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

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

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

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

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

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

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

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

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

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

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

Price Elasticity = -1 Price per Unit a/2b Quantity Sold a/2 TJM

Revenue looks like R = aP - bP 2 Revenue Price0 TJM Price Elasticity a/2b

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

Price per Unit $4$5 Quantity Sold 2,500 TJM 3, Eqp = -0.8

Revenue looks like R = aP - bP 2 Revenue Price0 TJM Arc Price Elasticity = -0.8 $4 $5

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

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

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

Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False Revenue Price 0 TJM

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

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

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

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

$ Price 0 TJM Pr* Pz* The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

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

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

$ Price 0 TJM Pr* Pz* The Elasticity of Price that maximizes profit is always more negative than the price that maximizes revenue

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!