Transfer Pricing with Technology Choice and Demand Fluctuations in a Simple Manufacturing Model
Aranoff, Gerald, Quarterly Journal of Business and Economics
This paper shows optimal (marginal-cost) transfer pricing with technology choice (K/L) and demand fluctuations (off-peak/peak) in a simple manufacturing model [Technology.sub.K] is making major components or use of new or capital-intensive technology. [Technology.sub.L] is buying major components or use of old or labor-intensive technology. We demonstrate graphically, mathematically, and numerically that with [Technology.sub.L] available to the manufacturing division to provide the excess off-peak over off-peak demand, then the optimal transfer price in [t.sub.2] is far lower than if only [Technology.sub.K] were available. This should make marginal-cost peak-load transfer pricing more tolerable to corporation managers. Further, not only [P.sub.2] becomes lower, but [Q.sub.2] becomes higher. The firm is producing more than if only [Technology.sub.K] were available (under negatively-sloped-demand schedules facing the firm). This has macroeconomic implications in aiding economic growth and increasing the sustain ability of economic upturns.
This paper shows transfer pricing with technology choice and demand fluctuations in a simple manufacturing model. No one has done this before. Our model is that of Hirshleifer as presented by a modern managerial economics text (Salvatore, 1989, p. 525). We incorporate features of our previous work on technology choice in a setting of competitive manufacturing.
Transfer prices are the prices that units of a company charge each other for goods or services. Transfer prices in this analysis have no direct effect on a company's consolidated financial statements because intracompany profits and losses are eliminated in consolidation. Further, we assume no tax considerations and no control frictions. Transfer prices can indirectly affect corporate profits if they affect management's decisions on how and what to manufacture and how to price the final goods. It is this indirect impact this article addresses. This is a theoretical paper that highlights implications for policy and for empirical analysis.
Consider a firm with two divisions: a manufacturing division, A, that sells an intermediate product to a marketing division, B. Division A has two ways to manufacture the product: using [technology.sub.K] a capital-intensive method (new machines or making components) or using [technology.sub.L] a labor-intensive method (old machines or buying components) or a combination. [Technology.sub.K] is output rigid and [technology.sub.L] is output flexible because [technology.sub.L] can handle changes in output rates more economically. Each technology is the common cost accounting model of linear total costs and capacity limits. Demand for the final product fluctuates between low demand with [w.sub.1] frequency and high demand with [w.sub.2] frequency.
We demonstrate graphically, mathematically, and numerically that the optimal transfer pricing is that [P.sub.1] must lie between the unit variable costs of the two technologies and [P.sub.2] must equal what would occur if A used the old or labor-intensive method exclusively in both periods. This argues for flexible transfer pricing: low in low demand times and high in high-demand times. Our new insight is that where managers can use [technology.sub.L], to supply the increment of peak over off-peak demand, then [P.sub.2] becomes dramatically decreased and the swing off-peak versus peak optimal prices becomes muted, compared with only [technology.sub.K] available. This should make marginal-cost peak-load pricing more understandable and tolerable to corporation managers.
Not only does [P.sub.2] become lower with diverse technology available to division A, but also [Q.sub.2] becomes higher. The firm is producing more than it would if only [technology.sub.K] were available (under negatively-sloped demand schedules facing the firm). This suggests a profound advantage to having [technology.sub.L], available in a manufacturing division to meet peak demands--the firm's output becomes higher in peak demand times. …