In the complementary-product pricing model in Example 7.3, the SolverTable results in Figure 7.18 indicate that the company can sometimes increase overall profit by selling suits below cost. How far might this behavior continue? Answer by extending the SolverTable to larger values of the sensitivity factor, so that more and more shirts and ties are being purchased per suit. Does there appear to be a lower limit on the price that should be charged for suits? Might it reach a point where the company gives them away? (Of course, this would require an unrealistically large purchase of shirts and ties, but is it mathematically possible?)
EXAMPLE 7.3 PRICING SUITS AT SULLIVAN’S
Sullivan’s is a retailer of upscale men’s clothing. Suits cost Sullivan’s $320. The current price of suits to customers is $350, which leads to annual sales of 300 suits. The elasticity of the demand for men’s suits is estimated to be -2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes $25 to profit, and each tie contributes $15 to profit. Determine a profit-maximizing price for suits.
Objective To use a nonlinear model to price men’s suits optimally, taking into account the purchases of shirts and ties that typically accompany purchases of suits.
WHERE DO THE NUMBERS COME FROM?
The dollar figures are likely supplied by a cost accountant. The elasticity of demand can be estimated from historical data on demands and prices, as discussed in Example 7.1. Finally, the average numbers of shirts and ties sold with suit purchases are available from historical data, assuming the company keeps track of such complementary purchases. (If the company doesn’t keep track of such data, it should.)