Question

​Johnny's Shop-and-Pay is a regional grocery​ chain, and its marketing manager is trying to determine the​ profit-maximizing coupon program for the​ store's laundry detergent brand. Coupon users at the store have an elasticity of demand for this product that equals minus​3, and the elasticity of demand for​ non-users of the coupon for the store brand equals minus1.5. If the full retail​ (undiscounted) price of the detergent is​ $10 per​ box, what is the optimal discount to provide for coupon​ users?

Answer 1

50% discount

Step-by-step explanation:

We have the formula

price = marginal cost*(E/(E + 1) )

We are given the following:

price per unit item = $10

elasticity of demand, E = -3 for coupon users

marginal cost MC = ?

Hence

10 = MC * (-3/(-3 + 1))

10 = MC * 1.5

MC = 10 / 1.5 = 6.67

So, the appropriate discount that can be given is

price - marginal cost = 10 - 6.67 = $3.33 per box

OR 3.33 / 6.67 = 50% discount over cost.