertical,and the quantity demanded would be almost independent of price. The caseof zero elasticity is described as being perfectly inelastic. Perfectly Inelastic Demand CurveFrom this demand curve, it is easy to visualize how even a very large changein price would have no impact on quantity demanded.Elasticity = 1This case is referred to as unitary elasticity. The change in quantitydemanded is in the same proportion as the change in price. A change in pricein either direction therefore would result in no change in revenue.Applications of Price Elasticity of DemandThe price elasticity of demand can be applied to a variety of problems inwhich one wants to know the expected change in quantity demanded orrevenue given a contemplated change in price.For example, a state automobile registration authority considers a price hikein personalized "vanity" license plates. The current annual price is $35 peryear, and the registration office is considering increasing the price to $40 peryear in an effort to increase revenue. Suppose that the registration officeknows that the price elasticity of demand from $35 to $40 is 1.3.Because the elasticity is greater than one over the price range of interest, weknow that an increase in price actually would decrease the revenue collectedby the automobile registration authority, so the price hike would be unwise.
Factors Influencing the Price Elasticity of DemandThe price elasticity of demand for a particular demand curve is influencedby the following factors: • Availability of substitutes: the greater the number of substitute products, the greater the elasticity. • Degree of necessity or luxury: luxury products tend to have greater elasticity than necessities. Some products that initially have a low degree of necessity are habit forming and can become "necessities" to some consumers. • Proportion of income required by the item: products requiring a larger portion of the consumers income tend to have greater elasticity. • Time period considered: elasticity tends to be greater over the long run because consumers have more time to adjust their behavoir to price changes. • Permanent or temporary price change: a one-day sale will result in a different response than a permanent price decrease of the same magnitude. • Price points: decreasing the price from $2.00 to $1.99 may result in greater increase in quantity demanded than decreasing it from $1.99 to $1.98.Point ElasticityIt sometimes is useful to calculate the price elasticity of demand at a specificpoint on the demand curve instead of over a range of it. This measure ofelasticity is called the point elasticity. Because point elasticity is for aninfinitesimally small change in price and quantity, it is defined usingdifferentials, as follows: dQ Q dP Pand can be written as: dQ P dP Q
The point elasticity can be approximated by calculating the arc elasticity fora very short arc, for example, a 0.01% change in price.The Supply CurvePrice usually is a major determinant in the quantity supplied. For a particulargood with all other factors held constant, a table can be constructed of priceand quantity supplied based on observed data. Such a table is called a supplyschedule, as shown in the following example: Supply Schedule Quantity Price Supplied 1 12 2 28 3 42 4 52 5 60By graphing this data, one obtains the supply curve as shown below: Supply Curve
As with the demand curve, the convention of the supply curve is to displayquantity supplied on the x-axis as the independent variable and price on they-axis as the dependent variable.The law of supply states that the higher the price, the larger the quantitysupplied, all other things constant. The law of supply is demonstrated by theupward slope of the supply curve.As with the demand curve, the supply curve often is approximated as astraight line to simplify analysis. A straight-line supply function would havethe following structure: Quantity = a + (b x Price)where a and b are constant for each supply curve.A change in price results in a change in quantity supplied and representsmovement along the supply curve.Shifts in the Supply CurveWhile changes in price result in movement along the supply curve, changesin other relevant factors cause a shift in supply, that is, a shift of the supplycurve to the left or right. Such a shift results in a change in quantity suppliedfor a given price level. If the change causes an increase in the quantitysupplied at each price, the supply curve would shift to the right: Supply Curve Shift
There are several factors that may cause a shift in a goods supply curve.Some supply-shifting factors include: • Prices of other goods - the supply of one good may decrease if the price of another good increases, causing producers to reallocate resources to produce larger quantities of the more profitable good. • Number of sellers - more sellers result in more supply, shifting the supply curve to the right. • Prices of relevant inputs - if the cost of resources used to produce a good increases, sellers will be less inclined to supply the same quantity at a given price, and the supply curve will shift to the left. • Technology - technological advances that increase production efficiency shift the supply curve to the right. • Expectations - if sellers expect prices to increase, they may decrease the quantity currently supplied at a given price in order to be able to supply more when the price increases, resulting in a supply curve shift to the left.Supply and DemandThe market price of a good is determined by both the supply and demand forit. In 1890, English economist Alfred Marshall published his work,Principles of Economics, which was one of the earlier writings on how bothsupply and demand interacted to determine price. Today, the supply-demandmodel is one of the fundamental concepts of economics. The price level of agood essentially is determined by the point at which quantity supplied equalsquantity demanded. To illustrate, consider the following case in which thesupply and demand curves are plotted on the same graph.
Supply and DemandOn this graph, there is only one price level at which quantity demanded is inbalance with the quantity supplied, and that price is the point at which thesupply and demand curves cross.The law of supply and demand predicts that the price level will move towardthe point that equalizes quantities supplied and demanded. To understandwhy this must be the equilibrium point, consider the situation in which theprice is higher than the price at which the curves cross. In such a case, thequantity supplied would be greater than the quantity demanded and therewould be a surplus of the good on the market. Specifically, from the graphwe see that if the unit price is $3 (assuming relative pricing in dollars), thequantities supplied and demanded would be: Quantity Supplied = 42 units Quantity Demanded = 26 unitsTherefore there would be a surplus of 42 - 26 = 16 units. The sellers thenwould lower their price in order to sell the surplus.Suppose the sellers lowered their prices below the equilibrium point. In thiscase, the quantity demanded would increase beyond what was supplied, andthere would be a shortage. If the price is held at $2, the quantity suppliedthen would be: Quantity Supplied = 28 units Quantity Demanded = 38 units
Therefore, there would be a shortage of 38 - 28 = 10 units. The sellers thenwould increase their prices to earn more money.The equilibrium point must be the point at which quantity supplied andquantity demanded are in balance, which is where the supply and demandcurves cross. From the graph above, one sees that this is at a price ofapproximately $2.40 and a quantity of 34 units.To understand how the law of supply and demand functions when there is ashift in demand, consider the case in which there is a shift in demand: Shift in DemandIn this example, the positive shift in demand results in a new supply-demandequilibrium point that in higher in both quantity and price. For each possibleshift in the supply or demand curve, a similar graph can be constructedshowing the effect on equilibrium price and quantity. The following tablesummarizes the results that would occur from shifts in supply, demand, andcombinations of the two. Result of Shifts in Supply and Demand Equilibrium Equilibrium Demand Supply Price Quantity
+ + + - - - + - + - + - + + ? + - - ? - + - + ? - + - ?In the above table, "+" represents an increase, "-" represents a decrease, ablank represents no change, and a question mark indicates that the netchange cannot be determined without knowing the magnitude of the shift insupply and demand. If these results are not immediately obvious, drawing agraph for each will facilitate the analysis.