Multi product pricing

managerial economics- pricing practices

1. Jyothi s, Assistant Professor, GFGCW, Holenarasipura . ARTHADHARE

2. PRICING PRACTICES Product or Multi Product Pricing Jyothi s, Assistant Professor, GFGCW, Holenarasipura .

3. INTRODUCTION: Most modern firms produce a variety of products rather than a single product. The products sold by a firm may be interrelated as substitutes or complements. Generally, organizations produce more than one product in their line of production.Even a single product of an organization can differ in styles and sizes.

4. Meaning: For example , a refrigerator manufacturing organization produces refrigerators in different colours, sizes, and features. Similarly , an automobile organization manufactures vehicles in different colours, sizes, and mileage. The pricing in case of multiple products is called multiple product pricing.

5. Pricing of Products with Interrelated Demands : In the pricing of interrelated products, a firm needs to consider the effect of a change in the price of one of its products on the demand for the others. The reason for this is that a reduction in the price of a product leads to a reduction in the demand for a substitute product sold by the same firm, and to an increase in the demand for complementary products.

6. Thus, profit maximization requires that the output levels and prices of the various products produced by the firm be determined jointly rather than independently.

7. For a two-product (A and B) firm, the marginal revenue functions of the firm are:

8. From the two equations above, we see that the marginal revenue for each product has two components, one associated with the change in the total revenue from the sale of the product itself , and the other associated with the change in the total revenue from the other product.

9. The second term on the right-hand side of each equation , thus, reflects the demand interrelationships. For example : the term ( ) in equation 1 measures the effect on the firm’s revenues from product B resulting from the sale of an additional unit of product A by the firm.  

10. Similarly, ( ) in equation 2 measures the effect on the firm’s total revenue from product A resulting from the sale of an additional unit of product B by the firm.  

11. If the second term on the right-hand side of each equation is positive , indicating that increased sales of one product stimulates sales of the other, the two products are complementary. If, on the other hand, second term in each equation is negative , indicating that increased sales of one product leads to reduced sales of the other, the two products are substitutes.

12. Plant Capacity Utilisation: A multi-product firm using a single plant should produce quantities where the marginal revenue ( MR i ) from each of its k products is equal to the marginal cost (MC) of production.

13. The quantity produced of the more profitable products is then determined by the point at which their marginal revenue equals the marginal revenue and marginal cost of the last unit of the least profitable product produced by the firm . The price of each product is then determined on its respective demand curve. This process is shown in figure 1 .

14. Optimal outputs and Prices of Multiple Products by a firm:

15. Figure 1 shows the situation of a firm selling three products(A, B, and C) with respective demand curves D A , D B , and D C , and corresponding revenue curves MR A , MR B , and MR C . The firm maximizes profits when MR A =MR B = MR C =MC . This is shown by points E A , E B , and E C , where the equal marginal revenue curve, at the level at which MR c =MC, crosses the MR A , MR B , and MR C curves .

16. Thus, Q A =60 and P A =₹16; Q B =90 (from 150-60) and P B =₹15; and Q C =180 (from 330-150) and P C =₹14. Note that each successive demand curve is more elastic and that the price of each successive product is lower , while its MC is higher.

17. Optimal Pricing of Joint Products Produced in Fixed proportions: The products produced by a firm can be related not only in demand but also in production. Production interdependenc e arises when products are jointly produced . Products can be jointly produced in fixed or variable proportions. An example of joint production with variable proportions is provided by petroleum refining, which results in gasoline, fuel oils etc…

18. Joint Products in Fixed Proportions:

19. In both panels, D A and MR A, and D B and MR B refer, respectively, to the demand and marginal revenue curves for products A and B, which are jointly produced in fixed proportions. The total marginal revenue (MR T ) curve is obtained from the vertical summation of the MR A and MR B curves .

20. When the marginal cost of the jointly produced production package is MC (see the left panel ), the best level of output of products A and B is 40 units and is given by point E, at which MR T =MC. At Q=40,P A = ₹12 on D A and P B = ₹5 on D B .

21. on the other hand, with MC’ (see the right panel), the best level of output of the joint product package is 60 units and is given by point E’, at which MR T =MC’. Q=60,P’ A = ₹10 on D’ A , but since MR B is negative for Q B >45, the firm sells only 45 units of product B at P B ’=₹4.50 (at which TR B is maximum at MR B =0) and disposes of the remaining 15 units of product B.

22. Optimal Pricing and Output of Joint Products Produced in Variable Proportions: The case of products that are produced jointly in fixed proportions is possible, more common is the case of products that are jointly produced in variable proportions. We can determine the profit-maximizing combination of products that are jointly produced in variable proportions with the aid of figure 3.

23. . Pricing of Multiple Products

24. The curved lines are product transformation curves showing the various combinations of products A and B that the firm can produce at each level of total cost (TC). The curvature arises because the firm’s productive resources are not perfectly adaptable in the production of products A and B that give rise to the same total revenue (TR) to the firm when sold at constant prices .

25. The tangency point of an isorevenue to a TC curve gives the combination of products A and B that leads to the maximum profit for the firm for the specific TC . The overall maximum profit of the firm is = ₹40 . this is earned by producing and selling 80A and 120B with TR=₹240 and TC=₹200 .

26. References: Managerial Economics, principles and worldwide applications, eighth edition(2019) , Dominick salvatore , siddhartha K.Rastogi . Modern Microeconomics,second edition(2017) A.Koutsoyiannis . Advanced economic theory: Microeconomic analysis, Nineteenth edition, H.L.Ahuja . Various Online sources.