Chapter 11
Pricing Practices
11.1PRICING OF MULTIPLE PRODUCTS
WITH INTERDEPENDENT DEMANDS
Optimal pricing and output decisions by a multiproduct firm require that the firm consider demand and production interrelationships. Demand interrelationships (substitutability and complementarity) among the products that the firm produces are reflected in the marginal revenue functions. For a two-product (A and B) firm the marginal revenue (MR) functions of the firm are:
(11-1)
(11-2)
where TR is total revenue and Q is the quantity of output. The second term in equations (11-1)and (11-2)is positive if products A and B are complements, and negative if A and B are substitutes (see Problem 11.1).
Firms produce more than one product in order to make fuller use of their plant and production capacities. The firm will introduce new products (or different varieties of existing products) in order of their profitability until MRA = MRB = MRC , where product C is the least profitable product. Prices PA,PB,and PCare then determined from their respective demand curves (see Problem 11.2).
11.2PRICING AND OUTPUTS OF JOINTLY PRODUCED PRODUCTS
When products are jointly produced in fixed proportions, there is no rational way of allocating the cost of producing the entire “production package” to the individual products in the package. The best level of output will then be at the point at which the total marginal revenue, MRT (obtained by vertically summing the marginal revenue curves of all the jointly produced products) equals the marginal cost (MC) of the joint production package. Prices are then determined from the demand curves of the respective products. A firm will not, however, sell any unit of a jointly produced product for which the marginal revenue is negative (see Example 1).
The optimal output of products that are jointly produced in variable proportions is given at the tangency point of the isorevenue (i.e., equal revenue) line and the product transformation (or total cost) curve that leads to the overall maximum profits for the firm (see Problems 11.6 and 11.7).
EXAMPLE 1.In both parts of Fig. 11-1, DAand MRA and DBand MRB refer, respectively, to the demand and marginal revenue curves of products A and B, which are jointly produced in fixed proportions. Products A and B can be thought of as beef and hides, which are produced in the ratio of one-to-one in slaughtering each cow. The total marginal revenue (MRT) curve is obtained from the vertical summation of the MRA and MRBcurves because the firm receives marginal revenues from the sale of both products. Note that for Q > 45, for which MRB < 0, MRT = MRA. When the marginal cost of the jointly produced package is MC [see Fig. 11-1(a)], the best level of output is 40 units and is given by point E,at which MRT= MC. At Q = 40,
PA = $11 on DAand PB = $5 on DB.However, with MC' [see Fig. 11-1(b)], the best level of output of the production package is 60 units (given by point E', at which
MRT = MC'). At Q = 60, PA'= $9 on DA,but since MRB < 0 for Q> 45, the firm sells only 45 units of product B at PB' = $4.50 (for which TRBis the maximum and
MRB= 0) and disposes of (i.e., keeps off the market) the remaining 15 units of product B.
Fig. 11-1
11.3PRICE DISCRIMINATION
Price discrimination refers to the charging of different prices for different quantities of a product, at different times, to different customer groups, or in different markets, when these price differences are not justified by cost differences. Three conditions must be met for a firm to be able to practice price discrimination: (1) the firm must have some market power, (2) the price elasticities of demand for the product in different markets must differ, and (3) the markets must be separable or be able to be segmented. First-degree price discrimination involves selling each unit of the product separately and charging the highest price possible for each unit sold. By practicing first-degree price discrimination, the firm can extract from consumers all of the consumers’ surplus (the difference between what consumers are willing to pay for a product and what they actually pay for it). Second-degree price discrimination refers to the charging of a uniform price per unit for a specific quantity or block of the product, a lower price per unit for an additional quantity or block of the product, and so on. By doing this, the firm can extract part, but not all, of the consumers’ surplus (see Problem 11.9). Third-degree price discrimination refers to the charging of different prices for the same product in different markets until the marginal revenue of the last unit of the product sold in each market equals the marginal cost of the product. This involves selling the product at a higher price in the market with the less elastic demand (see Example 2).
EXAMPLE 2.Figure 11-2 shows third-degree price discrimination by a firm that sells a product in two different markets. Figure 11-2(a) shows D1and MR1 (the demand and marginal revenue curves faced by the firm in market 1), part (b)shows D2and MR2, and part (c)shows D and MR (the total demand and marginal revenue curves for the two markets combined). D = D1+2 , and MR = MR1+2 , by horizontal summation. The best level of output of the firm is 90 units and is given by point E in part (c),at which MR = MC = $2. The firm sells 50units of the product in market 1 and 40 units in market 2, 50 that MR1 = MR2 = MR = MC = $2 (see points E1, E2,and E).For Q1 = 50, P1= $7 (on D1)in market 1, and for Q2 = 40, P2= $4 (on D2)in market 2. With an average total cost of $3 per unit for Q = 90, the firm earns a profit of $4 per unit and $200 in total in market 1, and $1 per unit and $40 in total in market 2, for an overall total profit of $240 in both markets. In the absence of price discrimination, Q = 90, P = $5[see part (c)],so that profits are $2 per unit and $180 in total.
Fig. 11-2
11.4TRANSFER PRICING
The rapid rise of the modern large-scale enterprise has been accompanied by decentralization and the establishment of semiautonomous profit centers in order to contain rising communication and organizational costs. This also gave rise to the need for transfer pricing,or the need to determine the price of intermediate products produced by one semiautonomous division of the firm and sold to another semiautonomous division of the same firm. Appropriate transfer pricing is essential in determining the optimal output of each division and of the firm as a whole, in evaluating divisional performance, and in determining divisional rewards. For simplicity, we assume here that the firm has only two divisions-a production division and a marketing division-and that one unit of the intermediate product is required to produce each unit of the final product.
In the absence of an external market for the intermediate product, the transfer price for the intermediate product is given by the marginal cost of the production division at the best level of output of the intermediate product (see Example 3). When a perfectly competitive external market for the intermediate product exists, the transfer price is given by the external competitive price of the intermediate product (see Example 4). When an imperfectly competitive external market exists for the intermediate product, the product’s (internal) transfer price is given at its best total level of output at which the net marginal revenue of the marketing division equals the marginal cost of the production division; the price on the external market is given on the external demand curve (see Problem 11.16).
EXAMPLE 3.In Fig. 11-3, the marginal cost of the firm (MC) is equal to the vertical summation of MCp and MCm the marginal cost curves of the firm’s production and marketing divisions, respectively. Dmis the external demand for the final product faced by the firm’s marketing division, and MRm is the corresponding marginal revenue curve. The firm’s best level of output of the final product is 30 units and is given by point Em ,at which MRm = MC, so that Pm = $9. Since the production of each unit of the final product requires one unit of the intermediate product, the transfer price for the intermediate product, Pt is set equal to MCp at
Q = 30. Thus, Pt = $4. Since the intermediate-product demand and marginal revenue curves faced by the firm’s production division equal Dpand MCp (i.e., with
Dp= MRp = Pt = MCp = $4) at Qp = 30 (see point Ep), Qp = 30 is the best level of output of the intermediate product for the production division.
Fig. 11-3
EXAMPLE 4.Figure 11-4 is identical to Fig. 11-3, except that MCp' is lower than MCp. At the perfectly competitive external price of Pt= $4 for the intermediate product, the production division of the firm faces Dp = MRp= Pt = $4. Therefore, the best level of output of the intermediate product is at Q = 40 and is given by point Ep'.at which Dp= MRp = Pt = MCp' = $4. Since the marketing division can purchase the intermediate product (internally or externally) at Pt= $4, the division’s total marginal cost curve, MCt , is equal to the vertical summation of its own marginal cost of assembling and marketing the product (MCm) and the price of the intermediate product (Pt).Thus, the best level of output of the final product by the marketing division is 30 units and is given by point Em , at which MRm = MCt , so that Pm= $9 (as in Fig. 11-3).
Fig. 11-4
11.5PRICING IN PRACTICE
Because it may be too expensive or impossible to collect precise marginal revenue and marginal cost data, most firms use cost-plus pricing.This involves calculating the average variable cost of producing the normal or standard level of output (usually between 70 percent and 80 percent of capacity), adding an average overhead charge so as to get the fully allocated average cost for the product, and then adding to this a markup on cost for profit. The markup-on-cost formula is
(11-3)
where m is the markup on cost, P is the product price, C is the fully allocated average cost of the product, and P – C is the profit margin.Solving equation (11-3)for P,we get the price of the product in a cost-plus pricing scheme. That is,
(11-4)
Cost-plus pricing has some important advantages and disadvantages (see Problem 11.18) but in view of its widespread use, the advantages must clearly outweigh the disadvantages. Since firms usually apply higher markups to products facing a less elastic demand than to products with a more elastic demand, cost-plus pricing can be shown to lead to approximately the profit-maximizing price (see Problem 11.19). However, correct pricing and output decisions by a firm involve incremental analysis,which should lead a firm to undertake a particular course of action only if the incremental revenue from the action exceeds the incremental cost (see Problem 11.20).
EXAMPLE 5.Suppose that a firm considers 80 percent of its capacity output of 125 units as the normal or standard output, that it projects total variable and total overhead costs for the year to be, respectively, $1,000 and $600, and that it wants to apply a 25 percent markup on costs. Then the normal or standard output of the firm is 100 units, AVC = $10, and the average overhead cost is $6. Thus, C= $16 and
P = 16(1 + 0.25) = $20, with m = ($20 – $16) / $16 = 0.25
Glossary
Consumers’ surplusThe difference between what consumers are willing to pay for a specific quantity of a product and what they actually pay.
Cost-plus pricingThe most common pricing practice by firms today, whereby a markup is added to the fully allocated average cost of the product.
Demand interrelationshipsThe relationship of substitutability or complementarity among the products produced by the firm.
First-degree price discriminationThe selling of each unit of product separately and charging the highest price possible for each unit sold.
Fully allocated average costThe sum of the average variable cost of producing the normal or standard level of output plus an average overhead charge.
Incremental analysisComparison of incremental revenue with incremental cost in managerial decision making.
Markup on costThe ratio of the profit margin to the fully allocated average cost of the product.
Price discriminationThe practice of charging different prices for different quantities of a product, at different times, to different customer groups, or in different markets, when these price differences are not justified by cost differences.
Profit marginThe difference between the price and the fully allocated average cost of the product.
Second-degree price discriminationThe charging of a uniform price per unit for a specific quantity or block of a product, a lower price per unit for an additional batch or block of the product, and so on.
Third-degree price discriminationThe charging of different prices for the same product in different markets until the marginal revenue of the last unit of the product sold in each market equals the marginal cost of the product.
Transfer pricingThe determination of the price of intermediate products sold by one semiautonomous division of a firm to another semiautonomous division of the same enterprise.
Review Questions
1.If a firm produces products A and B and TRB/ QAand TRA/ QB are negative, products A and B are
(a)complements.
(b)substitutes.
(c)independent.
(d)any of the above.
Ans.(b) See Section 11.1.
2.Which of the following statements is false?
(a)Firms produce multiple products in order to make fuller use of the production facilities.
(b)Firms usually introduce products in the order of their profitability.
(c)Successive products introduced by a firm are sold at higher prices and produced at lower marginal costs than previous products.
(d)To maximize profits a firm should produce the output level at which
MRA = MRB = MRC , where product C is the least profitable product.
Ans.(c)See Section 11.1.
3.For a firm producing products jointly in fixed proportions that are unrelated in consumption,
(a)it is impossible to rationally allocate the total cost of producing the package to the individual products in the package.
(b)the total marginal revenue curve for the two products is obtained by horizontally summing the marginal revenue curves of the jointly produced products.
(c)the firm sells a jointly produced product only if its MR < 0.
(d)all of the above.
Ans.(a)See Section 11.2 and Example 1.
4.A firm producing products jointly in fixed proportions
(a)may produce some units of the product for which MR is negative.
(b)will not sell any units of the product for which MR is negative.
(c)will receive revenues from the sale of each jointly produced product.
(d)all of the above.
Ans.(d)See Section 11.2 and Example 1.
5.When products are produced in variable proportions, they are
(a)complementary in production.
(b)substitutes in production.
(c)always interdependent in demand.
(d)all of the above.
Ans.(b)See Section 11.2 and Problems 11.6 and 11.7.
6.Which of the following is not an example of price discrimination?
(a)Lower prices for bulk than for small purchases because of cost savings to the firm in handling large orders
(b)Lower electricity charges to commercial than to residential users
(c)Lower medical fees for lower-income than for higher-income people
(d)Lower fares on public transportation for children and the elderly
Ans.(a) See Section 11.3.
7.Which of the following conditions is required for a firm to be able to practice price discrimination?
(a)The firm must have some control over price.
(b)The price elasticity of demand for the product must be different in different markets.
(c)The markets must be separable.
(d)All of the above.
Ans.(d)See Section 11.3.
8.Third-degree price discrimination refers to the charging of different prices (not justified by cost differences)
(a)for each unit of the product.
(b)for different batches of the product.
(c)in different markets.
(d)all of the above.
Ans.(c)See Section 11.3.
9.Which of the following statements is false?
(a)The rapid rise of the modern large-scale corporation has been accompanied by decentralization and the establishment of semiautonomous profit centers.
(b)Decentralization and the establishment of semiautonomous profit centers in modern large-scale enterprises have led to the need for transfer pricing.
(c)Transfer pricing refers to the determination of the price of intermediate products produced by one semiautonomous division of the firm and sold to another semiautonomous division of the same firm.
(d)None of the above.
Ans.(d)See Section 11.4.
10.When there is no external market for an intermediate product, its transfer price is given by the
(a)marginal cost of the marketing division.
(b)marginal cost of the production division.
(c)marginal revenue of the marketing division.
(d)price of the final product.
Ans.(b)See Section 11.4.
11.When an external perfectly competitive market for an intermediate product exists, the quantity of the intermediate product produced by the production division in relation to the quantity produced of the final product by the marketing division of the firm is
(a)larger.
(b)smaller.
(c)equal.
(d)any of the above.
Ans.(d)See Section 11.4 and Example 4.
12.Which of the following statements is false with regard to cost-plus pricing?
(a)It is the most prevalent pricing method used by business firms.
(b)It involves adding a markup or profit margin to the fully allocated average cost to determine the price of the product.
(c)It is a form of incremental cost pricing.
(d)It completely disregards demand conditions in actual real-world applications.
Ans.(c)See Section 11.5.
Solved Problems
PRICING OF MULIIPLE PRODUCTS WITH INTERDEPENDENT DEMANDS
11.1(a) What is meant by demand interrelationships for a multiproduct firm? (b)How are demand interrelationships measured? (c)Why must a multiproduct firm take into consideration demand interrelationships in its pricing and output decisions?
(a)Demand interrelationships refer to the substitutability and complementarity relationships that exist among the products produced by a firm.
(b)Demand interrelationships are measured by the cross-marginal revenue effects in the marginal revenue function for each product sold by the firm. For a two-product (A and B) firm, the MRA function includes a TRB/ QA term and the MRB function includes a TRA/ QB term, which measure demand interrelation-ships. Products A and B are complements if the terms TRB/ QA and TRA/ QB are positive and substitutes if these cross-marginal revenue effects are negative.