Las Vegas International Academic Conference

Las Vegas, Nevada USA 2012

Making Price Elasticity A Useful Metric For Maximizing Profit
Ted Mitchell, University of Nevada, Reno, USA Igor Makienko, University of Nevada, Reno, USA Shawn Mitchell, BA, MA, President of Chessboard Communications, Sparks, NV, USA Abstract An estimate of a product’s price elasticity can be used to calculate whether a price change will increase or decrease sales revenue. However, the price elasticity of demand does not indicate if a price change will increase or decrease gross profit because the marginal cost per unit confounds the calculation. However, an estimate of the price elasticity can be combined with the product’s markup to calculate if a change in the selling price will increase or decrease the profit. The purpose of this paper is to demonstrate how estimates of the price elasticity and the markup can be combined to help managers decide if greater profits can be realized with a price decrease or a price increase.

Introduction A few minutes searching on the Internet will demonstrate that the concept of price elasticity is very much alive and kicking. There are hundreds of sites that offer definitions of and provide explanations about the price elasticity of demand. The vast majority of sites indicate that elasticity is a useful metric for people who manage everything from the individual business firm to the entire economy. Some of the information is accurate and some is inaccurate. For example, one site proclaimed, “Once you figure out what the price elasticity is for your product, you can figure out how to maximize your profits by either raising prices if the price is inelastic, or CUTTING prices to increase sales if the price is very elastic (wliki.answers.com).” As a classroom exercise I took the above pronouncement as a lead-in to a lecture on the uses of price elasticity. I asked my students to solve the following questions: I am a marketing manager selling a well-differentiated product. I have a selling price of $8 per unit and my variable cost of manufacturing the product is $2 per unit. The estimate of my current price elasticity at the current price is Eqp = -4.0 1) Would a one dollar increase in the selling price have the effect of increasing or decreasing the total quantity of products being sold? 2) Would a one dollar increase in the selling price have the effect of increasing or decreasing the sales revenue? 3) Would a one dollar increase in the selling price have the effect of increasing or decreasing the gross profits? My students rapidly discovered that it is very easy to find definitions of elasticity. However, they also learned that the examples of managers using price elasticity to set prices or adjust prices are very hard to find. The students learned that there is an important difference between revenue and profit and that the price that maximizes revenue is seldom the price that maximizes profit. They reviewed many of the classical attributes associated with the price elasticity of demand. For example they learned the following: 1) Price elasticity of demand is a value free index that allows us to compare the price sensitivity of different products across different markets. 2) Price elasticity of demand is interpreted as the percentage change in the total quantity, %∆Q, that will be sold for a one percentage change in the selling price, %∆P, (i.e., Eqp = %∆Q/%∆P) © 2012 The Clute Institute http://www.cluteinstitute.com/ 719

Las Vegas International Academic Conference

Las Vegas, Nevada USA 2012

3) When the price elasticity is negative, then an increase in price will decrease the quantity sold. 4) When the demand is price inelastic (i.e., 0 > Eqp >-1.0), then a small price increase will increase the total revenue. 5) When the demand is price elastic (i.e., Eqp V |Eqp| = the absolute value of the price elasticity of demand However, it is the difference between the absolute value of the price elasticity and the inverse of the markup that makes the relationship a practical metric. We define the difference between the inverse of the markup and the absolute value of the price elasticity to be the optimal price guide, OPG. That is to say, OPG = 1/Mp - |Eqp| 722 http://www.cluteinstitute.com/ © 2012 The Clute Institute

Las Vegas International Academic Conference

Las Vegas, Nevada USA 2012

There are three possible solutions to the equation that make the OPG a practical aid for adjusting a current price towards greater profitability: 1) A Positive OPG: If the difference between the inverse of the markup and the absolute value of the elasticity is positive, 1/Mp - |Eqp| > 0, then the OPG is positive and a small increase in price will increase profits. 2) A Negative OPG: If the difference between the inverse of the markup and the absolute value of the elasticity is negative, 1/Mp - |Eqp| < 0, then the OPG is negative and a small decrease in price will increase profits. 3) An OPG equal to Zero: If the difference between the inverse of the markup and the absolute value of the elasticity is equal to zero, 1/Mp - |Eqp| = 0, then the OPG is zero, the price that maximizes profit is reached and any change in selling price will reduce the gross profit. It is the basic relationship between the markup on price and the price elasticity to changes in the selling price that provide the argument for making a price adjustment towards the optimal price. Changes in Markup on Price, Mp, With Changes in Price Markup on price is one of the most important metrics in cost-based pricing management. Markup on Price, Mp, is defined as a ratio of the dollar markup (i.e., profit margin per unit) over the selling price. The inverse of the markup is 1/Mp = P/(P-V) For the purposes of this discussion, we assume that the profit margin, P-V, is always positive (i.e., the selling price, P, is greater than the variable cost per unit, V,) and that the variable cost per unit represents a constant marginal cost. A dominant characteristic of the markup on price ratio is that when the price increases and the variable cost is held constant, then the value of the ratio moves closer and closer to 1.0 or 100%. When the price, P, is very low, then the profit margin, P-V, is very small. When the profit margin is very small, then the inverse of the markup is a very large positive number. When the selling price increases then the inverse value of the markup becomes smaller and approaches unity (Figure 2). For the markup to be equal to unity, 1/Mp = 1, then the variable cost must be equal to zero, V = 0. As discussed above when the variable cost is equal to zero, V = 0, then the price that maximizes revenue is equal to the price that maximizes profit. Changes in Elasticity, Eqp, With Changes in Price Price elasticity is a negative index reflecting the fact that a price decrease results in an increase in the quantity sold. However, it is common for economists to avoid the negative nature of price elasticity and use the absolute value of the index when discussing price sensitivity. The most important characteristic of using the absolute value of price elasticity is that its value starts at zero when the price is zero and becomes a larger and larger number as the selling price increases (Figure 2). When the price reaches the optimal level for maximizing revenue, Pr*, then the absolute value of elasticity is equal to unity, |Eqp| =1.When there is a variable cost greater than 0, V>0, then the price that maximizes profit, Pz*, is greater than the price that maximizes revenue, Pz*> Pr*.

© 2012 The Clute Institute http://www.cluteinstitute.com/

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Las Vegas International Academic Conference

Las Vegas, Nevada USA 2012

Figure 2 The Optimal Pricing Guide When the price increases to the optimal level for maximizing profit, Pz*, then the absolute value of the price elasticity is equal to the inverse value of the markup, 1/Mp = |Eqp| Figure 2 shows that when the price is lower than the price that maximizes profit, P |Eqp| and the optimal pricing guide is a positive number. When the optimal pricing guide is positive, OPG>0, then a small price increase will increase profits. When the price is higher than the price that maximizes profit, P>Pz*, then the value of the inverse markup is less than the value of the price elasticity, 1/Mp