Pricing of Multiple Products
In a multi-product corporation, production decisions relating to one product may affect the manufacturing or marketing costs of other related products. The product may be interrelated or independent. For example, Pringles and Tide of P and G are independent while Pantene and Head and Shoulders are interrelated. In case of independent products, demand and cost of one product is not influenced by that of the other. Each product will be produced where MR = MC However, pricing of related products requires that demand inter-dependencies should be taken into account.
Products with Interdependent Demand
Related products can be complementary or substitutes. Personal computer and keyboard are complements but two different sizes of PC's of different firms are substitutes. The effect of a change in the price of one product on the demand of the other has to be taken into account. Profit maximisation requires that the output levels and prices of various products produced by the firm be determined jointly.
假设一家公司生产并出售两种产品X和Y，其总收入（即销售）可以表示为
tr = trX= TRYEq 8.1
where TRXand TRYis the revenue from product X and Y, respectively. The marginal revenue (MR) of each product is
MRX= (dTRx/dQx) + (dTRy/dQ) Eq 8.2
MRY=(dTRy/dQy)+(dTRx/dQy)Eq 8.3
dtrX/ DQXrepresents a change in revenue for good X resulting from a unit increase in sales of X. While dTRY/ DQXreflects a change in revenue from the sale of good X. caused by a one unit increase in sales of good X (the demand interdependency). Similar interpretation can be made for the second equation. If the two goods are complements, this effect will be positive, since an increase in the quantity sold of one product will increase the total revenue from the other product. On the other hand, if products X and Yare substitutes, this effect will be negative, since an increase in the quantity sold of one product will reduce the total revenue from the other product. Thus, proper attention should be given to demand inter relationships among the products a firm sells. If two goods are complements profit maximisation requires greater role of output for product X. In fact, output of X should be increased until
dtrx/dQx + dTry/dQx= Mcx
where MCXis the additional cost incurred by the firm in producing an additional unit of product X. Similarly, for goods that are substitutes, it can be easily shown that ignoring demand interdependency will cause too many units of output' to be produced.
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