Quantitative Demand Analysis

1. Quantitative Demand Analysis

2. 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?

3. Elasticity Relative measure. Sign and magnitude show type of relationship and extent of demand response to a change in its determinant “Z”. EZ = %QX / %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)

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

5. 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 -8.64. • 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 25.92 percent!

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

7. 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.

8. MR Demand and Revenue P or AR • Demand FunctionQ = 70,000 – 100P • Inverse Demand FunctionP = 700 – .01Q • Total RevenueTR = P * Q = 700Q – .01Q2 • Average RevenueAR = TR / Q = 700 – .01Q = P • Marginal RevenueMR = dTR / dQ = 700 – .02Q For linear demand MR has the sameintercept and twice the slope of AR • Arc MR = TR / Q = (TR2-TR1) / (Q2-Q1) • Max TR: dTR / dQ = MR = 0 Solve for Q*

9. 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.

10. Elastic demand Unit elastic Inelastic demand Maximum total revenue When demand is elastic, price cut increases total revenue When demand is inelastic, price cut decreases total revenue Demand Curve orAverage Revenue At high prices and small quantities, the elasticity is large. 25.00 20.00 15.00 Price (dollars per pizza) 12.50 At low prices and large quantities, the elasticity is small. 10.00 5.00 Marginal Revenue 0 25 50 350.00 312.50 300.00 250.00 Total Revenue (billions of dollars) 200.00 150.00 100.00 50.00 Quantity (pizza per hour) 0 25 50

11. Cross Price Elasticity of Demand Substitutes (EQx,Py > 0) Complements (EQx,Py < 0)

12. Example: Impact of a change in a competitor’s price • According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. • 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 36.24 percent!

13. Income Elasticity Inferior Good (EQx,I < 0) Normal Good (EQx,I > 0) Superior Good (EQx,I > 1)

14. 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

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

16. Glossary of Cross Elasticityof Demand Which means that A relationship is described as When its magnitude is Perfect substitutes Infinity The smallest possible increase in price of one good causes an infinitely large in the demand of the other good. Substitutes Positive, less than infinity If the price of one good increases, the quantity demanded of the other good also increases. Independent Zero The demand for one good remains constant, regardless of the price of the other good. Complements Less than zero The demand for one good decreases when the price of the other good increases.

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