Introduction To Revenue

Transcription

1 Introduction To Sales R = PQ where R = Sales P = per Unit Q = (Demanded) Demand Function The that will be sold is also determined by the price per unit Q = ƒ(p) R = Pƒ(P) 2 3 Higher Sells Fewer Units 1??? Higher Sells Fewer Units 1??? Higher Sells Fewer Units 1??? is an area! R=PQ $5 $75 per Unit $5 $75 per Unit $5 $75 per Unit

2 How To Calculate Demand? Demand equation is represented by How To Calculate Demand? Demand equation is represented by How To Calculate Demand? Demand equation is represented by 7 8 Q = That Will Be Demanded At A Given 9 a = quantity that could be given away at a zero price How To Calculate Demand? Demand equation is represented by How To Calculate Demand? Demand equation is represented by Example Market research has estimated your demand to be Q = 15-5P The current price is $2 per unit. What is the current Demand? 1 b = number of units or lost sales if the price is increased by one unit 11 P = Per Unit 12

3 Example Market research has estimated your demand to be Q = 15-5P The current price is $2 per unit. What is the current Demand? The Equation substitute looks like Q = 15-5(2) Q = 15-1 = 5 units R = P(a - bp) $6 & $4 Examples The Demand For Your Product Changes with The You Charge As Q = 5-5P R = P(5-5P) $6 Example R = P(5-5P) What is your total sales revenue if your price is six dollars? $6 Example R = P(5-5P) substitute

4 $6 Example R = P(5-5P) Substitute P = 6 R = 6(5-5(6)) R =12, $4 Example R = P(5-5P) What is your total sales revenue if your price is four dollars? $4 Example R = P(5-5P) Substitute 4 = P $4 Example R = P(5-5P) Substitute 4 = P R = 4(5-5(4)) R = 12, How Can The $12, At $6 Be The Same As The At $4? $12, Because looks like R = 5,P - 5P $4 $6

5 $? $12, What Happens At $5. R = 5,P - 5P 2 $5 Example *** R = P(5-5P) What is your total sales revenue if your price is five dollars? $5 Example R = P(5-5P) Substitute P=5 R = 5(5-5(5)) R = 12,5 $4 $6 $ $12,5 $12, $5 Maximizes??? R = 5,P - 5P 2 R looks like Slope of Curve is R P R $4 $5 $6 P P

6 Slope Of Curve Is Zero R Find The First Derivative of The Curve and Set It Equal to Zero Find The First Derivative of The Curve and Set It Equal to Zero P Equation Find The First Derivative of The Curve and Set It Equal to Zero Find The First Derivative of The Curve and Set It Equal to Zero R P = a 2bP Find The First Derivative of The Curve and Set It Equal to Zero Set = R P = a 2bP a 2bP =

7 a 2bP = Solve for P a 2bP = Solve for P P = a 2b $6 & $4 Examples The Demand For Your Product Changes with The You Charge As Q = 5-5P P = a 2b 4 $6 & $4 Examples The Demand For Your Product Changes with The You Charge As Q = 5-5P P = a 2b P = 5 2( 5) = 5 Rule of Thumb The That Maximizes Is Give-Away- Divided by Twice The Number Of Lost Sales For Any Dollar Increase In P = a 2b 42 Exam Question What Is The Maximum That Can Be Generated If The Demand For The Product Is

8 Optimal Max Rev Optimal price Max Rev a/2 a/2 = 5/2= 2,5 Q = 5 5P 3, 2,5 $4 x 3, =12, a/2b per Unit a/2b = 5/2(5) = $5 per Unit $4 $5 per Unit Lower Sells More Units 3, 2,5 $4 x 3, =12, Looks Familiar 3, 2,5 This looks Familiar in Period 2 $4 x 3, =12, $4 $5 per Unit 47 $4 $5 per Unit

9 49 Impact Analysis Impact of a Change in on the Change In Impact of a Change in on the Change in Period 1 Period 2 Change Impact of Change on price, Q 2,5 3, Q= 5 I Q = $4(5) = $2,, P $5 $4 P = -$1 I P = 2,5(-$1) = -$2,5 Joint Impact $12,5 $12, R= -$5 R = I Q+I P = -$5 Arc or Average price Elasticity = I Q/I P = $2,/$2.5 = Elasticity is Useful! Lower Sells More Units 3, 2,5 Gain = $4 x 5 =$2, Elasticity = Customer Sensitivity to Change = Sensitivity of Changes in the purchased for a Change in = % Q/% P Elasticity = a/2 $4 $5 per Unit 53 a/2b per Unit

10 looks like Elasticity Period 1 Period 2 Change Impact of Change on price, Q 2,5 3, Q= 5 I Q = $4(5) = $2,, P $5 $4 P = -$1 I P = 2,5(-$1) = -$2,5 Joint Impact 3, 2,5 Eqp = $12,5 $12, R= -$5 R = I Q+I P = -$5 a/2b Arc or Average price Elasticity = I Q/I P = $2,/$2.5 = $4 $5 per Unit looks like Arc Elasticity = $4 $5 59 Three Big Uses for Elasticity 1) Forecasting Qty change for a change in 2) Comparing 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

11 Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False Exam Question If your price elasticity is -1.5 then a price increase increase your revenue? True or False Exam Question # 2 If your price elasticity is -1.5 then a small price decrease will increase your revenue? True or False Exam Question # 2 If your price elasticity is -1.5 then a small price decrease will increases your revenue? True or False Elasticity is Almost Never Used to discuss a price change increasing or decreasing! $ The That Maximizes Profit is always the that maximizes True 65 BUT Why!!! Pr* Pz*

12 $ The Elasticity of that maximizes profit is always more negative than the price that maximizes revenue Most firms are maximizing profit most of the time Elasticity in Most markets most of the time is between Most manager expect a revenue increase if they decrease their selling price Eqp = -1.2 and Pr* Pz* $ The Elasticity of that maximizes profit is always more negative than the price that maximizes revenue Don t Need A Max Indicator What we want is a NEW Elasticity That Indicates if a change in price will increase the Profits or not! Pr* Pz* 71