1. Impact of ∆P and ∆Q on Changing Revenue and Measuring Price Elasticity Ted Mitchell

2. Exam Question What Is the Price that maximizes Revenue If The Demand For The Product Is » Q = a - bP

3. Optimal Price Max Rev Price per Unit a/2b Quantity Sold a/2 Demand Equation Q = a - bP TJM

4. Optimal price Max Rev Price per Unit a/2b = 5000/2(500) = $5 Quantity Sold a/2 = 5000/2= 2,500 Demand Equation Q = 5000 – 500P TJM

5. Price per Unit $4$5 Quantity Sold 2,500 Demand Equation Q = a - bP TJM 3,000 $4 x 3,000 =12,000

6. Lower Price Sells More Units Price per Unit $4$5 Quantity Sold 2,500 Demand Equation Q = a - bP TJM 3,000 $4 x 3,000 =12,000

7. Price per Unit $4$5 Quantity Sold 2,500 TJM 3,000 Revenue in Period 2 $4 x 3,000 =12,000

8. Impact Analysis Impact of a Change in Price on the Change In Revenue Impact of a Change in Quantity on the Change in Revenue

9. Period 1Period 2ChangeImpact of Change on price Quantity, Q 2,5003,000 ∆Q= 500I∆Q = $4(500) = $2,000 Price, P $5$4 ∆P = -$1I∆P = 2,500(-$1) = -$2,500 Joint Impact0 Revenue $12,500$12,000 ∆R= -$500 ∆R = I∆Q+I∆P = - $500 Arc or Average price Elasticity = I∆Q/I∆P = $2,000/$2.500 = -0.8

10. Lower Price Sells More Units Price per Unit $4$5 Quantity Sold 2,500 Demand Equation Q = a - bP TJM 3,000 Gain = $4 x 500 =$2,000

11. Price Elasticity = Customer Sensitivity to Price Change = Sensitivity of Changes in the Quantity purchased for a Change in Price = %∆Q/%∆P

12. Price Elasticity = -1 Price per Unit a/2b Quantity Sold a/2 TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75

13. Revenue looks like R = aP - bP 2 Revenue Price0 TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75 Price Elasticity a/2b

14. Period 1Period 2ChangeImpact of Change on price Quantity, Q 2,5003,000 ∆Q= 500I∆Q = $4(500) = $2,000 Price, P $5$4 ∆P = -$1I∆P = 2,500(-$1) = -$2,500 Joint Impact0 Revenue $12,500$12,000 ∆R= -$500 ∆R = I∆Q+I∆P = - $500 Arc or Average price Elasticity = I∆Q/I∆P = $2,000/$2.500 = -0.8

15. Price per Unit $4$5 Quantity Sold 2,500 TJM 3,000 -0.5 -0.75 -1 -1.25 -1.5 -1.75 Eqp = -0.8

16. Revenue looks like R = aP - bP 2 Revenue Price0 TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75 Arc Price Elasticity = -0.8 $4 $5

17. Three Big Uses for Price Elasticity 1) Forecasting Qty change for a change in Price 2) Comparing Price Sensitivity Across Markets 3) Indicates if a price change will increase or decrease revenue

18. Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False TJM

19. Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75

20. Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False Revenue Price 0 TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75

21. Exam Question # 2 If your price elasticity is -1.5 then a small price decrease will increase your revenue? True or False TJM

22. Exam Question # 2 If your price elasticity is -1.5 then a small price decrease will increases your revenue? True or False Revenue Price 0 TJM -0.5 -0.75 -1 -1.25 -1.5 -1.75

23. Price Elasticity is Almost Never Used to discuss a price change increasing or decreasing Revenue! True BUT Why!!!

24. The Price That Maximizes Profit is always ≥ the Price that maximizes Revenue $ Price 0 TJM Pr* Pz*

25. $ Price 0 TJM Pr* Pz* -0.5 -0.75 -1 -1.25 -1.5 -1.75 The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

26. Most firms are maximizing profit most of the time Most manager expect a revenue increase if they decrease their selling price

27. Price Elasticity in Most markets most of the time is between Eqp = -1.20 and -2.75

28. $ Price 0 TJM Pr* Pz* -0.5 -0.75 -1 -1.25 -1.5 -1.75 The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

29. Don’t Need A Max Revenue Indicator What we want is a NEW Elasticity That Indicates if a change in price will increase the Profits or not!