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OPM Optimal P ricing Metric

OPM Optimal P ricing Metric. Ted Mitchell. OPM. A Simple and a Fast way to decide if your current price is above or below the optimal price for maximizing profit , Pz. Optimal Price Metric, OPM , is a new marketing metric that is either a positive or a negative number.

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OPM Optimal P ricing Metric

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  1. OPMOptimal Pricing Metric Ted Mitchell

  2. OPM • A Simple and a Fast way to decide if your current price is above or below the optimal price for maximizing profit, Pz

  3. Optimal Price Metric, OPM, is a new marketing metric that is either a positive or a negative number. • When OPM is a negative number then your current price needs to be decreased to maximize profits • When OPM is a positive number then your current price needs to be increased to maximize profits • When OPM = 0 , then you have the price that is maximizing profits

  4. To calculate the OPM you need 2 pieces of information • 1) Your current markup on price,Mp,(aka profit returned on the price per unit sold) • 2) An estimate of your current price elasticity, Eqp (Price elasticity is negative)

  5. To calculate the Optimal Price Metric • OPM = is the inverse of the markup on price, 1/Mp, Plus the price elasticity, Eqp • OPM = 1/Mp + Eqp • For example if your markup is Mp = 66.67% and your price elasticity is Eqp = -1.5, then • OPM = 1/0.6667 +( – 1.5) • OPM = 1.5 – 1.5 = 0

  6. Why does the OPM predict the direction of the optimal price for maximum profit? • First some simple observations about Price Elasticity, Eqp • Eqp = %∆Q/%∆P

  7. Why does the OPM predict the direction of the optimal price for maximum profit? • First some simple observations about Price Elasticity, Eqp • Eqp = %∆Q/%∆P -bP Eqp = a - bP (Q2-Q1)/Q1 Eqp = (P2-P1)/P1

  8. 1) Elasticity is a negative number that changes when the price changes. As the price, P, is increased from 0 over a linear demand curve, the Elasticity Eqp starts at 0 becomes a larger and larger negative number until the quantity sold reaches zero -bP Eqp = a - bP

  9. Q = a-bP Quantity sold, Q Inelastic Price Elasticity Eqp = -bP/(a-bP) -0.5 -0.75 -1.0 -1.25 -1.5 -1.75 Elastic 0 Selling price, P

  10. Elasticity of Price, Eqp • 2) the price that maximizes revenue, PR* occurs when the price elasticity isEqp = -1.0

  11. Q = a-bP Quantity sold, Q Q* Price Elasticity Eqp = %∆Q/%∆P Revenue = P(Q) -0.5 -0.75 -1.0 -1.25 -1.5 -1.75 0 Selling price, P Price Max Rev, PR*

  12. Elasticity of Price, Eqp • 3)The price that maximizes revenue, PR* , is the same price that maximizes profit, PZ*, when the variable cost equals, V = 0 • When there is a variable cost per unit, V, then the price that maximizes profit. Pz, is always greater than the price that maximizes Revenue, Pr • PR* ≤ PZ*

  13. Dollars Elasticity, Eqp = %∆Q/%∆P -0.5 -1 -2 -3.0 Maximum Revenue Maximum Profit Selling Price Pr* Pz* Inelastic Elastic

  14. 4) The absolute elasticity |Eqp| = %∆P/%∆Q= bP/(a-bP)becomes larger as the selling price, P, becomes larger

  15. |Eqp| 3.0 2.5 2.0 1.5 |Eqp| =ab/(a-bP) |Eqp| = 1 0 Price, P Pz* Max Profit Pr* Max Revenue

  16. Observations about Markup on Price • 1) We know there is an optimal price that maximizes profitPz* = a/2b + V/2 = Pr* + V/2 • 2) We know that there is an optimal markup (P-V)/P for maximizing profit Mp* = (a/2b - V/2) / (a/2b + V/2)

  17. Observation about Markup on Price • 3) as the price, P, is increased the markup on price, • Mp = (P-V)/P becomes larger and approaches 1 1

  18. Observation about Markup on Price • Think about the Inverse of the Markup. 1/Mp • 1) as the price, P, is increased the inverse of the markup on price1/Mp = P/(P-V)becomes smaller and smaller and approaches 1

  19. 1/Mp =P/(P-V) Eqp = 1/Mp 0 P =V Price, P Pz* Max Profit

  20. OPM = 1/Mp + Eqp • 5) Economists have proven that when the optimal price for maximum profit is reached then the relationship between markup and elasticity is|Eqp| = 1/Mp

  21. 1/Mp =P/(P-V) |Eqp| =ab/(a-bP) Eqp = 1/Mp Eqp = 1 0 Price, P P =V Pz* Max Profit Pr* Max Revenue

  22. OPM is defined as • the difference between the inverse of the markup and the elasticity of price • OPM = 1/Mp + Eqp • When 1/Mp = Eqp the optimal price is reached • When 1/Mp > Eqp the OPM is positive then the price is too low • When 1/Mp < Eqp the OPM is negativethen the price is too high

  23. 1/Mp =P/(P-V) |Eqp| =ab/(a-bP) Eqp = 1/Mp Eqp = 1 0 Price, P Pz* Max Profit OPM is Positive OPM is Negative

  24. The Positive or Negative Sign of the OPM indicates the direction for the change in price that maximizes profits

  25. Four Basic Questions that involve The Price Elasticity of Demand

  26. What are the Three Classic Uses of Price Elasticity? • 1) for comparing the sensitivity of changes in variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized

  27. Sample Price Elasticities • Restaurant meals -2.3 • Foreign travel, long-run - 4.0 • Airline travel, long-run -2.4 • Fresh green peas -2.8 • Automobiles, short-run -1.2 to - 1.5 • Chevrolet automobiles -4.0 • Fresh tomatoes -4.6

  28. Classic Uses of Price Elasticity? • 1) for comparing the sensitivity of changes in variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized

  29. Exam Question #1 • If the car market has a price elasticity of -2.5 and the housing market has a price elasticity of -1.7, then which one is more sensitive to a price change? • A) the car market • B) the housing market • C) not enough information to know?

  30. Exam Question #1 • If the car market has a price elasticity of -2.5 and the housing market has a price elasticity of -1.7, then which one is more sensitive to a price change? • A) the car market is more sensitive • B) the housing market • C) not enough information to know?

  31. Classic Uses of Price Elasticity • 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (price) should be changed if an outcome (revenue) is to be maximized

  32. Exam Question #2 • If the price elasticity in your market is Eqp = -2.5 and you decrease your price by 2%, then you can expect your sales volume to increase by 5%. True or False? • True • False

  33. Exam Question #2 • If the price elasticity in your market is Eqp = -2.5 and you decrease your price by 2%, then you can expect your sales volume to increase by 5%. True or False? • True is correct • %∆Q = Elasticity of Price x %∆P%∆Q = Eqp x %∆P • %∆Q = -2.5 x -2% = 5%increase in quantity

  34. Classic Uses of Price Elasticity • 1) for comparing the sensitivity of changes in a variables across situations using different units of measure (e.g., apple and orange markets) • 2) for estimating the consequences of making a change in one variable (price) on another variable (quantity) • 3) for estimating the direction a variable (Price) should be changed if an outcome (Revenue) is to be maximized

  35. Exam Question #3 • If the price elasticity of your market is -2.75, then an increase in your selling price will decrease your revenue. True or false? • A) True • B) False

  36. Exam Question #3 • If the price elasticity of your market is -2.75, then an increase in your selling price will decrease your revenue. True or false? • A) True is the correct answer • B) False

  37. Dollars Elasticity, Eqp = %∆Q/%∆P -0.5 -1 -2 -3.0 Maximum Revenue Maximum Profit Selling Price Pr* Pz*

  38. A Fourth Use for Price Elasticity • 4) Deciding on the direction of a price change when the maximum profit is desired. • You need to calculate the OPM

  39. A Fourth Use for Price Elasticity Your current price elasticity is Eqp = -2.5 and your current markup on price is Mp = 60%. If you increase your selling price will your profit increase or decrease? • A) Increase • B) Decrease • C) Not enough information to know • OPM = 1/Mp + Eqp = 1/0.6 + (-2.5) • OPM = 1.667 -2.5 = negative number therefore a price increase will increase profit.

  40. A Fourth Use for Price Elasticity Your current price elasticity is Eqp = -2.5 and your current markup on price is Mp = 60%. If you increase your selling price will your profit increase or decrease? • A) Increase • B) Decrease is true • C) Not enough information to know • OPM = 1/Mp + Eqp= 1/0.6 + (-2.5) • OPM = 1.667 -2.5 = a negative number therefore a price increase will decrease profit.

  41. 1/Mp =P/(P-V) |Eqp| =ab/(a-bP) Eqp = 1/Mp Eqp = 1 0 Price, P Pz* Max Profit OPM is Positive OPM is Negative

  42. Any Questions about the Optimal Pricing Metric? Ted Mitchell

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