Market structure and organizational form.

• Author: Zhou, Haiwen

1. Introduction

   Two kinds of organizational forms have been studied extensively in the literature: the unitary organizational form (U-form) and the multidivisional organizational form (M-form). (1) A U-form firm is organized by functions, such as production and marketing. The Ford Motor Company before World War II was an example of the U-form firm. An M-form firm is organized by products and each product has its own production and sales divisions. An example of an M-form firm is the General Motors Company. As firms frequently engage in costly reshuffling of their structure, one interesting thing to know is what determines a firm's choice of organizational form.

   This article studies how market structure affects a firm's choice between the U-form and the M-form organizational forms. Market structure refers specifically to the number of firms in the industry and how market demand for different products may be related. Each firm produces two products. To produce each product, both production and marketing activities are needed. In a U-form organization, there is a middle manager of production and a middle manager for marketing. Each functional manager maximizes his or her division's profit. In an M-form organization, there is a middle manager for each product. Each product manager maximizes his or her product division's profit. Firms are assumed to engage in Cournot competition.

   Each organizational form has its own advantages and disadvantages. In a U-form firm, demand externalities between different products are taken into consideration. However, a U-form firm may suffer from double marginalization because the middle manager of production chooses transfer prices to maximize the production division's profit. An M-form firm eliminates double marginalization. On the other hand, a product manager in an M-form firm may be only concerned with the profit of the product she supervises, ignoring the fact that market demand for different goods are interdependent.

   In this article, we show that a firm's optimal choice of organizational form depends on the number of firms in the industry and whether goods are substitutes or complements. As firms face the same price, a firm has a higher profit if and only if it has a higher output. Whether a U-form or an Mform firm has a higher output depends on whether the two products are substitutes or complements. When the two products are substitutes, it is shown that adopting the M-form organizational mode gives a firm higher profit than adopting the U-form organizational mode. When there are multiple firms in the industry, the overexpansion of output of an M-form firm is beneficial to this firm as this expansion makes other firms in the industry less aggressive. In contrast, the U-form firm's output is too low, but it is a positive externality to other firms. As a result, an M-form firm makes a higher profit than a U-form firm when there are multiple firms in the industry. In this sense, the economics is similar to that of Fershtman and Judd (1987), except that the choice of organizational form is probably a far more credible commitment than the contractual commitments considered in their paper. (2) When products are strong complements, the U-form firm has a higher output and profit because the demand externalities are taken into consideration. As the number of firms in the industry increases, whether the difference of output increases or not. depends on whether the slope of the U-form firm's reaction curve is larger or smaller than that of an M-form firm.

   Two issues merit some explanation. The first issue is that neither the U-form nor the M-form organizational mode may be optimal. Even if this is the case, a study of the choice between the U-form and the M-form organizational mode can still be justified. One reason is that the optimal organizational form may be too complex to be implemented in real-world situations. As the U-form and the M-form organizations are commonly observed in real-world situations, there is some merit in understanding the advantages and disadvantages of adopting these organizational forms. The second issue is that one may wonder whether a U-form firm suffers from double marginalization or not. In real-world situations, double marginalization is frequently observed. How to decide transfer prices between different functional departments is not a trivial issue in a large organization. (3) Based on survey data, Eccles and White (1988) find that mandated market-based transfer pricing is one of the three kinds of transfer-pricing policies commonly used by firms. (4) When a firm adopts this kind of pricing policy, internal transactions are valued at market prices. "Buying profit centers that pay market price commonly complain that the intermediate good is being 'marked up twice', once by the selling profit center and again by the buying profit center" (Eccles and White 1988, p. $31). Eccles and White (1988) record a case in which the transfer price of an intermediate input is twice the production cost of that input.

   For the literature on organizational forms, see Holmstrom and Tirole (1991), Aghion and Tirole (1995), Maskin, Qian, and Xu (2000), and Qian, Roland, and Xu (2002). The approach of modeling organizational forms used in this article is similar to that of Aghion and Tirole (1995). In their paper, a firm produces two products and each product needs production and marketing activities. A U-form organizational form is organized into the production department and the marketing department. An M-form organizational firm is organized by products. None of the above papers studies how a firm's choice of organizational form is affected by the market structure. However, market structure, such as the number of firms in the industry and how market demand for different products is related, provides the basic environment in which firms operate. As a firm's marginal benefit and marginal cost are affected by market structure, a firm's optimal choice of organizational form is affected by market structure. In fact, the influence of market structure on a firm's behavior is well recognized in the literature. For example, Fershtman and Judd (1987) show that a firm's choice of incentive scheme depends on market structure. When a firm is a monopolist in an industry, owners of this firm will try to get the managers to maximize profit. When a firm is one of multiple firms in the industry, owners will provide incentives to managers to expand output to take advantage of the strategic interaction among firms.

   The rest of the article is organized as follows. Section 2 sets up the model and compares the equilibrium output and profit of the two organizational forms. In section 3, equilibrium organizational forms are studied. Section 4 studies the special case of linear market demand. Section 5 discusses some assumptions of this article and concludes.

2. The Model

   There are n firms in an industry, n [greater than or equal to] 1. For all these n firms, suppose m of them adopt the U-form and n - m of them adopt the M-form organizational mode. Each firm produces two products, i and j. Producing each product requires two activities, production and marketing. How activities are organized depends on the decision of the top manager of a firm. There are three levels of managers in each firm: top-, middle-, and low-level managers. The top manager of a firm chooses which organizational form to adopt. If a top manager chooses the M-form for each of the two products, the production stage and the marketing stage will be supervised by the same middle manager. The two middle managers in an M-form firm will be called the middle manager for product i and the middle manager for product j. If the top manager chooses the U-form, one middle manager will supervise the two production departments and the other middle manager will supervise the two marketing departments. The two middle managers in a U-form firm will be called the middle manager for production and the middle manager for marketing. Middle managers choose quantities of production. A low-level manager follows the instruction of a middle manager on how much to produce.

   All firms have the same fixed and marginal costs of production. The fixed cost of production is f. Let the constant marginal cost of production be denoted by c. The marginal cost of marketing is also assumed to be constant and is normalized to zero.

   When multiple firms produce the same product, they engage in Cournot competition. For x, y = i, j, and x [not equal to] y, let [p.sup.x] denote the price of product x. Let [Q.sup.x] denote total industry output of product x. Market demand for product x is given by an inverse demand function,

   (1) [p.sup.x] = [p.sup.x]([Q.sup.x], [Q.sup.x]), x,y = i,j, and x [not equal to] y.

   Let a and b be positive constants. A special case of Equation 1 is given by

   (2) [p.sup.x] = a - b[Q.sup.x] - d[Q.sup.y], x,y = i,j, and x [not equal to] y.

   It is assumed that the inverse demand functions are symmetric with respect to the two products. As a result,

   [differential][p.sup.x]([Q.sup.x], [Q.sup.x])/[differential][Q.sup.y] = [differential][p.sup.y] ([Q.sup.y],[Q.sup.x])/[differential][Q.sup.x]

   for all [Q.sup.x] and [Q.sup.y].

   Whether the two products are complements or substitutes depends on the sign of [differential][p.sup.x]([Q.sup.x], [Q.sup.y])/[differential][Q.sup.y]. If [differential][p.sup.x](Q.sup.x], [Q,sup.y])/[differential][Q.sup.y] 0, the two products are complements; if [differential][p.sup.x]([Q.sup.x] [Q.sup.y])/[differential][Q.sup.y] = 0, the market demand of the two goods is independent. If [differential][p.sup.x]([Q.sup.x] [Q.sup.y]) = [differential]([Q.sup.x], [Q.sup.y])/[differential][Q.sup.x], the two products are perfect substitutes.

   The following assumptions about the inverse demand functions are made.

   ASSUMPTION 1.

   [differential][p.sup.x]([Q.sup.x], [Q.sup.y]/[differential][Q.sup.x]

   ASSUMPTION 2.

   [absolute value of...