In this chapter we have considered the firm’s pricing problem in practical market situations. Firms typically lack full information concerning their cost and revenue functions and must make a decision whether or not to incur search costs to get the cost and demand information required to set prices that are optimal in light of their objectives. If the search costs involved are expected to be less than the value of information derived, the firm should first estimate its demand and cost curves and then set the short-run profit-maximizing price, the sales-maximizing price, or the limit price, as desired.
When search costs are expected to be prohibitive, the firm may earn greater profit by proceeding in ignorance, using some proxy pricing policy that may not give the “correct” price but that also does not require search costs for its implementation, such that the firm’s objective may be better served if the revenues forgone because of the “incorrect” price are less than the search costs avoided. Markup pricing is typically used in practice, as is some form of price followership, including the following of “suggested” retail prices.
We showed that markup pricing can be profit maximizing if chosen at the level commensurate with the product’s price elasticity of demand. If longer-term profit maximization is desired, the markup percentage is likely to be somewhat lower than for short-run profit maximization, since long-term price elasticities tend to be higher than short-term price elasticities. As well as saving information search costs, markup
pricing acts to pass cost increases along to the customer and to maintain the purchasing power, or real value, of the firm’s profits, and it assists in coordinating the pricing behavior of firms in oligopolistic markets.
We saw that there will be a range of acceptable markup rates if the firm does not incur search costs and that any one of these rates will allow higher profits or greater market share as compared to setting the optimal price after incurring search costs. The optimal markup rate remains optimal despite shifts in costs and demand curves, under certain conditions. Periodic search activity is recommended to ensure that the markup rate remains profit maximizing.
Choosing the appropriate price level in established product markets requires an evaluation of the attributes perceived to exist in your product vis-a-vis those in competing products. In these markets the general level of prices is established, and the problem is to ensure that each product is positioned in the existing price range such that the firm’s objectives are best served. The price chosen should reflect the presence, absence, or degree of desirable attributes in each product, relative to the prices and attributes offered by competing products. Product-line pricing involves essentially the same problem, except that a particular firm produces several of the competing or complementary products and must also consider the demand interdependencies. Again, attention must be paid to the relative price elasticities of demand, with allowances made for a “basic” product which has several complementary products, for the use of products as “loss leaders,” and for the “entry-level” and “flagship” products in a line of substitutes.
Prices may be set higher to infer higher product quality if price is the best indicator of quality available to the buyer. This method may be applicable to new products, to highly technical products which contain what we later called “credence” attributes, and to any product where the cost of information to the consumer is high relative to the price of the product.
Product bundling can allow a firm to increase its profit by raising individual product prices and setting the bundle price at less than the sum of the prices of the component products. Some consumers will be induced to buy the bundle and consequently spend more than they would have at the prices set for each of the products separately. At the same time this strategy discriminates against those buyers who want only one, or a subset, of the products in the bundle. Setting quantity discounts is also a bundle pricing problem. Larger sizes or multiples of the product are simply bundles of the same product, and the firm can increase profit by offering the buyers a choice of small sizes (or single units) at relatively high prices per unit and larger sizes (or multiple units) at lower prices per unit.
Promotional pricing, or putting an item temporarily on sale, is also expected to increase the firm’s revenues and profit, although there are some problems to be wary of. Promotional pricing, as well as price competition in general, is likely to work better for products comprised of “search” attributes, namely, attributes that are observable or measurable by the consumer at relatively low search costs. By way of corollary, products containing “experience” and “credence” attributes are less suitable for price
competition, and their demand is probably better stimulated by advertising, which we consider in Chapter 13.
DISCUSSION QUESTIONS
10-1. When is it likely to be profit maximizing to use a rule-of-thumb price determination procedure rather than to determine price on the basis of estimated cost and revenue curves.
10-2. Can the markup formula linking price, average variable cost, and the price elasticity of demand be used to “plug in” the price elasticity and AVC figures to “solve for’ the profit-maximizing price? Why or why not? What cost conditions are built into that formula?
10-3. Explain why there is a range of markup rates which make it preferable to avoid search costs. What does this range depend on?
10-4. Discuss the conditions under which a markup rate, if initially optimal in terms of the firm s objective, will remain optimal despite shifts in the cost and demand curves.
10-5. Explain why the presence or absence of desirable attributes in your product influences the optimal price positioning of that product in an established market.
10-6. Summarize the issues involved in product-line pricing strategy.
10-7. For what type of product is it feasible to infer higher product quality by setting a higher price? Under what circumstances, and for what objective, would it serve the firm’s objective to set price above the short-run profit-maximizing level?
10-8. Explain how the firm may benefit from a product-bundling strategy, in the context of a computer manufacturer offering to sell the computer and various software programs separately, or the computer with several software programs as a package deal.
10-9. What considerations enter the firm’s decision to offer a discount for quantity? How deep can its discount be? Explain your answer in terms of marginal costs and revenues.
10-10. Why would a firm place items temporarily “on sale”? What dangers are there in this practice?
For what kind of products does promotional pricing work best? What kind of person responds to promotional pricing?
PROBLEMS AND SHORT CASES
10-1. The Ajzenkopf Company has been in operation for almost fifteen years and has enjoyed considerable success in the manufacture and sale of its glass vases.
The Ajzenkopf plant at present has a capacity of 35,000 units per year, and the facilities at the plant are highly specialized. Sales of vases are currently 29,000 units a year. The selling price is $7.00 per unit. Last month the average costs of production were determined to be as follows: average fixed costs, $1.03; average cost of labor, $1.98; and average cost of materials, $1.05. At those present price and cost levels the Ajzenkopf Company received a profit that
management believed was quite acceptable.
This agreement situation came to an abrupt halt, however, when it was learned that the suppliers of raw materials were raising their prices and that there was a labor dispute which forced negotiations to begin. An agreement was reached, and the final settlement had the effect of increasing the average cost per unit of labor by 20 percent. A new contract has been signed with the suppliers of the raw materials, and the new prices of raw materials had the effect of increasing the average materials cost by 30 percent. This contract had been signed after other suppliers were contacted and no less expensive prices of raw materials could be found.
Faced with this situation, a meeting was called to determine what action should be undertaken to maintain an acceptable level of profit. It was agreed that a profit level of $75,000 was the minimum acceptable point. Two alternative suggestions were made. The first suggestion, made by the marketing manager, was to raise prices to $9.00 a unit, since he was fairly certain that this price level would reduce quantity demanded by only 8,500 units per annum. The marketing manager also offered an estimate of the average variable costs, stating that the average labor cost would be $3.10 and the average materials cost would be $1.39 at this level of output.
The plant manager proposed that the price should be reduced to $6.00. The plant manager was also fairly certain about the demand situation, stating that at this price level 32,500 vases would be demanded. He also offered his estimates of average variable costs, stating that at this level of output the average costs of labor and materials per unit would be $2.85 and $1.24, respectively. The plant manager further supported his proposal by stating that under this alternative, laborers need not be laid off and thus low labor morale would not reduce productivity of the workers.
(a) Using the information given above, derive graphical estimates of the firm’s revenue and cost functions.
(b) Assuming that the firm wishes to maximize sales volume subject to obtaining a minimum profit of $75,000, what price do you suggest they charge? Discuss your answer fully. What qualifications do you wish to add to your analysis?
10-2. Regression analysis of the variations in prices and quantity demanded for Winton Garden Equipment’s major product (conducted under controlled conditions in a consumer clinic by their marketing research department) provides the following results (where P is in dollars and Q represents thousands of units):
Regression equation Coefficient of determination Standard error of estimate Standard error of the coefficient
Q = 49.147 - 2.941P R 2 = 0.96 = 0.128 = 0.086
The production department has conducted its own study of weekly total variable costs and output levels over the past three months. Its results (with TVC in thousands of dollars and Q representing thousands of units) are as follows:
Regression equation Coefficient of determination Standard error of estimate Standard error of the coefficient
TVC = 102.35 + 0.025Q R 2 = 0.92 = 0.232 = 0.003
You are an executive assistant to the marketing manager, Derek Winton. Mr. Winton feels that the present price of $9.95 is fine. He argues that it positions our product in the upper part of the range of our competitors’ prices and that the current sales level of approximately 20,000 units a week is fine in view of our full capacity limit of only 25,000 units weekly. While he agrees that a price change of a dollar or so either way would go unchallenged by competitors, he does not think such a price change would improve the contribution made by this product.
(a) What is the contribution-maximizing price? Is the associated output level feasible?
(b) How confident are you that your prediction will in fact generate a greater contribution than the present price level? Explain in detail with supporting calculations.
(c) Are there any reservations you wish to attach to your recommendation?
10-3. The Pittsburgh Plastics Company introduced a new product in January which received strong initial support and has shown a steady growth of sales in subsequent months. The initial price was set somewhat arbitrarily as a 25 percent markup over average costs. The company s objective is to maximize the contribution to overheads and profits, and it is now anxious to know whether the $6.88 price is optimal. In light of the continual growth in sales and changes in certain cost components, it has commissioned a study by Market Researchers Incorporated, who report that the price elasticity of demand is approximately —2.5 at the current (March) price and output level.
The output and cost data for the past three months are as follows:
|
January |
February |
March |
|
|
Sales (units) |
2,246 |
2,471 |
2, 718 |
|
Direct materials |
$1,415 |
$1,557 |
$1,712 |
|
Direct labor |
3,369 |
4,077 |
4,933 |
|
Indirect factory labor |
3,000 |
3,075 |
3,154 |
|
Office and administrative salaries |
2,000 |
2,000 |
2,000 |
|
Light and heat |
485 |
470 |
320 |
|
Other overheads |
2,100 |
2,100 |
2,100 |
(a) Supposing that price can be varied each month, estimate the optimal price for the month of April.
(b) What output level could be sold at the optimal price level in April?
(c) What qualifications and other considerations do you wish to add to the above pricing and output decision?
10-4. The Laura Ann Boutique purchases a line of ladies dresses from a wholesaler and pays $30 per dress regardless of quantity purchased. These dresses are marked up 33.33 percent over their invoice cost and sell quite readily. The firm’s objective is to maximize contribution to overheads and profits, and management is concerned whether or not 33.33 percent is the profit-maximizing markup rate.
(a) What would price elasticity of demand have to be in order for 33.33 percent to be the optimal markup rate?
(b) Suppose Laura Ann commissions a study, costing $500, that indicates that price elasticity of demand for these dresses is e = -3.5. Given the present price of $40 per dress and weekly sales averaging 300 dresses, was the present markup rate within the range of acceptable markups?
(c) Was the study worth it? Will it pay for itself in the future weeks?
10-5. The Archibald Truck Service (ATS) Company has been successfully servicing and repairing large trucks and tractor trailers for several years, specializing in Kenworth, Peterbilt, and Mack tractor service. Their pricing policy on each job is to charge $25 per hour labor and the book price” for materials and replacement parts. The labor charge represents the actual cost to ATS plus 25 percent, and the “book prices” represent the invoice cost of the materials and parts plus 25 percent Thus, ATS effectively sets price by marking up its direct costs by 25 percent. The founder and general manager, Mr. Joseph Archibald, reasons that this relatively low price structure is the best approach, since there is a lot of repeat business in service and repair work. He would rather have more work in the present period and maximize profits over the longer
term.
For a typical service and repair job his cost is $600, and he charges $750. He does, on the average, 60 jobs per month. His overhead costs are $8,000 per month. Mr. Archibald is con-
cerned that his monthly profits are too low; he wants at least $2,000 per month and is not earning that amount at present. He has asked all his customers over the past two months to complete a questionnaire, and from this he has been able to estimate that price elasticity for his service and repair job is approximately e = —1.1.
(a) Construct the demand, total revenue, and total cost curves for ATS from the data given.
(b) Advise Mr. Archibald of the price level and the implied markup rate on the average service and repair job which would maximize sales volume subject to the attainment of his profit target.
(c) Explain to Mr. Archibald the conditions under which that markup rate will remain optimal despite shifts in the cost and demand curves.
(d) Give him some guidance on how he should adjust the markup rate if the conditions referred to in part (c) do not hold.
10-6. The Napper Bag and Canvas Company, Ltd., is a specialist manufacturer of down-filled sleeping bags for sale in the camping equipment market. In this market there are several large companies with annual sales between $25 million and $30 million and many smaller companies with sales between $1 million and $5 million. Most of these companies have diversified product lines of camping equipment, including tents, cooking equipment, camping furniture, and sleeping bags with various types of filling. Napper’s sales of $1.6 million last year came entirely from down-filled sleeping bags, however. Although more expensive than other materials, down has substantially more insulating value by weight and volume and commands the attention of a loyal segment of serious outdoorspeople. Only a few firms produce quality down-filled bags, but these firms face peripheral competition from other firms producing bags filled with other natural and artificial materials.
Last year Napper sold 21,000 bags directly to large department stores, catalog sales companies, and specialty sporting equipment stores. These clients typically require contracts guaranteeing prices for one year. The cost of manufacturing sleeping bags depends on the size of the bag, the materials used, and the amount of fill. A breakdown of Napper’s latest manufacturing costs for a typical style is as follows:
|
Item |
Cost per Unit |
|
Down filling |
$30.00 |
|
Other raw materials |
14.40 |
|
Direct labor |
8.12 |
|
Manufacturing overhead |
6.09 |
|
Total unit cost |
$58.61 |
To the manufacturing cost is added a markup of 30 percent to provide for selling, administration, financial expenses, and profit.
During the past year the cost of down increased by between 80 to 95 percent, depending on the grade and blend. Napper was able to pass this on to its customers without any apparent loss of sales or share of the market. The suppliers of down are forecasting a minimum increase of 80 percent over the next year. For Napper the average price of down will increase from the current $12 per pound to $22 per pound. It is anticipated that the cost of other raw materials will rise by 8 percent and labor by 5 percent over the next year.
George Napper, the marketing manager, is concerned about the prospects for the coming year, and you are called upon to advise him.
(a) What price level do you advise for Napper’s typical style bag?
(b) Do you have any other advice for Mr. Napper concerning future marketing strategy?
10-7. The refrigerator market is characterized by a wide diversity of product offerings and a price range from less than $400 to more than $1,200, depending on the features of the specific refrigerator. Within this range, each manufacturer has a product line extending from the basic nofrills smaller refrigerators to the top-of-the-line luxury units.
A large chain of department stores buys various refrigerators from various manufacturers and sells them under its own brand name “Valhalla.” Given the stores’ reputation for quality products and after-sales service, this refrigerator line has achieved a substantial market share in the areas where it is sold. The marketing vice-president of the chain has been considering an addition to the Valhalla line. The new refrigerator, designated the Valhalla GE12456A, is made by General Electric and is similar to several sold by other major manufacturers, but it would fill a gap in the product line offered by the chain stores. The details of the Valhalla GE12456A are as follows: It is a 12-cubic-feet upright refrigerator/freezer, with two doors, a freezer at the top and freezer capacity of 3.2 cubic feet, and it has four large aluminum trays for fresh meat and vegetables (taking up the lower two shelves), fully compartmentalized inner doors, butter and cheese compartments with individual temperature controls, and “easy-glide” wheels underneath. It comes in four colors and with door hinges on either side.
The refrigerators available that would seem most competitive with the Valhalla GE12456A are as follows (apart from the details shown, they are similar in all other respects to the Valhalla GE12456A):
|
Make/Model |
Price ($) |
Total Size (cu ft) |
Freezer Size |
Trays |
Wheels |
|
General Electric GE12456 |
525 |
12.0 |
3.2 |
4 |
Yes |
|
Westinghouse WH11521 |
505 |
11.5 |
2.3 |
3 |
No |
|
Store A house brand XY-4823 |
485 |
12.0 |
3.0 |
3 |
No |
|
Store B house brand BK-7742 |
505 |
12.5 |
3.5 |
4 |
No |
|
RCA RC-6821 |
515 |
11.8 |
2.8 |
4 |
Yes |
|
Kelvinator K-7742 |
535 |
12.5 |
3.5 |
4 |
No |
You are asked to assist in pricing the new addition to the Valhalla line.
(a) What price level would you recommend?
(b) Explain the basis for your recommendation in detail.
(c) Outline all qualifications you feel should be made to this recommendation.
10-8 Last fall Peripherals conducted a three-month national mail-order campaign with its line of personal’accessories relating to BMW automobiles. An advertisement, complete with photographs of the items, ran for three consecutive months in the BMW Owners Club magazine and generated orders over a six-month period. All of the items sold, including tiepins, key rings,
446 Pricing Analysis and Decisions
caps, T-shirts, jackets, and umbrellas, carried the BMW logo and were designed to appeal to the pride of ownership felt by most BMW owners.
Peripherals’ management is wondering whether the screen-printed T-shirts were priced at the contribution-maximizing level. The price charged was $8.95, and Peripherals sold 120 units during the period. The cost per unit of these shirts was $4, regardless of volume (once the initial costs, of design and of the screens, were paid for). The design was original, showing the colors of the BMW logo in a heart shape, and words which effectively said “I (love) my Bim- mer.” The shirts were high quality, 50 percent cotton and 50 percent polyester, and were advertised as such. Several other BMW T-shirts were available to buyers, being advertised in automobile magazines (including the club magazine) and typically priced at $9.50 or $9.95, as well as the T-shirt which is sold at the BMW dealerships for $11.50. Each of these shirts has a different design, ranging from the simple logo with the footnote “The Ultimate Driving Machine, sold by the dealerships, to a much more complex design including a car being driven at speed. Peripherals had pretested their design at a regional meeting of the club, and it was greeted favorably by virtually everyone who saw it. These respondents were told it would be priced competitively.”
The decision to price the shirt at $8.95 was made after consideration of the following factors. First, it did not seem fair to exploit fellow club members by pricing too much above direct cost. By pricing below the competition Peripherals felt they were giving very good value to club members. Second, Peripherals guessed that demand for the shirt would be somewhat elastic at prices below the competition, since all prices were stated in print, and the lead time necessary to change prices was at least three months. No estimates of quantity demanded were attempted, but a supplier was organized to produce the printed shirts in small batches as required. Third, it was recognized that demand for T-shirts would be somewhat softer in the fall, as compared to the spring or summer.
This summer, Peripherals plans to repeat their BMW campaign. Before choosing the price for T-shirts, however, Peripherals is considering taking several “experts” to lunch in order to find their views on the appropriate price of the shirts. These people are in the custom T-shirt business and seem to be quite successful. These lunches are expected to cost Peripherals $150 in total.
Based on the $8.95 price and the 120 units sold, Peripherals calculates that price elasticity would have had to be —1.80808 in order for the price to be contribution maximizing. This figure seems higher (in absolute terms) than Peripherals would have guessed. Their best estimate, considering that this will be a summer campaign, and given their experience last fall, is that price elasticity will be unitary at the $8.95 price level. They expect sales volume to be about 25 percent greater in the summer than in the fall.
(a) Given the estimated price elasticity, and quantity demanded, at $8.95 in the summer, estimate the demand curve which Peripherals thinks it will face.
(b) What is the contribution-maximizing price suggested by the estimated demand curve?
(c) Based on these estimates, should Peripherals spend the $150 finding out what the “experts” think?
(d) Outline all assumptions and qualifications which underlie your analysis.
10-9. Emerson Electric Corporation is considering the appropriate prices for two video cassette recorders that are being made in Japan and imported (as are all VCRs at this time) with Emerson’s brand name attached. These will be Emerson’s first VCRs, although its name is well known in electric appliances generally. Model A being assembled for Emerson has four video heads, can record four programs in a fourteen-day period, has a varactor tuner capable of tuning ninety-nine channels, and has stereo with the Dolby feature. It does not have high-fidelity, but it has multichannel television sound (MTS) capability. Model B has six heads, can record eight programs in twenty-one days, has a quartz tuner, stereo, Dolby, high-fidelity sound, and MTS capability. Emerson has asked you to recommend price levels which will appropriately
Pricing Decisions in Practice 447
position their products in the market. They supply you with the following information on VCR models available from Quasar and some other firms that they feel will be direct competitors. They tell you that the quartz tuner is superior to the varactor tuner, because it can pick up an unlimited number of channels and tune them in very finely. Varactor tuners must be preset to a given number of channels, and consumers typically prefer more than fourteen if they receive more than that number of channels on cable. Video quality is increased by having more heads. Both video and sound signals are derived from the two or four heads, except in the case of six- head systems, where the extra two heads are used exclusively for sound. In general, video and sound quality increase with the number of heads.
|
Brand and Model |
Price |
Heads |
Programs |
Tuner |
Stereo |
Dolby |
Hi-fi |
MTS |
|
Quasar VH5154 |
$ 520 |
2 |
4/14 |
Var/14 |
No |
No |
No |
No |
|
Quasar VH5254 |
790 |
4 |
4/14 |
Var/99 |
Yes |
Yes |
No |
No |
|
Quasar VH5355 |
799 |
2 |
4/14 |
Var/99 |
No |
No |
Yes |
Yes |
|
Quasar VH5346 |
830 |
2 |
4/14 |
Var/14 |
Yes |
Yes |
Yes |
No |
|
Quasar VH5655 |
899 |
4 |
4/14 |
Var/99 |
No |
No |
Yes |
Yes |
|
Quasar VH5645 |
950 |
4 |
8/14 |
Quartz |
Yes |
Yes |
No |
No |
|
Quasar VH5845 |
1,000 |
4 |
8/14 |
Quartz |
Yes |
Yes |
Yes |
No |
|
Akai VS303U |
600 |
2 |
4/28 |
Quartz |
No |
No |
No |
No |
|
Akai VS603U |
900 |
6 |
8/28 |
Quartz |
Yes |
No |
Yes |
No |
|
Hitachi VT65A |
750 |
4 |
4/14 |
Var/80 |
Yes |
Yes |
No |
Yes |
|
JVC HRD725U |
1,199 |
6 |
8/14 |
Quartz |
Yes |
No |
Yes |
No |
|
Magnavox VR8530 |
699 |
2 |
4/14 |
Var/99 |
Yes |
No |
Yes |
Yes |
|
Magnavox VR8544 |
750 |
4 |
4/14 |
Var/99 |
Yes |
No |
Yes |
Yes |
(a) Considering the “quality” of model A relative to these rival products, choose the price which you think appropriately positions it in this market? Outline the reasoning behind your decision.
(b) Now select a price for model B such that it is positioned appropriately in the VCR market, and explain your reasoning.
(c) What product-line pricing considerations entered your decisions?
(d) What qualifications and assumptions underlie your decisions?
10 - 10 . Admiral Computer Company is planning to introduce a new version of its rather successful personal computer. The new model, designated the Personal Assistant, will have 128K bytes of RAM memory standard, with upgrades to 256K and 512K at. extra cost. The Word Perfect word-processing software program will run on the 128K version, but Lotus 1-2-3 requires at least 256K memory, although some users will require 512K. Word Perfect is widely available for $695, and Lotus 1-2-3 now costs $495. Admiral could buy both programs on chips and bundle them with the computer, at half the retail price. The extra 128K memory chips cost Admiral $50 each, and $20 to install if bundled with the computer, or $100 to install if retrofitted to a customer’s previously purchased computer. (To upgrade from 128K to 512K would require three additional 128 chips.)
Comparable personal computers (with 128K) are currently selling in the range $1,950 to $2,950, with IBM being the most expensive, and the IBM-compatibles being in the upper half of that range. Admiral’s Personal Assistant becomes IBM-compatible if an extra wafer board is installed. This board has a direct cost to Admiral of $150, and, like the extra memory, can
448 Pricing Analysis and Decisions
either be bundled in for $170 or installed later for $250. Admiral has asked you to advise them what price they should set for the 128K model, the 256K model, the 512K model, the IBM- compatible version of each of these models, the 256K model with Lotus, Word Perfect, and IBM-compatibility bundled in, and the 512K model with these bundled in. Also, they want to know what price to set for the separate sale (and installation) of the Lotus and Word Perfect chips and IBM-compatibility board.
(a) Analyze this pricing problem on the basis of the information given here, and recommend prices for each product in Admiral’s product line.
(b) Now suppose that IBM charges $400 for one extra 128K memory chip if it is bundled in and $750 if it is retrofitted, and its charges for the upgrade to 256K and 512K (from 128K) are $750 and $1,100, respectively. Others charge $200-300 less, citing the lower price as a positive feature in favor of their products. IBM’s bundle prices tend to be about 95 percent of the sum of the prices of the products purchased separately, whereas the bundle prices of others tend to be between 70 and 80 percent of the sum of the products purchased separately. Does this factor change your recommended prices?
(c) What assumptions and qualifications underlie your analysis, and what further information would you seek, if any, before recommending the prices to Admiral?