Managerial Economics

Managerial Economics

This course contains the basics of Managerial Economics

Course introduction
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Pragnya Meter Exam

Managerial Economics

Pricing Practices

Pricing practices sometimes seem peculiar. When first-class hotel rooms in London, Tokyo, or Paris go for $300 to $500 per night, Holiday Inns offers Weekend WebSaversSM rates at Chicago’s O’Hare International Airport from as low as $62.48 per night—more than 50 percent off regular prices. Not to be outdone, Howard Johnson’s says vacations are more fun with family package rates up to 70 percent off regular prices. Meanwhile, Marriott offers advance purchase rates on the Internet for as low as $59 per night at the Courtyard Marriott Village at Lake Buena Vista, Florida. At the Hilton Durham, in North Carolina, weekday rates are $109.95 and $89.95 on the weekend. What is going on here?

Rather than a mad scramble to build market share at any cost, hotelchain rates represent a shrewd use of information technology. Any night that hotel rooms stand empty represents lost revenue, and because hotel costs are largely fixed, revenue losses translate directly into lost profits. A room rate of $59 per night does not begin to cover fixed construction, maintenance, and interest costs, but it makes a nice profit contribution when the alternative is weekend vacancy. By segmenting their markets, hotels are able to charge the maximum amount the market will bear on weekdays and on weekends. Similarly, hotel marketing gets fierce for convention business, especially when conventions meet at traditionally slack periods. Is it any wonder that the American Economic Association holds annual meetings around New Year’s Day in cold-weather cities?

This chapter examines common pricing practices and illustrates their value as a practical means for achieving profit-maximizing prices under a wide variety of demand and cost conditions.


Markup pricing is the most commonly employed pricing method. Given the popularity of the technique, it behooves managers to fully understand the rationale for markup pricing. When this rationale is understood, markup pricing methods can be seen as the practical means for achieving optimal prices under a wide variety of demand and cost conditions.

Markup Pricing Technology

The development of pricing practices to profitably segment markets has reached a fine art with the Internet and use of high-speed computer technology. Why do Business Week, Forbes, Fortune, and The Wall Street Journal offer bargain rates to students but not to business executives? It is surely not because it costs less to deliver the Journal to students, and it is not out of benevolence;

it is because students are not willing or able to pay the standard rate. Even at 50 percent off regular prices, student bargain rates more than cover marginal costs and make a significant profit contribution. Similarly, senior citizens who eat at Holiday Inns enjoy a 10 to 15 percent discount and make a meaningful contribution to profits. Conversely, relatively high prices for popcorn at movie theaters, peanuts at the ball park, and clothing at the height of the season reflect the fact that customers can be insensitive to price changes at different places and at different times of the year. Regular prices, discounts, rebates, and coupon promotions are all pricing mechanisms used to probe the breadth and depth of customer demand and to maximize profitability.

Although profit maximization requires that prices be set so that marginal revenues equal marginal cost, it is not necessary to calculate both to set optimal prices. Just using information on marginal costs and the point price elasticity of demand, the calculation of profit-maximizing prices is quick and easy. Many firms derive an optimal pricing policy using prices set to cover direct costs plus a percentage markup for profit contribution. Flexible markup pricing practices that reflect differences in marginal costs and demand elasticities constitute an efficient method for ensuring that MR = MC for each line of products sold. Similarly, peak and off-peak pricing,

price discrimination, and joint product pricing practices are efficient means for operating so that MR = MC for each customer or customer group and product class.

Markup on Cost

In a conventional approach, firms estimate the average variable costs of producing and marketing a given product, add a charge for variable overhead, and then add a percentage markup, or profit margin. Variable overhead costs are usually allocated among all products according to average variable costs. For example, if total variable overhead costs are projected at $1.3 million per year and variable costs for planned production total $1 million, then variable overhead is allocated to individual products at the rate of 130 percent of variable cost. If the average variable cost of a product is estimated to be $1, the firm adds a charge of 130 percent of variable costs, or $1.30, for variable overhead, obtaining a fully allocated cost of $2.30. To this figure the firm might add a 30 percent markup for profits, or 69¢, to obtain a price of $2.99 per unit.

Markup on cost is the profit margin for an individual product or product line expressed as a percentage of unit cost. The markup-on-cost, or cost-plus, formula is given by the expression:


The numerator of this expression, called the profit margin, is measured by the difference between price and cost. In the example cited previously, the 30 percent markup on cost is calculated as


Solving Equation 12.1 for price provides the expression that determines price in a cost-plus pricing system:

Price = Cost (1 + Markup on Cost)

Continuing with the previous example, the product selling price is found as

Price = Cost (1 + Markup on Cost)
         = $2.30(1.30)
         = $2.99

Markup on Price

Profit margins, or markups, are sometimes calculated as a percentage of price instead of cost.

Markup on price is the profit margin for an individual product or product line expressed as a percentage of price, rather than unit cost as in the markup-on-cost formula. This alternative means of expressing profit margins can be illustrated by the markup-on-price formula:

Markup on Price = Price – Cost/Price

Profit margin is the numerator of the markup-on-price formula, as in the markup-on-cost formula. However, unit cost has been replaced by price in the denominator. The markup-on-cost and markup-on-price formulas are simply alternative means for expressing the relative size of profit margins. To convert from one markup formula to the other, just use the following expressions:

Markup on Cost = Markup on Price/1 – Markup on Price
Markup on Price = Markup on Cost/1 + Markup on Cost

Therefore, the 30 percent markup on cost described in the previous example is equivalent to a 23 percent markup on price:

Markup on Price = 0.3 /1 + 0.3 = 0.23 or 23%

An item with a cost of $2.30, a 69¢ markup, and a price of $2.99 has a 30 percent markup on cost and a 23 percent markup on price. This illustrates the importance of being consistent in the choice of a cost or price basis when comparing markups among products or sellers. Markup pricing is sometimes criticized as a naive pricing method based solely on cost considerations— and the wrong costs at that. Some who employ the technique may ignore demand conditions, emphasize fully allocated accounting costs rather than marginal costs, and arrive at suboptimal price decisions. However, a categorical rejection of such a popular and successful pricing practice is clearly wrong. Although inappropriate use of markup pricing formulas will lead to suboptimal managerial decisions, successful firms typically employ the method in a way that is consistent with profit maximization. Markup pricing can be viewed as an efficient ruleof- thumb approach to setting optimal prices.

Role of Cost in Markup Pricing

Although a variety of cost concepts are employed in markup pricing, most firms use a standard, or fully allocated, cost concept. Fully allocated costs are determined by first estimating direct costs per unit, then allocating the firm’s expected indirect expenses, or overhead, assuming a standard or normal output level. Price is then based on standard costs per unit, irrespective of short-term variations in actual unit costs.

Unfortunately, use of the standard cost concept can create several problems. Sometimes, firms fail to adjust historical costs to reflect recent or expected price changes. Also, accounting costs may not reflect true economic costs. For example, fully allocated costs can be appropriate when a firm is operating at full capacity. During peak periods, when facilities are fully utilized, expansion is required to increase production. Under such conditions, an increase in production requires an increase in all plant, equipment, labor, materials, and other expenditures. However, if a firm has excess capacity, as during off-peak periods, only those costs that actually rise with production—the incremental costs per unit—should form a basis for setting prices.

Successful firms that employ markup pricing use fully allocated costs under normal conditions but offer price discounts or accept lower margins during off-peak periods when excess capacity is available. In some instances, output produced during off-peak periods is much cheaper than output produced during peak periods. When fixed costs represent a substantial share of total production costs, iscounts of 30 percent to 50 percent for output produced during off-peak periods can often be justified on the basis of lower costs.

“Early bird” or afternoon matinee discounts at movie theaters provide an interesting example. Except for cleaning expenses, which vary according to the number of customers, most movie theater expenses are fixed. As a result, the revenue generated by adding customers during off-peak periods can significantly increase the theater’s profit contribution. When off-peak customers buy regularly priced candy, popcorn, and soda, even lower afternoon ticket prices can be justified. Conversely, on Friday and Saturday nights when movie theaters operate at peak capacity, a small increase in the number of customers would require a costly expansion of facilities. Ticket prices during these peak periods reflect fully allocated costs. Similarly, McDonald’s, Burger King, Arby’s, and other fast-food outlets have increased their profitability substantially by introducing breakfast menus. If fixed restaurant expenses are covered by lunch and dinner business, even promotionally priced breakfast items can make a notable contribution to profits.

Role of Demand in Markup Pricing

Successful companies differentiate markups according to variations in product demand elasticities. Foreign and domestic automobile companies regularly offer rebates or special equipment packages for slow-selling models. Similarly, airlines promote different pricing schedules for business and vacation travelers. The airline and automobile industries are only two examples of sectors in which vigorous competition requires a careful reflection of demand and supply factors in pricing practice. In the production and distribution of many goods and services, successful firms quickly adjust prices to different market conditions.

Examining the margins set by a successful regional grocery store chain provides interesting evidence that demand conditions play an important role in cost-plus pricing. Table shows the firm’s typical markup on cost and markup on price for a variety of products. Afield manager with over 20 years’ experience in the grocery business provided the author with useful insight into the firm’s pricing practices. He stated that the “price sensitivity” of an item is the primary consideration in setting margins. Staple products like bread, coffee, ground beef, milk, and soup are highly price sensitive and carry relatively low margins. Products with high margins tend to be less price sensitive.

Note the wide range of margins applied to different items. The 0 percent to 10 percent markup on cost for ground beef, for example, is substantially lower than the 15 percent to 35 percent margin on steak. Hamburger is a relatively low-priced meat with wide appeal to families, college students, and low-income groups whose price sensitivity is high. In contrast, relatively expensive sirloin, T-bone, and porterhouse steaks appeal to higher-income groups with lower price sensitivity.

It is also interesting to see how seasonal factors affect the demand for grocery items like fruits and vegetables. When a fruit or vegetable is in season, spoilage and transportation costs are at their lowest levels, and high product quality translates into enthusiastic consumer demand, which leads to high margins. Consumer demand shifts away from high-cost/low-quality fresh fruits and vegetables when they are out of season, thereby reducing margins on these items.

In addition to seasonal factors that affect margins over the course of a year, some market forces affect margins within a given product class. In breakfast cereals, for example, the markup on cost for highly popular corn flakes averages only 5 percent to 6 percent, with brands offered

Markups Charged on a Variety of Grocery Items

by Post and Kellogg’s competing with a variety of local store brands. Cheerios and Wheaties, both offered only by General Mills, Inc., enjoy a markup on cost of 15 percent to 20 percent. Thus, availability of substitutes directly affects the markups on various cereals. It is interesting to note that among the wide variety of items sold in a typical grocery store, the highest margins are charged on spices. Apparently, consumer demand for nutmeg, cloves, thyme, bay leaves, and other spices is quite insensitive to price. The manager interviewed said that in more than 20 years in the grocery business, he could not recall a single store coupon or special offered on spices.

This retail grocery store pricing example provides valuable insight into how markup pricing rules can be used in setting an efficient pricing policy. It is clear that the price elasticity concept plays a key role in the firm’s pricing decisions. To examine those decisions further, it is necessary to develop a method for determining optimal markups in practical pricing policy.


There is a simple inverse relation between the optimal markup and the price sensitivity of demand. The optimal markup is large when the underlying price elasticity of demand is low; the optimal markup is small when the underlying price elasticity of demand is high.

Optimal Markup on Cost

Recall from Chapter 4 that there is a direct relation among marginal revenue, price elasticity of demand, and the profit-maximizing price for a product. This relation was expressed as


To maximize profit, a firm must operate at the activity level at which marginal revenue equals marginal cost. Because marginal revenue always equals the right side of Equation, at the profit-maximizing output level, it follows that MR = MC and


Equation 12.8 provides a formula for the profit-maximizing price for any product in terms of its price elasticity of demand. The equation states that the profit-maximizing price is found by multiplying marginal cost by the term


To derive the optimal markup-on-cost formula, recall from Equation that the price established by a cost-plus method equals cost multiplied by the expression (1 + Markup on Cost). Equation implies that marginal cost is the appropriate cost basis for cost-plus pricing and that


By dividing each side of this expression by MC and subtracting 1 yields the expression


After simplifying, the optimal markup on cost, or profit-maximizing markup-on-cost, formula can be written


The optimal markup-on-cost formula can be illustrated through use of a simple example. Consider the case of a leading catalog retailer of casual clothing and sporting equipment that wishes to offer a basic two-strap design of Birkenstock leather sandals for easy on-and-off casual wear. Assume the catalog retailer pays a wholesale price of $25 per pair for Birkenstock sandals and markets them at a regular catalog price of $75 per pair. This typical $50 profit margin implies a standard markup on cost of 200 percent because


In a preseason sale, the catalog retailer offered a discounted “early bird” price of $70 on Birkenstock sandals and noted a moderate increase in weekly sales from 275 to 305 pairs per week. This $5 discount from the regular price of $75 represents a modest 6.7 percent markdown. Using the arc price elasticity formula, the implied arc price elasticity of demand on Birkenstock sandals is


In the absence of additional evidence, this arc price elasticity of demand EP = –1.5 is the best available estimate of the current point price elasticity of demand. Using Equation, the $75 regular catalog price reflects an optimal markup on cost of 200 percent because


Optimal Markup on Price

Just as there is a simple inverse relation between a product’s price sensitivity and the optimal markup on cost, so too is there a simple inverse relation between price sensitivity and the optimal markup on price. The profit-maximizing markup on price is easily determined using relations derived previously. Dividing each side of Equation by P yields the expression


Subtracting 1 from each side of this equation and simplifying gives


Then, multiplying each side of this expression by –1 yields


Notice that the left side of Equation is an expression for markup on price. Thus, the optimal markup-on-price formula is


The optimal markup-on-price formula can be illustrated by continuing with the previous example of a catalog retailer and its optimal pricing policy for Birkenstock leather sandals. As you may recall from that example, the catalog retailer pays a wholesale price of $25 per pair for Birkenstock sandals, markets them at a regular catalog price of $75 per pair, and the arc price elasticity of demand EP = –1.5 is the best available estimate of the current point price elasticity of demand. This typical $50 profit margin implies a standard markup on price of 66.7 percent because


If it can again be assumed that the arc price elasticity of demand EP = –1.5 is the best available estimate of the current point price elasticity of demand, the $75 regular catalog price reflects an optimal markup on price because


Table shows the optimal markup on marginal cost and on price for products with varying price elasticities of demand. As the table indicates, the more elastic the demand for a product, the more price sensitive it is and the smaller the optimal margin. Products with relatively less elastic demand have higher optimal markups. In the retail grocery example, a very low markup is consistent with a high price elasticity of demand for milk. Demand for fruits and vegetables during their peak seasons is considerably less price sensitive, and correspondingly higher markups reflect this lower price elasticity of demand.

Another Optimal Markup Example

The use of the optimal markup formulas can be further illustrated by considering the case of Betty’s Boutique, a small specialty retailer located in a suburban shopping mall. In setting its

Optimal Markup on Marginal Cost and Price at Various Price Elasticity Levels

initial $36 price for a new spring line of blouses, Betty’s added a 50 percent markup on cost. Costs were estimated at $24 each: the $12 purchase price of each blouse, plus $6 in allocated variable overhead costs, plus an allocated fixed overhead charge of $6. Customer response was so strong that when Betty’s raised prices from $36 to $39 per blouse, sales fell only from 54 to 46 blouses per week. Was Betty’s initial $36 price optimal? Is the new $39 price suboptimal? If so, what is the optimal price? At first blush, Betty’s pricing policy seems clearly inappropriate. It is always improper to consider allocated fixed costs in setting prices for any good or service; only marginal or incremental costs should be included. However, by adjusting the amount of markup on cost or markup on price employed, Betty’s can implicitly compensate for the inappropriate use of fully allocated costs. It is necessary to carefully analyze both the cost categories included and the markup percentages chosen before judging a given pricing practice.

To determine Betty’s optimal markup, it is necessary to calculate an estimate of the point price elasticity of demand and relevant marginal cost, and then apply the optimal markup formula. Betty’s standard cost per blouse includes the $12 purchase cost, plus $6 allocated variable costs, plus $6 fixed overhead charges. However, for pricing purposes, only the $12 purchase cost plus the allocated variable overhead charge of $6 are relevant. Thus, the relevant marginal cost for pricing purposes is $18 per blouse. The allocated fixed overhead charge of $6 is irrelevant for pricing purposes because fixed overhead costs are unaffected by blouse sales.

The $3 price increase to $39 represents a moderate 7.7 percent rise in price. Using the arc price elasticity formula, the implied arc price elasticity of demand for Betty’s blouses is


If it can be assumed that this arc price elasticity of demand _P = –2 is the best available estimate of the current point price elasticity of demand, the $36 price reflects an optimal markup of 100 percent on relevant marginal costs of $18 because


Similarly, the $36 price reflects an optimal markup on price because


Betty’s actual markup on relevant marginal costs per blouse is an optimal 100 percent, because


Similarly, Betty’s markup on price is an optimal 50 percent, because


Therefore, Betty’s initial $36 price on blouses is optimal, and the subsequent $3 price increase should be rescinded. This simple example teaches an important lesson. Despite the improper consideration of fixed overhead costs and a markup that might at first appear unsuitable, Betty’s pricing policy is entirely consistent with profit-maximizing behavior because the end result is an efficient pricing policy. Given the prevalence of markup pricing in everyday business practice, it is important that these pricing practices be carefully analyzed before they are judged suboptimal.

The widespread use of markup pricing methods among highly successful firms suggests that the method is typically employed in ways that are consistent with profit maximization. Far from being a naive rule of thumb, markup pricing practices allow firms to arrive at optimal prices in an efficient manner.


With multiple markets or customer groups, the potential exists to enhance profits by charging different prices and markups to each relevant market segment. Market segmentation is an important fact of life for firms in the airline, entertainment, hotel, medical, legal, and professional services industries. Firms that offer goods also often segment their market between wholesale and retail buyers and between business, educational, not-for-profit, and government customers.

Requirements for Profitable Price Discrimination

Price discrimination occurs whenever different classes of customers are charged different markups for the same product. Price discrimination occurs when different customers are charged the same price despite underlying cost differences, and when price differentials fail to reflect cost discrepancies.

For price discrimination to be profitable, different price elasticities of demand must exist in the various submarkets. Unless price elasticities differ among submarkets, there is no point in segmenting the market. With identical price elasticities and identical marginal costs, profitmaximizing pricing policy calls for the same price and markup to be charged in all market segments. A market segment is a division or fragment of the overall market with unique demand or cost characteristics. For example, wholesale customers tend to buy in large quantities, are familiar with product costs and characteristics, and are well-informed about available alternatives. Wholesale buyers are highly price sensitive. Conversely, retail customers tend to buy in small quantities, are sometimes poorly informed about product costs and characteristics, and are often ignorant about available alternatives. As a group, retail customers are often less price sensitive than wholesale buyers. Markups charged to retail customers usually exceed those charged to wholesale buyers.

For price discrimination to be profitable, the firm must also be able to efficiently identify relevant submarkets and prevent transfers among affected customers. Detailed information must be obtained and monitored concerning customer buying habits, product preferences, and price sensitivity. Just as important, the price-discriminating firm must be able to monitor customer buying patterns to prevent reselling among customer subgroups. Ahighly profitable market segmentation between wholesale and retail customers can be effectively undermined if retail buyers are able to obtain discounts through willing wholesalers. Similarly, price discrimination among buyers in different parts of the country can be undermined if customers are able to resell in high-margin territories those products obtained in bargain locales.

Role Played by Consumers’ Surplus

The underlying motive for price discrimination can be understood using the concept of consumers’surplus. Consumers’ surplus is the value of purchased goods and services above and beyond the amount paid to sellers. To illustrate, consider Figure, in which a market equilibrium price/output combination of P* and Q* is shown. The total value of output to customers is given by the area under the demand curve, or area 0ABQ*. Because the total revenue paid to producers is price times quantity, equal to area 0P*BQ*, the area P*AB represents the value of output above the amount paid to producers—that is, the consumers’ surplus. For example, if a given customer is willing to pay $200 for a certain overcoat but is able to obtain a bargain price of $150, the buyer enjoys $50 worth of consumers’ surplus. If another customer places a value of only $150 on the overcoat, he or she would enjoy no consumers’ surplus following a purchase for $150.

Consumers’ surplus arises because individual consumers place different values on goods and services. Customers that place a relatively high value on a product will pay high prices; customers that place a relatively low value on a product are only willing to pay low prices. As one proceeds from point A downward along the market marginal curve in Figure, customers that place a progressively lower marginal value on the product enter the market. At low prices, both high-value and low-value customers are buyers; at high prices, only customers that place a relatively high value on a given product are buyers.

When product value differs greatly among various groups of customers, a motive for price discrimination is created. By charging higher prices to customers with a high marginal value of consumption, revenues will increase without affecting costs. Sellers with the ability to vary prices according to the value placed on their products by buyers are able to capture at least some of the value represented by consumers’ surplus. Such price discrimination will always increase profits because it allows the firm to increase total revenue without affecting costs. A firm that is precise in its price discrimination always charges the maximum each market segment is willing to pay. Price discrimination is charging what the market will bear. Finally, it is important to recognize that price discrimination does not carry any evil connotation in a moral sense. In some circumstances, price discrimination leads to lower prices for some customer groups and to a wider availability of goods and services. For example, a municipal bus company might charge lower prices for the elderly and the handicapped. In such circumstances, the bus company is price discriminating in favor of elderly and handicapped riders and against other customers. This type of price discrimination provides elderly and handicapped customers a greater opportunity to ride the bus. Because of incremental revenues provided by elderly and handicapped riders, the bus company may also be able to offer routes that could not be supported by revenues from full-fare customers alone, or it may be able to operate with a lower taxpayer subsidy.

Degrees of Price Discrimination

The extent to which a firm can engage in price discrimination is classified into three major categories. Under first-degree price discrimination, the firm extracts the maximum amount each customer is willing to pay for its products. Each unit is priced separately at the price indicated along each product demand curve. Such pricing precision is rare because it requires that sellers know the maximum price each buyer is willing to pay for each unit of output. Purchase decisions must also be monitored closely to prevent reselling among customers. Although first-degree price discrimination is uncommon, it has the potential to emerge in any market where discounts from posted prices are standard and effective prices are individually negotiated between buyers and sellers. When sellers possess a significant amount of market power, consumer purchases of big-ticket items such as appliances, automobiles, homes, and professional services all have the potential to involve first-degree price discrimination.

Second-degree price discrimination, a more frequently employed type of price discrimination, involves setting prices on the basis of the quantity purchased. Bulk rates are typically set with high prices and markups charged for the first unit or block of units purchased, but

Consumers’ Surplus

progressively greater discounts are offered for greater quantities. Quantity discounts that lead to lower markups for large versus small customers are a common means of discriminating in price between retail and wholesale customers. Book publishers often charge full price for small purchases but offer 40 percent to 50 percent off list prices when 20 or more units are purchased. Public utilities, such as electric companies, gas companies, and water companies, also frequently charge block rates that are discriminatory. Consumers pay a relatively high markup for residential service, whereas commercial and industrial customers pay relatively low markups. Office equipment such as copy machines and servers (mainframe computers) are other examples of products for which second-degree price discrimination is practiced, especially when time sharing among customers is involved.

The most commonly observed form of price discrimination, third-degree price discrimination, results when a firm separates its customers into several classes and sets a different price for each customer class. Customer classifications can be based on for-profit or not-forprofit status, regional location, or customer age. Barron’s, Forbes, The Wall Street Journal, and other publishers routinely offer educational discounts that can be in excess of 30 percent to 40 percent off list prices. These publishers are eager to penetrate the classroom on the assumption that student users will become loyal future customers. Auto companies, personal computer manufacturers, and others also prominently feature educational discounts as part of their marketing strategy. Many hospitals also offer price discounts to various patient groups. If unemployed and uninsured patients are routinely charged only what they can easily afford to pay for medical service, whereas employed and insured medical patients are charged maximum allowable rates, the hospital is price discriminating in favor of the unemployed and against the employed. Widespread price discounts for senior citizens represent a form of price discrimination in favor of older customers but against younger customers.


Price discrimination is profitable because it allows the firm to enhance revenues without increasing costs. It is an effective means for increasing profits because it allows the firm to more closely match marginal revenues and marginal costs. A firm that can segment its market maximizes profits by operating at the point where marginal revenue equals marginal cost in each market segment. Adetailed example is a helpful means for illustrating this process.

Price/Output Determination

Suppose that Midwest State University (MSU) wants to reduce the athletic department’s operating deficit and increase student attendance at home football games. To achieve these objectives, a new two-tier pricing structure for season football tickets is being considered. A market survey conducted by the school suggests the following market demand and marginal revenue relations:

Public Demand                                                           Student Demand

PP = $225 – $0.005QP                                             PS = $125 – $0.00125QS
MRP = ΔTRPQP = $225 – $0.01QP                      MRS = ΔTRSQS = $125 – $0.0025QS

From these market demand and marginal revenue curves, it is obvious that the general public is willing to pay higher prices than are students. The general public is willing to purchase tickets up to a market price of $225, above which point market demand equals zero. Students are willing to enter the market only at ticket prices below $125. During recent years, the football program has run on an operating budget of $1.5 million per year. This budget covers fixed salary, recruiting, insurance, and facility-maintenance expenses. In addition to these fixed expenses, the university incurs variable ticket-handling, facility-cleaning, insurance, and security costs of $25 per season ticketholder. The resulting total cost and marginal cost functions are

TC = $1,500,000 + $25Q
MC = ΔTCQ = $25

What are the optimal football ticket prices and quantities for each market, assuming that MSU adopts a new season ticket pricing policy featuring student discounts? To answer this question, one must realize that because MC = $25, the athletic department’s operating deficit is minimized by setting MR = MC = $25 in each market segment and solving for Q. This is also the profit-maximizing strategy for the football program. Therefore

Public Demand

$225 – $0.01QP = $25
$0.01QP = $200
QP = 20,000


PP = $225 – $0.005(20,000)
      = $125

Student Demand

$125 – $0.0025QS = $25
$0.0025QS = $100
QS = 40,000


PS = $125 – $0.00125(40,000)
     = $75

The football program’s resulting total operating surplus (profit) is

Operating Surplus

  (Profit) = TRP + TRS TC
              = $125(20,000) + $75(40,000)– $1,500,000 – $25(60,000)
              = $2.5 million

To summarize, the optimal price/output combination with price discrimination is 20,000 in unit sales to the general public at a price of $125 and 40,000 in unit sales to students at a price of $75. This two-tier pricing practice results in an optimal operating surplus (profit) of $2.5 million.

Comparison with the One-Price Alternative

To gauge the implications of this new two-tier ticket pricing practice, it is interesting to contrast the resulting price/output and surplus levels with those that would result if MSU maintained its current one-price ticket policy.

If tickets are offered to students and the general public at the same price, the total amount of ticket demand equals the sum of student plus general public demand. The student and general public market demand curves are

QP = 45,000 – 200PP and QS = 100,000 – 800PS

Under the assumption PP = PS, total demand (QT) equals

QT = QP + QS
      = 145,000 – 1,000P


P = $145 – $0.001Q

which implies that

MR = ΔTRQ = $145 – $0.002Q

These aggregate student-plus-general-public market demand and marginal revenue curves hold only for prices below $125, a level at which both the general public and students purchase tickets. For prices above $125, only nonstudent purchasers buy tickets, and the public demand curve PP = $225 – $0.005QP represents total market demand as well. This causes the actual total demand curve to be kinked at a price of $125, as shown in Figure.

The uniform season ticket price that maximizes operating surplus (or profits) is found by setting MR = MC for the total market and solving for Q:

$145 – $0.002Q = $25
$0.002Q = $120
Q = 60,000
P = $145 – $0.001(60,000)
= $85


QP = 45,000 – 200($85)                        QS = 100,000 – 800($85)
      = 28,000                                                   = 32,000

Operating surplus (profit) = TR TC
                                     = $85(60,000) – $1,500,000– $25(60,000)
                                     = $2.1 million

Observe that the total number of tickets sold equals 60,000 under both the two-tier and the single-price policies. This results because the marginal cost of a ticket is the same under each scenario. Ticket-pricing policies featuring student discounts increase student attendance from 32,000 to 40,000 and maximize the football program’s operating surplus at $2.5 million (rather than $2.1 million). It is the preferred pricing policy when viewed from MSU’s perspective. However, such price discrimination creates both “winners” and “losers.” Winners following adoption of student discounts include students and MSU. Losers include members of the general public, who pay higher football ticket prices or find themselves priced out of the market.

Graphic Illustration

The MSU pricing problem and the concept of price discrimination can be illustrated graphically. Figure shows demand curves for the general public in part (a) and for students in part (b). The aggregate demand curve in part (c) represents the horizontal sum of the quantities demanded at each price in the public and student markets. The associated marginal revenue curve, MRP+S, has a similar interpretation. For example, marginal revenue equals $25 at an attendance level of 20,000 in the public market and $25 at an attendance level of 40,000 in the student market. Accordingly, one point on the total marginal revenue curve represents output of 60,000 units and marginal revenue of $25. From a cost standpoint, it does not matter whether tickets are sold to the public or to students. The single marginal cost curve MC = $25 applies to each market.

Graphically solving this pricing problem is a two-part process. The profit-maximizing total output level must first be determined, and then this output must be allocated between submarkets. Profit maximization occurs at the aggregate output level at which marginal revenue and marginal cost are equal. Figure shows a profit-maximizing output of 60,000 tickets, where marginal cost and marginal revenue both equal $25. Proper allocation of total output between the two submarkets is determined graphically by drawing a horizontal line to indicate that $25 is the marginal cost in each market at the indicated aggregate output level. The intersection of this horizontal line with the marginal revenue curve in each submarket indicates the optimal distribution of sales and pricing structure. In this example, profits are maximized at an attendance (output) level of 60,000, selling 20,000 tickets to the public at a price of $125 and 40,000 tickets to students at a price of $75.

Price Discrimination for an Identical Product Sold in Two Markets


When products have different values for different customers, profits can sometimes be enhanced by using multiple-unit pricing strategies. With multiple-unit pricing, all customers typically face the same pricing schedule, but the price paid is determined by the value to consumers of the total amount purchased. Unlike single-unit pricing, where all customers are charged a unit price that sets MR= MC, multiple-unit pricing can result in some combination of per-unit and “lump sum” fees. Like price discrimination, multiple-unit pricing strategies have proven an effective means for extracting consumers’ surplus for the benefit of producers.

Two-Part Pricing

Athletic clubs, time-share vacation resorts, golf courses, and a wide variety of “membership organizations” offer goods and services using two-part pricing. Acommon two-part pricing technique is to charge all customers a fixed “membership” fee per month or per year, plus a per-unit usage charge. In general, a firm can enhance profits by charging each customer a perunit fee equal to marginal cost, plus a fixed fee equal to the amount of consumers’ surplus generated at that per-unit fee.

In the case of golf course memberships, for example, two-part pricing often consists of a large lifetime membership fee plus “greens fees” charged for each round of golf played. To illustrate how such a two-part pricing practice might prove profitable, assume that an individual avid golfer’s demand and marginal revenue curves can be written P = $100 – $1QMR = ΔTRQ = $100 – $2Q where P is the price of a single round of golf, and Q is the number of rounds played during a given year. For simplicity, also assume that the marginal cost of a round of golf is $20, and that fixed costs are nil. This gives the following total and marginal cost relations:

TC = $20Q
MC = ΔTCQ = $20

As shown in Figure, the profit-maximizing single-unit price for a monopoly golf course is found by setting MR = MC, where

$100 – $2Q = $20
2Q = 80
Q = 40

At the profit-maximizing quantity of 40, the optimal single-unit price is $60 and total profits

equal $1,600 because
P = $100 – $1(40)
   = $60

π = TR TC
    = $60(40) – $20(40)
    = $1,600

Notice from Figure that the value of consumers’ surplus at a standard per-unit price is equal to the region under the demand curve that lies above the profit-maximizing price of $60. Because the area of a such a triangle is one-half the value of the base times the height, the value of consumers’ surplus equals Consumers’ Surplus = 1/2 [(40 _ ($100 – $60)] = $800 In words, this means that at a single-unit price of $60, such an individual will choose to play 40 rounds of golf, resulting in total revenues of $2,400 and total profits of $1,600 for the golf course.

The fact that consumers’ surplus equals $800 means that the avid golfer in question would have been willing to pay an additional $800 to play these 40 rounds of golf. This is an amount above and beyond the $2,400 paid. The avid golfer received a real bargain.

As an alternative to charging a single-unit price of $60 per round, consider the profits that could be earned using a two-part pricing scheme. To maximize profits, the golf course would choose to charge a per-unit price that equals marginal cost, plus a fixed fee equal to the amount of consumers’ surplus received by each consumer at this price. Remember, in Figure, that the value of consumers’ surplus is equal to the region under the demand curve that lies above the perunit price. When the per-unit price is set equal to marginal cost, P = $20 and Q = 80 because

P = MC
$100 – $1Q = $20
Q = 80

At the per-unit price of $20 and output level of 80, the value of consumers’ surplus equals

Monopoly Per-Unit Pricing Versus Two-Part Pricing

Consumers’ Surplus = 1/2 [(80 _ ($100 – $20)]
                              = $3,200

Thus, $3,200 is the maximum membership fee the golfer in question would pay to play 80 rounds of golf per year when modest additional “greens fees” of $20 per round are charged. It follows that the profit-maximizing two-part pricing scheme is to charge each player an annual membership fee of $3,200 per year plus “greens fees” of $20 per round played. Total golf course revenues of $4,800 represent the full value derived from playing 80 rounds of golf per year, cover marginal costs of $1,600 (= $20 _ 80), and result in a $3,200 profit for the golf course.

Throughout this discussion it has implicitly been assumed that the seller must enjoy at least some market power in order to institute any two-part pricing scheme. Otherwise, competitors would undercut the amount of annual membership fees, and per-unit prices would converge on marginal costs. Therefore, it is unsurprising that high golf membership fees tend to be most common in urban areas where conveniently located golf courses are in short supply. In outlying or rural areas, where restrictions on the location of new golf courses are less stringent, large membership fees tend to be relatively rare.

Bundle Pricing

Another way firms with market power enhance profits is by a variant of two-part pricing called bundle pricing. If you’ve ever purchased a 12-pack of soft drinks, a year’s supply of tax preparation services, or bought a “two-for-the-price-of-one” special, you have firsthand experience with the bundle pricing concept. When significant consumers’ surplus exists, profits can be enhanced if products are purchased together as a single package or bundle of goods or services.

Bundles can be of a single product, like soft drinks or legal services, or they can be comprised of closely related goods and services. For example, car manufacturers often bundle “luxury packages” comprised of new car options like power steering, power brakes, automatic transmissions,

tinted glass, and so on. Similarly, car dealers often bundle services, like oil changes, transmission fluid changes, radiator flushes, and tune-ups at a “special package price.” In the case of a single product sold in multiple-unit bundles, the optimal bundle price is derived in a manner similar to the optimal two-part price calculation described in Figure.

As in the case of two-part pricing, the optimal level of output is determined by setting price equal to marginal cost and solving for quantity. Then, the optimal bundle price is a single lump sum amount equal to the total area under the demand curve at that point. In Figure, for example, the optimal bundle price of $4,800 would include the total value of consumers’ surplus generated with a single per-unit price (or $3,200), plus total cost (or $1,600).

Optimal pricing for bundles of related but not identical products is figured in an analogous manner. Again, the total amount charged equals the value of the total area under the demand curve at the optimal output level, where output is defined as a bundle of related goods or services.

As in the case of two-part pricing, the optimal level of output is determined by setting price equal to marginal cost and solving for quantity. Then, the optimal bundle price is simply a lump sum amount equal to the total area under the demand curve at that activity level. In the case of related but not identical products, bundle pricing is sometimes used because firms are not able to precisely determine the amounts different consumers are willing to pay for different products.

If managers had precise information about the value of each individual product for each individual consumer, the firm could earn even higher profits by precisely tying the price charged to the value derived by each customer.


It is difficult to think of a firm that does not produce a variety of products. Almost all companies produce multiple models, styles, or sizes of output, and each of these variations can represent a separate product for pricing purposes. Although multiple-product pricing requires the same basic analysis as for a single product, the analysis is complicated by demand and production interrelations.

Demand Interrelations

Demand interrelations arise because of competition or complementarity among various products or product lines. If products are interrelated, either as substitutes or complements, a change in the price of one affects demand for the other. Multiple-product pricing decisions must reflect such influences. In the case of a two-product firm, the marginal revenue functions for each product can be written as


The first term on the right side of each equation represents the marginal revenue directly associated with each product. The second term depicts the indirect marginal revenue associated with each product and indicates the change in revenues due to a change in sales of the alternative product. For example, ΔTRBQA in Equation 12.12 shows the effect on product B revenues of an additional unit sold of product A. Likewise, ΔTRAQB in Equation 12.13 represents the change in revenues received from product A when an additional unit of product B is sold.

Cross-marginal revenue terms that reflect demand interrelations can be positive or negative. For complementary products, the net effect is positive because increased sales of one product lead to increased revenues from another. For substitute products, increased sales of one product reduce demand for another, and the cross-marginal revenue term is negative. Accurate price determination in the case of multiple products requires a complete analysis of pricing decision effects. This often means that optimal pricing requires an application of incremental analysis to ensure that the total implications of pricing decisions are reflected.

Production Interrelations

Whereas many products are related to one another through demand relationships, others are related in terms of the production process. Aby-product is any output that is customarily produced as a direct result of an increase in the production of some other output. Although it is common to think of by-products as resulting only from physical production processes, they are also generated in the process of providing services. One of the primary reasons why top accounting firms have become such a leading force in the management information systems (MIS) consulting business is that information generated in the auditing process has natural MIS implications, and vice versa. In this way, auditing and consulting services are joint products produced in variable proportions. The cost of providing each service depends greatly on the extent to which the other is also provided. Given the efficiencies of joint production, it is common for an accounting firm’s auditing clients to also become MIS consulting clients.

Multiple products are produced in variable proportions for a wide range of goods and services. In the refining process for crude oil, gasoline, diesel fuel, heating oil, and other products are produced in variable proportions. The cost and availability of any single by-product depends on the demand for others. By-products are also sometimes the unintended or unavoidable consequence of producing certain goods. When lumber is produced, scrap bark and sawdust are also created for use in gardening and paper production. When paper is produced, residual chemicals and polluted water are created that must be treated and recycled. Indeed, pollution can be thought of as the necessary by-product of many production processes. Because pollution is, by definition, a “bad” with harmful social consequences rather than a “good” with socially redeeming value, production processes must often be altered to minimize this type of negative joint product.

Production interrelations are sometimes so strong that the degree of jointness in production is relatively constant. For example, many agricultural products are jointly produced in a fixed ratio. Wheat and straw, beef and hides, milk and butter are all produced in relatively fixed proportions.

In mining, gold and copper, silver and lead, and other precious metals and minerals are often produced jointly in fixed proportions. Appropriate pricing and production decisions are possible only when such interrelations are accurately reflected.

Joint Products Produced in Variable Proportions

Firms can often vary the proportions in which joint products are created. Even the classic example of fixed proportions in the joint production of beef and hides holds only over short periods:

Leaner or heavier cattle can be bred to provide differing proportions of these two products. When the proportions of joint output can be varied, it is possible to construct separate marginal cost relations for each product.

The marginal cost of either joint product produced in variable proportions equals the increase in total costs associated with a one-unit increase in that product, holding constant the quantity of the other joint product produced. Optimal price/output determination for joint products in this case requires a simultaneous solution of marginal cost and marginal revenue relations. The firm maximizes profit by operating at the output level where the marginal cost of producing each joint product just equals the marginal revenue it generates. The profit-maximizing combination of joint products A and B, for example, occurs at the output

level where MRA = MCB and MRB = MCB.

It is important to note, however, that although it is possible to determine the separate marginal costs of goods produced in variable proportions, it is impossible to determine their indi- vidual average costs. This is because common costs are expenses necessary for manufacture of a joint product. Common costs of production—raw material and equipment costs, management expenses, and other overhead—cannot be allocated to each individual by-product on any economically sound basis. Only costs that can be separately identified with a specific by-product can be allocated. For example, tanning costs for hides and refrigeration costs for beef are separate identifiable costs of each by-product. Feed costs are common and cannot be allocated between hide and beef production. Any allocation of common costs is wrong and arbitrary.

Joint Products Produced in Fixed Proportions

An interesting case of joint production is that of by-products produced in fixed proportions. Products that must be produced in fixed proportions should be considered as a package or bundle of output. When by-products are jointly produced in fixed proportions, all costs are common, and there is no economically sound method of cost allocation. Optimal price/output determination for output produced in fixed proportions requires analysis of the relation between marginal revenue and marginal cost for the combined output package. As long as the sum of marginal revenues obtained from all by-products is greater than the marginal cost of production, the firm gains by expanding output.

Figure illustrates the pricing problem for two products produced in fixed proportions. Demand and marginal revenue curves for each by-product and the single marginal cost curve for production of the combined output package are shown. Vertical summation of the two marginal revenue curves indicates the total marginal revenue generated by both by-products. Marginal revenue curves are summed vertically because each unit of output

Optimal Pricing for Joint Products Produced in Fixed Proportions

provides revenues from the sale of both by-products. The intersection of the total marginal revenue curve MRT with the marginal cost curve identifies the profit-maximizing output level. The optimal price for each by-product is determined by the intersection of a vertical line at the profit-maximizing output level with each by-product’s demand curve. Q1 represents the optimal quantity of the output package to be produced, and PA and PB are the prices to be charged for each by-product.

Notice that the MRT curve in Figure coincides with the marginal revenue curve for product B at all output quantities greater than Q2. This is because MRA becomes negative at that point, and the firm would not sell more than the quantity of product A represented by output package Q2. The total revenue generated by product A is maximized at output Q2; sales of any larger quantity of product A would reduce revenues and profits.

If the marginal cost curve for the output package intersects the total marginal revenue curve to the right of Q2, profit maximization requires that the firm raise output up to this point of intersection. At that point, product B must be priced as indicated by its demand and marginal revenue curves. Because product B sales offer the sole motivation for production beyond the Q2 level, the marginal revenue generated from product B sales must be sufficient to cover the marginal costs of producing the entire output package. In this instance, profit maximization requires that MRB = MC. Beyond the Q2 level, the marginal cost of product A is zero; product A is the unavoidable by-product of product B production. Beyond the Q2 level, the price of product A is set in order to maximize profits in that MRA = MCA = 0. This pricing situation is illustrated in Figure, which shows the same demand and marginal revenue curves presented in Figure, along with a new marginal cost curve. The optimal output quantity is Q3, determined by the intersection of the marginal cost curve and the total marginal revenue

Optimal Pricing for Joint Products Produced in Fixed Proportions with Excess Production of One Product

curve. Product B is sold in the amount indicated by output package Q3 and is priced at PB. The sales quantity of product Ais limited to the amount in output Q2 and is priced at PA. The excess quantity of product A produced, shown as Q3 – Q2, must be destroyed or otherwise kept out of the market so that its price and total revenue is not lowered below that indicated at Q2. An example of joint output that is sometimes destroyed or otherwise held off the market is provided by sliced pineapple and pineapple juice; juice is produced as a by-product as pineapples are peeled and sliced. Some years ago, an excessive amount of pineapple juice was produced, and rather than put it on the market and depress prices, the excess was destroyed.

Seeing a profit-making opportunity, Dole, Del Monte, and other producers advertised heavily to shift the demand curve for pineapple juice outward. New products were also created, such as pineapple-grapefruit juice, to spur demand for the waste by-product. Canning machinery was also improved to reduce the amount of juice. Today, little if any pineapple excess juice by-product is produced. Similarly, firms in many other industries have discovered new and valuable uses for previously discarded by-products.


Agraphic approach offers a useful introduction to the solution of joint product pricing problems, but many real-world problems require a more detailed analytic treatment. An example of a price/output decision for two products produced in fixed proportions will help clarify the technique.

Joint Products Without Excess By-Product

The Vancouver Paper Company, located in Vancouver, British Columbia, produces newsprint and packaging materials in a fixed 1:1 ratio, or 1 ton of packaging materials per 1 ton of newsprint. These two products, A (newsprint) and B (packaging materials), are produced in equal quantities because newsprint production leaves scrap by-product that is useful only in the production of lower-grade packaging materials. The total and marginal cost functions for Vancouver can be written

TC = $2,000,000 + $50Q + $0.01Q2
MC = ΔTCQ = $50 + $0.02Q

where Q is a composite package or bundle of output consisting of 1 ton of product A and 1 ton of product B. Given current market conditions, demand and marginal revenue curves for each product are as follows:

Newsprint                                                                  Packaging Materials

PA = $400 – $0.01QA                                               PB = $350 – $0.015QB
MRA = ΔTRAQA = $400 – $0.02QA                     MRB = ΔTRBQB = $350 – $0.03QB

For each unit of Q produced, the firm obtains one unit of product A and one unit of product B for sale to customers. The revenue derived from the production and sale of one unit of Qis composed of revenues from the sales of one unit of product A plus one unit of product B. Therefore, the total revenue function is merely a sum of the revenue functions for products A and B:


Substituting for PA and PB results in the total revenue function


Because one unit of product A and one unit of product B are contained in each unit of Q, QA = QB = Q. This allows substitution of Q for QA and QB to develop a total revenue function in terms of Q, the unit of production:


This total revenue function assumes that all quantities of product A and B produced are also sold. It assumes no dumping or withholding from the market for either product. It is the appropriate total revenue function if, as in Figure, the marginal revenues of both products are positive at the profit-maximizing output level. When this occurs, revenues from each product contribute toward covering marginal costs. The profit-maximizing output level is found by setting MR = MC and solving for Q:

   MR = MC
    $750 – $0.05Q = $50 + $0.02Q
    0.07Q = 700
    Q = 10,000 units

At the activity level Q = 10,000 units, marginal revenues for each product are positive:

Each product makes a positive contribution toward covering the marginal cost of production, where

  MC = $50 + $0.02Q
        = $50 + $0.02(10,000)
        = $250

There is no reason to expand or reduce production because MR = MRA + MRB = MC = $250, and each product generates positive marginal revenues. Prices for each product and total profits for Vancouver can be calculated from the demand and total profit functions:



Vancouver should produce 10,000 units of output and sell the resulting 10,000 units of product A at a price of $300 per ton and 10,000 units of product B at a price of $200 per ton. An optimum total profit of $1.5 million is earned at this activity level.

Joint Production with Excess By-Product (Dumping)

The determination of a profit-maximizing activity level is only slightly more complex if a downturn in demand for either product A or B causes marginal revenue for one product to be negative when all output produced is sold to the marketplace. Suppose that an economic recession causes the demand for product B (packaging materials) to fall dramatically, while the demand for product A (newsprint) and marginal cost conditions hold steady. Assume new demand and marginal revenue relations for product B of


Adramatically lower price of $90 per ton [= $290 – $0.02(10,000)] is now required to sell 10,000 units of product B. However, this price and activity level is suboptimal. To see why, the profit-aximizing activity level must again be calculated, assuming that all output is sold. The new marginal revenue curve for Q is

      = $400 – $0.02QA + $290 – $0.04QB
      = $690 – $0.06Q

If all production is sold, the profit-maximizing level for output is found by setting MR = MC and solving for Q:

$690 – $0.06Q = $50 + $0.02Q
0.08Q = 640
Q = 8,000

At Q = 8,000, the sum of marginal revenues derived from both by-products and the marginal cost of producing the combined output package each equal $210, because

MR = $690 – $0.06Q                                                 MC = $50 + $0.02Q
= $690 – $0.06(8,000)                                                = $50 + $0.02(8,000)
= $210                                                                          = $210

However, the marginal revenue of product B is no longer positive:


Even though MR = MC = $210, the marginal revenue of product B is negative at the Q = 8,000 activity level. This means that the price reduction necessary to sell the last unit of product B causes Vancouver’s total revenue to decline by $30. Rather than sell product B at such unfavorable terms, Vancouver would prefer to withhold some from the marketplace. In contrast, Vancouver would like to produce and sell more than 8,000 units of productAbecause MRA > MCat the 8,000 unit activity level. It would be profitable for the company to expand production of Q just to increase sales of product A, even if it had to destroy or otherwise withhold from the market the unavoidable added production of product B.

Under these circumstances, set the marginal revenue of product A, the only product sold at the margin, equal to the marginal cost of production to find the profit-maximizing activity level:

$400 – $0.02Q = $50 + $0.02Q
$0.04Q = $350
Q = 8,750 units

Under these circumstances, Vancouver should produce 8,750 units of Q = QA = QB. Because this activity level is based on the assumption that only product A is sold at the margin and that the marginal revenue of product A covers all marginal production costs, the effective marginalcost of product B is zero. As long as production is sufficient to provide 8,750 units of product A, 8,750 units of product B are also produced without any additional cost.

With an effective marginal cost of zero for product B, its contribution to firm profits is maximized by setting the marginal revenue of product B equal to zero (its effective marginal cost):


Whereas a total of 8,750 units of Qshould be produced, only 7,250 units of product B will be sold. The remaining 1,500 units of QB must be destroyed or otherwise withheld from the market. Optimal prices and the maximum total profit for Vancouver are as follows:


No other price/output combination has the potential to generate as large a profit for Vancouver.


Expanding markets brought about by improvements in communication and transportation, as well as falling trade barriers, have led to the development of large, multidivision firms that cut across national boundaries. Avexing challenge for many large corporations surrounds the need to set an appropriate price for the transfer of goods and services among divisions.

Transfer Pricing Problem

The transfer pricing problem results from the difficulty of establishing profitable relationships among divisions of a single company when each separate business unit stands in verticalrelation to the other. A vertical relation is one where the output of one division or company is the input to another. Vertical integration occurs when a single company controls various links in the production chain from basic inputs to final output. Media powerhouse AOL-Time Warner, Inc., is vertically integrated because it owns AOL, an Internet service provider (ISP) and cable TV systems, plus a number of programming properties in filmed entertainment (e.g., Warner Bros.) and television production (e.g., HBO, CNN), commonly referred to as content providers. Vertically integrated companies in this field own and operate the distribution network and the programming that is sold over that network.

To combat the problems of coordinating large-scale enterprises that are vertically integrated, separate profit centers are typically established for each important product or product line. Despite obvious advantages, this decentralization has the potential to create problems. The most critical of these is the problem of transfer pricing, or the pricing of intermediate products transferred among divisions. To maximize profits for the vertically integrated firm, it is essential that a profit margin or markup only be charged at the final stage of production. All intermediate products transferred internally must be transferred at marginal cost.

Transfer Pricing for Products Without External Markets

Think of the divisionalized firm as a type of internal market. Like external markets, the internal markets of divisionalized firms act according to the laws of supply and demand. Supply is offered by various upstream suppliers to meet the demand of downstream users. Goods and services must be transferred and priced each step along the way from basic raw materials to finished products.

For simplicity, consider the problem faced by a vertically integrated firm that has different divisions at distinct points along the various steps of the production process, and assume for the moment that no external market exists for transferred inputs. If each separate division is established as a profit center to provide employees with an efficiency incentive, a transfer pricing problem can occur. Suppose each selling division adds a markup over its marginal cost for inputs sold to other divisions. Each buying division would then set its marginal revenue from output equal to the division’s marginal cost of input. This process would culminate in a marginal cost to the ultimate upstream user that exceeds the sum total of marginal costs for each transferring division. All of the markups charged by each ransferring division drive a wedge between the firm’s true marginal cost of production and the marginal cost to the last or ultimate upstream user. As a result, the ultimate upstream user buys less than the optimal amount of input and produces less than the profit-maximizing level of output.

For example, it would be inefficient if AOL, a major ISP, paid more than the marginal cost of programming produced by its own subsidiaries. If each subsidiary added a markup to the marginal cost of programming sold to the parent company, AOL would buy less than a profitmaximizing amount of its own programming. In fact, AOL would have an incentive to seek programming from other purveyors so long as the external market price was less than the internal transfer price. Such an incentive could create extreme inefficiencies, especially when the external market price is less than the transfer price but greater than the marginal cost of programming produced by AOL’s own subsidiaries.

An effective transfer pricing system leads to activity levels in each division that are consistent with profit maximization for the overall enterprise. This observation leads to the most basic rule for optimal transfer pricing: When transferred products cannot be sold in external markets,the marginal cost of the transferring division is the optimal transfer price. One practical means for insuring that an optimal amount of input is transferred at an optimal transfer price is to inform buying divisions that the marginal cost curve of supplying divisions is to be treated like a supply schedule. Alternatively, supplying divisions could be informed about the buying division’s marginal revenue or demand curve and told to use this information in determining the quantity supplied. In either case, each division would voluntarily choose to transfer an optimal amount of input at the optimal transfer price.

Transfer Pricing with Perfectly Competitive External Markets

The transfer pricing problem is only sightly more complicated when transferred inputs can be sold in external markets. When transferred inputs can be sold in a perfectly competitive external market, the external market price represents the firm’s opportunity cost of employing such inputs internally. As such, it would never pay to use inputs internally unless their value to the firm is at least as great as their value to others in the external market. This observation leads to a second key rule for optimal transfer pricing: When transferred products can be sold in perfectly competitiveexternal markets, the external market price is the optimal transfer price. If upstream suppliers wish to supply more than downstream users desire to employ at a perfectly competitive price, excess input can be sold in the external market. If downstream users wish to employ more than upstream suppliers seek to furnish at a perfectly competitive price, excess input demand can be met through purchases in the external market. In either event, an optimal amount of input is transferred internally.

Of course, it is hard to imagine why a firm would be vertically integrated in the first place if all inputs could be purchased in perfectly competitive markets. Neither Kellogg’s nor McDonald’s, for example, have extensive agricultural operations to ensure a steady supply of foodstuffs. Grains for cereal and beef for hamburgers can both be purchased at prices that closely approximate marginal cost in perfectly competitive input markets. On the other hand, if an input market is typically competitive but punctuated by periods of scarcity and shortage, it can pay to maintain some input producing capability. For example, ExxonMobil Corp. has considerable production facilities that supply its extensive distribution network with gasoline, oil, and petroleum products. These production facilities offer ExxonMobil some protection against the threat of supply stoppages. Similarly, Coca-Cola has long-term supply contracts with orange growers to ensure a steady supply of product for its Minute Maid juice operation.

Both ExxonMobil and Coca-Cola are examples of vertically integrated firms with inputs offered in markets that are usually, but not always, perfectly competitive.

Transfer Pricing with Imperfectly Competitive External Markets

The typical case of vertical integration involves firms with inputs that can be transferred internally or sold in external markets that are not perfectly competitive. Again, it never pays to use inputs internally unless their value to the firm is at least as great as their value to others in the external market. This observation leads to a third and final fundamental rule for optimal transfer pricing: When transferred products can be sold in imperfectly competitive external markets, the optimaltransfer price equates the marginal cost of the transferring division to the marginal revenuederived from the combined internal and external markets. In other words, when inputs can be sold in imperfectly competitive external markets, internal input demand must reflect the opportunity to supply input to the external market at a price in excess of marginal cost. If upstream suppliers wish to offer more input than downstream users desire to employ when input MC= MR from the combined market, excess supply can be sold in the external market. If downstream users want to employ more than upstream suppliers seek to furnish when MC = MR, excess internal demand can be met through added purchases in the external market. In both cases, an optimal amount of input is transferred internally.


Although the transfer pricing concept can be introduced conceptually through the use of graphic analysis, most real-world applications are complex and must be solved algebraically. For this reason, examination of a detailed numerical example can be fruitful.

Profit Maximization for an Integrated Firm

Josiah Bartlet & Sons, Inc., is a small integrated domestic manufacturer of material handling equipment. Demand and marginal revenue curves for the firm are

P = $100 – $0.001Q
MR = ΔTRQ = $100 – $0.002Q

Relevant total cost, marginal cost, and profit functions are

TC = $312,500 + $25Q + $0.0015Q2
MC = ΔTCQ = $25 + $0.003Q
π = TR TC
    = $100Q – $0.001Q2 – $312,500 – $25Q – $0.0015Q2
    = –$0.0025Q2 + $75Q – $312,500

Profit maximization occurs at the point where MR = MC, so the optimal output level is

$100 – $0.002Q = $25 + $0.003Q
75 = 0.005Q
Q = 15,000

This implies that

P = $100 – $0.001(15,000)
   = $85
π = TR TC
   = –$0.0025(15,0002) + $75(15,000) – $312,500
   = $250,000

Therefore, the optimal price/output combination is $85 and 15,000 units for this integrated firm, and profits total $250,000. To be optimal, transfer prices must ensure operation at these levels.

Transfer Pricing with No External Market

Consider how the situation changes if the firm is reorganized into separate manufacturing and distribution division profit centers, and no external market exists for the transferred product. The demand curve facing the distribution division is precisely the same as the firm’s output demand curve. Although the total cost function of the firm is unchanged, it can be broken down into the costs of manufacturing and distribution. Assume that such a breakdown results in the following divisional cost functions:


With divisional operation, the total and marginal cost functions for the firm are


and precisely the same as before. To demonstrate the derivation of an appropriate activity level, the net marginal revenue for the distribution division is set equal to the marginal cost of the manufacturing division:

The 15,000-unit output level remains optimal for profit maximization. If the distribution division determines the quantity it will purchase by movement along its marginal revenue curve, and the manufacturing division supplies output along its marginal cost curve, then the market-clearing transfer price is the price that results when MR MCDistr = MCMfg. At 15,000 units of output, the
optimal transfer price is

PT = MCMfg
     = $20 + $0.002(15,000)
     = $50

At a transfer price of PT = $50, the quantity supplied by the manufacturing division equals 15,000. This is the same quantity demanded by the distribution division at a PT = $50, because


At a transfer price of PT > $50, the distribution division will accept fewer units of output than the manufacturing division wants to supply. If PT < $50, the distribution division will seek to purchase more units than the manufacturing division desires to produce. Only at a $50 transfer price are supply and demand in balance in the firm’s internal market.

Competitive External Market with Excess Internal Demand

To consider the effects of an external market for the transferred product, assume that the company is able to buy an unlimited quantity of a comparable product from a foreign supplier at a price of $35. The product supplied by the foreign manufacturer meets the exact same specifications as that produced by Josiah Bartlet & Sons. Because an unlimited quantity can be purchased for $35, a perfectly competitive external market exists for the transferred product, and the optimal transfer price equals the external market price. For PT = $35, the quantity demanded by the distribution division is


whereas the quantity supplied by the manufacturing division is


In this case of excess internal demand, the distribution division will purchase all 7,500 units produced internally plus an additional 12,500 units from the foreign supplier. The price impact for customers and the profit impact for Josiah Bartlet & Sons are dramatic. Domestic customer prices and total profits are now calculated as

P = $100 – $0.001(20,000)
   = $80



Josiah Bartlet & Sons’ domestic customers benefit from the increased availability of goods, 20,000 versus 15,000 units, and lower prices, $80 versus $85 per unit. The opportunity to purchase goods at a price of $35 from a foreign supplier benefits the company because profits grow from $250,000 to $343,750. The firm now manufactures only 7,500 of the units sold to customers and has become much more of a distributor than an integrated manufacturer and distributor.

Josiah Bartlet & Sons has been able to make its business and profits grow by focusing efforts on distribution, where it enjoys a comparative advantage.

Competitive External Market with Excess Internal Supply

It is interesting to contrast these results with those achieved under somewhat different circumstances. For example, assume that Josiah Bartlet & Sons is able to sell an unlimited quantity of its goods to a foreign distributor at a price of $80. For simplicity, also assume that sales to this new market have no impact on the firm’s ability to sell to current domestic customers and that this market can be supplied under the same cost conditions as previously. If PT = $80, the quantity demanded by the distribution division is


whereas the quantity supplied by the manufacturing division is


In this instance of excess internal supply, the distribution division will purchase all 5,000 units desired internally, while the manufacturing division will offer an additional 25,000 units to the new foreign distributor. Again, the price impact for customers and the profit impact for Josiah Bartlet & Sons are dramatic. Domestic customer prices and total profits are now as follows:

P = $100 – $0.001(5,000)
   = $95



Under this scenario, Josiah Bartlet & Sons’ domestic market shrinks from an initial 15,000 to 5,000 units, and prices rise somewhat from $85 to $95 per unit. At the same time, foreign customers benefit from the increased availability of goods, 25,000 versus none previously, and the attractive purchase price of $80 per unit. The opportunity to sell at a price of $80 to a foreign distributor has also benefited the company, because profits grew from $250,000 to $625,000.

The company now distributes only 5,000 of 30,000 units sold to customers and has become much more of a manufacturer than a distributor. By emphasizing manufacturing, Josiah Bartlet & Sons makes its business and profits grow by focusing efforts on what it does best.


As this chapter illustrates, economic reasoning is a powerful tool that can be used to understand and improve pricing practices. For example, popular markup pricing methods can be interpreted as an efficient rule-of-thumb approach toward setting profit-maximizing prices.

Similarly, multiple-unit pricing methods, like two-part pricing and bundle pricing, are efficient means for capturing additional profits when the value of goods and services varies from one consumer to another.

Still, it would be misleading to infer that there are no important remaining mysteries in pricing practice. In fact, significant riddles remain. For example, no doubt you have noticed the popularity of what is sometimes called “odd-number pricing.” Prices like $6.99 are much more common than $7; 99¢ is much more commonly employed than $1. You and I both know that 99¢ is much more commonly employed than $1 because buyers feel they are getting a “bargain” for 99¢. A $1 price seems “significantly” more expensive. For buyers, 99¢ often “feels” more than 1¢ cheaper than $1. This we all know. What economists and marketing scholars don’t know is why buyers can be lured by a 99¢ price, and be turned off by a $1 price. Is there some failure in the computational ability of buyers? Does it have something to do with the way the brain processes information? To this point, there is no conclusive answer.

One innovative explanation for the popularity of odd-number pricing is that readers of Latin-based languages like English process written material from left to right. For example, as you read this page, you are processing information from left to right. As a result, the first digit processed when a consumer notes a price of $6.99 is the number six, not the higher number seven, as would be the case with a price of $7. Thus, in the English-speaking world, a price of $6.99 often seems “significantly” less than $7.

This interpretation gains favor when one considers the fact that the popularity of oddnumbered pricing is greatest in the case of goods and services offered in vigorously price competitive environments. For example, most states have regulations governing both the octane content, or quality, of motor car gasoline and the advertising of pump prices. It is a typical requirement that gasoline prices must be prominently displayed so that drivers can easily evaluate prices from curbside as they drive down the street. This makes the retail gasoline market one of the most viciously price competitive of all consumer markets. Just think of the times you have gone out of your way to save 2¢ or 3¢ per gallon, or a total of only 30¢ or 40¢ on a tank of gas. Gasoline customers are notoriously price sensitive, and gasoline retailers know this. Perhaps that is why gasoline retailers use odd-numbered pricing to such an extreme that gas prices are typically expressed in terms of 9/10 of a cent! Can you think of another product you buy regularly where the price charged is expressed in terms of 9/10 of a cent? I can’t. Of course, it is difficult to explain why such pricesensitive gasoline customers will feverishly search for the very best bargain on gasoline and then turn around and spend 99¢ at that same gasoline station on a large ice-filled cup of Coca-Cola! In short, economic reasoning has long proved an effective means for understanding pricing practices and for designing improvements in the pricing practices of individual firms. At the same time, the relevance of input from psychology and other social and physical sciences should not be minimized. The ongoing design of effective pricing practices benefits from knowledge gained in a wide variety of areas.