Thought Experiment Transfer Pricing Alternatives in Corporation under Demand Fluctuations

The object of this study is to compare numerical results for a hypothetical numerical model comparing transfer pricing alternatives of a multi-division corporation selling cement facing demand fluctuations, prosperity versus depression, with two alternate technologies, high fixed cost versus low fixed costs. The transfer pricing alternatives: A) short-run marginal cost pricing high price volatility over the business cycle versus B) John M. Clark’s workable competition pricing low price volatility over the business cycle. The article is a thought experiment in economics, carried out only in the imagination. The article presents a detailed numerical model of a two-division corporation having a manufacturing division that produces cement and a marketing division that sells cement from the manufacturing division. In the model cement manufacturing plants have linear total cost functions with absolute capacity restrictions. The article considers two alternative technologies: 1) plant L old plants with low fixed costs but high marginal costs and 2) plant K new plants with high fixed costs and low marginal costs. In opposition to marginal cost theory, this study argues in support of John M. Clark (1884-1963) workable competition theory. The study assumes frequency of off periods 6/7 and frequency of peak periods 1/7. The study claims, under the assumptions of the model, workable competition transfer pricing B adds to consumer surplus and to corporate profits over the cycle in comparison to marginal cost pricing A because the gains in consumer surplus in peak demand times 1/7 frequency with more output and lower prices will outweigh the loss in consumer surplus and to corporate profits in off-peak times 6/7 with higher prices and lower output. The gains in prosperity times, though infrequent 1/7, are large, especially with relatively elastic demand curves. The loss in depression times, though frequent 6/7 are


John M. Clark: Overhead Costs and the Business Cycle
The fundamental challenges of the economic cycle, according to John M. Clark , are due to the dominance of fixed costs that are incurred regardless of output rates. According to Clark (1923), overcapacity is typical and expected for the vast majority of the time (Clark, 1923: pp. 437-439): "What governs the supply of productive capacity in an industry? The usual answer is that it adjusts itself to the demand by the construction of additional facilities whenever producers see a profit of marketing their output at a profit. This, it is natural to assume, will not happen until there is demand in sight sufficient to utilize all the existing capacity at a profitable price. But the thing is not quite so simple as this, and will repay a more detailed analysis. In the first place, owing to the forces already studied in connection with the business cycle, plant capacity is governed far more by the peak demand than by the minimum or the average. If this were not true, and if business did not build for the peak at the time of the upswing, one of the chief causes of business cycle would disappear. This very building for the peak, timed as it is, tends powerfully to increase the height of the peak itself. …To sum up, it appears that there are strong forces at work which tend naturally to produce an oversupply of permanent capital, and there are decided indications that such as oversupply exists." Fluctuations in demand for agriculture, raw materials, and manufacturing intermediate products are far more intense than fluctuations in demand for final goods and services. This is due to economic reasons that Clark explains well 1 : "The demand for means of production fluctuate more violently than that for finished consumers' goods, and also appears to fluctuate sooner, taking the lead in a way which would suggest that its changes are a cause, rather than an effect, of the changes in consumers' demand. In point of fact they are both effect and cause, as we shall see in a moment. Something similar is true of raw materials as compared to finished goods, while wholesale prices fluctuate more than retail." Clark is a business-cycle economist. Clark writes (Clark, 1934: p. 3): "The reader should be warned at the start that this study is not exclusively or mainly devoted to the current depression, but is a study of business cycles in general, as they have been experienced during the period for which

Research Structure
This study compares numerical results for a hypothetical mathematical model of a corporation selling cement facing demand fluctuations, prosperity and depression. The corporation has a manufacturing division that produces cement and sells its output entirely to a marketing division that sells cement it buys only from the manufacturing division to the construction industry. Each division is a responsibility center. This study compares two transfer pricing alternatives, short-run marginal cost pricing and John M. Clark's workable competition pricing each with two alternate technologies, high fixed cost and low fixed costs.  (Aranoff, 1995: p. 1):

Transfer Pricing: Peak-Load Pricing Problem
"The writer contends that the transfer pricing problem in pricing goods or services from one division to another within a corporation, as many people understand the term, is in reality another form of the peak-load problem." Transfer pricing is an important topic in cost accounting texts (Polimeni et al., 1986: p. 973).
"Transfer pricing has become one of the most important and sometimes most controversial elements in performance measurement."

Transfer Pricing Alternatives: SRMC v WC Pricing
Transfer pricing alternative short-run marginal cost pricing means setting the transfer price at exactly the short-run cost of manufacturing cement, the intermediate product. In depression times the manufacturing division shows $0 contribution margin.
Transfer pricing alternative John M. Clark's workable competition pricing means setting the transfer price in depression times slightly above short-run marginal costs of manufacturing cement. In depression times the manufacturing division shows a positive contribution margin. In Clark's view short-run marginal cost pricing in depression times is against the social interest in production (Clark, 1923: Chapter 21: Cut-throat Competition and the Public Interest).

Research Questions
Welfare economics theory claims that under certain conditions short-run mar- In Figure 1 for only plant L and Figure 2 for only pant K , the consumer surplus is the area under the 1 1 D w off-peak period and 2 2 D w peak period demand curves above the cost lines 2 A D , 2 B C , 1 B F , and 1 A H .

Model
This study models a hypothetical a corporation selling cement, product Q, a homogeneous costly-to store, low-cost product, used in the construction industry. The corporation has two independently managed divisions: 1) a manufacturing division that produces cement and sells only to the selling division and 2) a selling division with many offices that buys cement only from the manufacturing division with its many plants and sells cement to the construction industry using a quote price system.
The model assumes periods of a week. q is the operating rate in the manufacturing division, tons of cement, produced in a week. The corporation seeking to In the model all divisions of the corporation know the industry supply and demand data.

Theoretical Analysis Transfer Pricing System A: SRMC Pricing
See Table 1 data transfer pricing pricing set at short-run marginal cost pricing.
The two left columns of Table 1 show data for the corporation using only technology L . The two right column of Table 1 show data for the corporation using only technology K . See Figure 1 only plant L a graph of the data of the left columns of Table 1 and Table 2. See Figure 2 only plant K a graph of the data of the right columns of Table 1 and Table 2.
The model assumes 1 6 7 w = and 2 1 7 w = . The model assumes For only plant L long-equilibrium.
For only plant K long-equilibrium.
For only plant L

Theoretical Analysis Transfer Pricing System B: Workable Competition Pricing
See Table 2 data transfer pricing pricing using John M. Clark's workable competition pricing. The two left columns of Table 2 show data for the corporation using only technology L . The two right column of Table 2 show data for the corporation using only technology K . See Figure 1 only plant L a graph of the data of the left columns of Table 1 and Table 2. See Figure 2 only plant K a graph of the data of the right columns of Table 1 and Table 2.
The model assumes to raise transfer prices above SRMC pricing in off-peaks and to lower transfer prices below SRMC pricing in peak periods. The model assume downward sloping demand schedules so that a rise in prices leads to less quantities demanded and a reduction in prices leads to more quantities demanded. A reasonable assumption is that off-peak demand is relatively inelastic so that a rise in prices would lead to higher revenues for sellers though they are The model assumes in transfer pricing using workable competition pricing firms will expand capacity more over the cycle. In high demand times transfer prices would be lower with workable competition pricing than would be under transfer prices SRMC pricing. Table 2 shows a reasonable long-run equilibrium arrangement under workable competition pricing. I use round numbers and rough estimates in Table 2 for workable competition to get approximate zero expected profits over the cycle. In Table 1 for SRMC pricing I use precise numbers to get exactly zero long-run equilibrium.
The model assumes 1 6 7 w = and 2 1 7 w = . The model assumes For only plant L long-equilibrium.
For only plant K long-equilibrium.
For only plant L As an be seen the high FC plant, plant K under workable competition pricing requires wider price differences between 2 P and 1 P and narrower output rates differences between 2 Q and 1 Q .
With transfer prices set at workable competition pricing in off-peak periods, transfer price is above VC. This allows the manufacturing division to show modest contribution margins during off-peaks. I assume manufacturing division produces to meet the demand schedules in the off-peak, no more and no less. In

Corporation Profit Comparisons
Long-run equilibrium requires expected profits for the manufacturing division over the cycle = 0. I proved mathematically that a rigid pricing system over demand fluctuations that gives same expected revenues and same expected outputs is superior to a varying pricing (see Aranoff, 2011

Conclusion
We present a theoretical model of corporation division manufacturing cement with two technologies, plant L and plant K . We compare two transfer pricing policies for each technology short-run marginal cost pricing versus workable competition over the business cycle. We show in our model a gain in expected consumer surplus with workable competition transfer pricing. We give a detailed numerical example with graphs for each transfer pricing system. The main result is that workable competition pricing over the business cycle increases the amplitude of Q outputs over the cycle and increases consumer surplus for both technologies under certain conditions. The positive effects of workable competition transfer pricing seem more pronounced with plant L .
Much of our work is based on John M. Clark. He argued against SRMC pric- pricing in cyclical industries firms would be operating at a loss for the great majority of the time, with vain hopes of exploiting the infrequent peak times (Clark, 1961: pp. 121-122): "It is decidedly doubtful whether it would be economically feasible to make profits enough in such periods to offset the losses incurred in normal and subnormal periods. And if it were economically feasible, there might be other serious obstacles and drawbacks in the way of exploiting the profitable periods by raising prices as graspingly as would be necessary to balance accounts." Clark's last paragraph in his 1961 book applies today (Clark, 1961: p. 490): "Meanwhile it remains true that the imperfectly competitive mixed economy we have is better than the impossible abstraction of perfect competi-tion… The system has serious shortcomings, but there is room to hope that our performance in these respects may be substantially improved, if all groups concerned to attack the problems with a realization of their importance and with the necessary understanding and goodwill."

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.