Quantitative Demand Analysis

Headlines: In 1989 Congress passed and president signed a minimum-wage bill. The purpose of this bill was to increase the purchasing power of unskilled workers. We know that the consequences of price floor is decrease in demand. Now lets quantify it. How many minimum-wage workers lost their jobs? What happened to the total wage bill of firms that hire unskilled workers?

Elasticity Relative measure. Sign and magnitude show type of relationship and extent of demand response to a change in its determinant “Z”. E Z = %  Q X / %  Z Percentage proportion Units-free measure: %  independent of the units of measurement Continuous variables (function, curve) => precise point elasticity (derivative) Discrete variables (schedule, points) => approximate arc elasticity (averages)

Own Price Elasticity of Demand Negative according to the “law of demand” Elastic: Inelastic: Unitary:

Example: Quantifying the Change According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T? Calls would increase by percent!

Perfectly Elastic & Inelastic Demand Perfectly Elastic D Price Quantity Perfectly Inelastic D Price Quantity

Factors Affecting Own Price Elasticity Available Substitutes The more substitutes available for the good, the more elastic the demand. Time Demand tends to be more inelastic in the short term than in the long term. Time allows consumers to seek out available substitutes. Expenditure Share Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

MR Demand and Revenue Demand Function Q = 70,000 – 100P Inverse Demand Function P = 700 –.01Q Total Revenue TR = P * Q = 700Q –.01Q 2 Average Revenue AR = TR / Q = 700 –.01Q = P Marginal Revenue MR = dTR / dQ = 700 –.02Q For linear demand MR has the same intercept and twice the slope of AR Arc MR =  TR /  Q = (TR 2 -TR 1 ) / (Q 2 -Q 1 ) Max TR:dTR / dQ = MR = 0 Solve for Q* P or AR

Own-Price Elasticity and Total Revenue Elastic An increase (a decrease) in price leads to a decrease (an increase) in total revenue. Inelastic An increase (a decrease) in price leads to an increase (a decrease) in total revenue. Unitary Total revenue is maximized at the point where demand is unitary elastic.

Total Revenue (billions of dollars) Maximum total revenue When demand is inelastic, price cut decreases total revenue Unit elastic Elastic demand Quantity (pizza per hour) Price (dollars per pizza) Inelastic demand When demand is elastic, price cut increases total revenue At high prices and small quantities, the elasticity is large. At low prices and large quantities, the elasticity is small. Demand Curve or Average Revenue Marginal Revenue

Cross Price Elasticity of Demand Substitutes (E Qx,Py > 0) Complements (E Qx,Py < 0)

According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is If MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services? AT&T’s demand would fall by percent! Example: Impact of a change in a competitor’s price

Income Elasticity Normal Good (E Qx,I > 0) Inferior Good (E Qx,I < 0) Superior Good (E Qx,I > 1)

Uses of Elasticities Pricing Managing cash flows Impact of changes in competitors’ prices Impact of economic booms and recessions Impact of advertising campaigns And lots more: CDC study Du Pont antitrust law suit

Glossary of Price Elasticity of Demand A relationship is described as When its magnitude is Which means that Perfectly elastic or infinitely elastic Unit elastic Inelastic Perfectly inelastic or completely inelastic Infinity The smallest possible increase in price causes an infinitely large decrease in quantity demanded Less than infinity but greater than 1 Greater than zero but less than 1 Elastic 1 Zero % decrease in quantity demanded exceeds % increase in price % decrease in quantity demanded equals % increase in price % decrease in quantity demanded is less than % increase in price. The quantity demanded is the same at all prices

Glossary of Cross Elasticity of Demand A relationship is described as When its magnitude is Which means that Perfect substitutesInfinityThe smallest possible increase in price of one good causes an infinitely large in the demand of the other good. Positive, less than infinity SubstitutesIf the price of one good increases, the quantity demanded of the other good also increases. IndependentZeroThe demand for one good remains constant, regardless of the price of the other good. ComplementsLess than zeroThe demand for one good decreases when the price of the other good increases.

Glossary of Income Elasticity of Demand A relationship is described as When its magnitude is Which means that Negative income elastic (inferior good) Less than zeroWhen income increases, quantity demanded decreases. Greater than zeroPositive income elastic (normal good – every normal is not superior) The percent increase in the quantity demanded is less than the percentage increase in income. Positive income elastic (superior good – every superior is normal) Greater than 1The percentage increase in the quantity demanded is greater than the percentage increase in income.