Your job is to help the ABC Corporation to identify customized prices for clients different order sizes.ABC Corporation makes and sells medical testing equipment to laboratories at hospitals, clinics, and universities across North America. One popular item is a gas chromatograph refill cartridge that has a list price of $11.85. The refill cartridges are ordered in batches that may range in size from 100 to 1000 or even more. Orders for fewer than 200 units are purchased through the company’s website or through resellers with no associated discount. At the other extreme, the company receives about 100 orders per year for more than 1000 units, and these deals are negotiated by a national account manager, usually as part of a much larger sale. Orders for 200-1000 units are handled by regional sales staff who have considerable leeway with regard to discounting.
ABC wants to improve the profitability of its regional account sales. On theHomework4.RDatayou will find data for all bids made by ABC regional sales staff during 2003. The first column is the bid number; bids are arranged and numbered in chronological order through the year. The second column indicates whether the bid was won or lost: 1 indicates a win and 0 indicates a loss. The third column is ABC’s price-per-unit bid, including the effect of all discounts. The next column is the number of units ordered by the customer. The marginal cost for the cartridges was $6 per unit throughout the year, so the net contribution for each bid that ABC won is (price-$6) * order size.
Do not create estimation and hold-out samples to answer the questions below (i.e., use the whole specified sample for this exercise).
(a) Fit the logit model (i.e., Prob{win} = exp(a+bp)/(1+exp(a+bp))) to the win-loss data from 2003, where p = ABC's price for each bid opportunity. What are the estimated values of brand premium and brand sensitivity?
(b) ABC believes that buyers ordering 700 units or more are noticeably more price sensitive than those with smaller orders. Estimate separate values of a and b for orders larger than or equal to 700 units, and orders smaller than 700 units.
(c) Using the two values (each) of a and b derived in part (b), determine the price-per-unit that ABC should have bid for orders larger than or equal to 700 units, and orders smaller than 700 units -- that is, the price that would have maximized the expected net contribution for that bid of a client with an order larger than or equal to 700 units, or an order smaller than 700 units. (Remember, there is a marginal cost of $6 for each unit sold.)