Suppose we 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 we take advantage of this when pricing Menthos? If we charge a single price for each pack of Menthos, few people are going to buy more than one or two packs. Alternatively, however, we can try the two-part tariff approach, in which we 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 two-part 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”—we refer to the two-part tariff as 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 8.8. 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 market. If it costs $0.40 to produce a pack of Menthos, determine a profitmaximizing 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.