In Example 8.2, determine the best pricing policy if quantity discounts with a single-pr...

In Example 8.2, determine the best pricing policy if quantity discounts with a single-price breakpoint are used.

(Reference Example 8.2)

Suppose you sell Menthos candy. Most people value the first pack of Menthos they purchase more than the second pack. They also value the second pack more than the third pack, and so on. How can you take advantage of this when pricing Menthos? If you charge a single price for each pack of Menthos, only a few people are going to buy more than one or two packs. Alternatively, however, you can try the two-part tariff approach, where you charge an “entry fee” to anyone who buys Menthos, plus a reduced price per pack purchased. For example, if a reasonable single price per pack is $1.10, then a reasonable twopart tariff might be an entry fee of $1.50 and a price of $0.50 per pack. This gives some customers an incentive to purchase many packs of Menthos. Because the total cost of purchasing n packs of Menthos is no longer a linear function of n—it is now piecewise linear—the two-part tariff is a nonlinear pricing strategy.

As usual with pricing models, the key input is customer sensitivity to price. Rather than having a single demand function, however, we now assume that each customer has a unique sensitivity to price. To keep the example fairly small, we assume that four typical customers from the four market segments for the product have been asked what they would pay for each successive pack of Menthos, with the results listed in Figure 8.7. For example, customer 1 is willing to pay $1.24 for the first pack of Menthos, $1.03 for the second pack, and only $0.35 for the tenth pack. These four customers are considered representative of the four market segments. If it costs $0.40 to produce a pack of Menthos, determine a profit-maximizing single price and a profit-maximizing two-part tariff. Assume that the four market segments have 10,000, 5000, 7500, and 15,000 customers, respectively, and that the customers within a market segment all respond identically to price.

Objective To use Evolutionary Solver to find the best pricing strategies for customers who value each succeeding unit of a product less than the previous unit.

WHERE DO THE NUMBERS COME FROM?

The price sensitivity data listed in Figure 8.7 would be the most difficult to find. However, a well-studied technique in marketing research called conjoint analysis can be used to estimate such data. See Green et al. (2001) for a nontechnical discussion of conjoint analysis.