Economy of scope, added value chain and cost dynamics: A tentative optimization model

Abstract

The added value chain model shows how products flow through successive design, manufacturing and distribution activities: the added value steps [1]. In firms with related product strategies some of these added value steps may be shared across various product lines [2]. Others may be specific to one product line. The economy of scope concept describes how a firm may enjoy synergies among its products sharing expertise and experience accumulated on cross-sectional activities. Although the economy of scope concept has been widely developed over the years, more has to be done to provide an explicit model of the phenomenon. This paper first presents an illustration of the concept of ‘shared activity’. It stresses that activities embody the real technological core of a firm. An organization's expertise, its real accumulated experience, are embedded in its various cross-sectional activities where competitive advantages are built and defended. The paper then develops an optimization model that evaluates the impact on cost of activities shared among product lines. It builds upon the added value chain model. It further assumes a cost/production relationhship which may or may not be that given by the experience curve, i.e. cost decreases as a function of the accumulated volume of production. The model leads to selecting out the products that bring a global negative financial contribution to the firm. However, it shows that some money-losing product lines should be kept alive since the decrease in cost they generate on related products through shared activities actually increases the margins of these related products. The direct loss on the one side is then more than balanced by the indirect economy on the other side. The optimization model is presented both under monopoly and pure competition conditions. It leads to the well-known ‘bang-bang’ solutions: either stopping the product line totally or keeping the output at maximum sellable volumes. However, the test for keeping a product alive or not is no longer a simple cost/price comparison. The model shows that the test should be modified to include a ‘shared cost’ that explicitly takes into account the ‘shared economy’ that each product will induce on related products. Under simple assumptions, analytical expressions for both the shared cost and the shared economy are provided. The model presented thus explicitly shows why in related product situations the economy of scope concept may suggest the advantage of keeping some products that at first may be regarded as money losers.