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Part II: Considering Which Side You’re On in the Decision-Making Process without changing the price of soft drinks, sales have increased to 3,000 bottles per week. The advertising elasticity of demand tells you how responsive your vending machine soft drink sales are to the change in advertising expenditures. To determine the advertising elasticity of demand, follow the customary steps:
1. Because $400 and 2,000 are the initial advertising expenditures and quantity sold, put $400 into A0 and 2,000 into Q0.
2. Because $500 and 3,000 are the new spending on advertising and sales, put $500 into A1 and 3,000 into Q1.
3. Divide the expression on top of the equation.
(Q1 – Q0) equals 1,000 and (Q1 + Q0) equals 5,000. Dividing 1,000 by 5,000 equals 1⁄5.
4. Divide the expression in the bottom of the equation.
(A1 – A0) equals $100, and (A1 + A0) equals $900. Dividing $100 by $900 equals 1⁄9.
5. Divide the top result, 1⁄5, by the bottom result, 1⁄9.
You get the advertising elasticity of demand equal to 9⁄5 or 1.8. Thus, the advertising elasticity of demand for soft drinks equals
You can conclude that a 1 percent increase in advertising expenditures increases demand 1.8 percent.
Calculating Elasticity with Calculus (If You Must) The formulas throughout this chapter determine average elasticities for a range of values. For example, in the section “Determining the price elasticity of demand: Formulas are your friend,” you calculate the price elasticity of demand for the range of values between P0 and P1. Similarly, you calculate the income elasticity of demand for the income range between I0 and I1 in the section “Determining the income elasticity of demand: Yet another formula friend.” However, sometimes you need a more precise elasticity value. In these cases, you need to determine what is called the point elasticity, and calculus comes to your rescue. The most important point elasticity is the point price elasticity of demand. This value is used to calculate marginal revenue, one of the two critical components in profit maximization. (The other critical component is
