11.i. Transfer Pricing
Case 1: No External Market for the Manufactured Good
Suppose that a firm manufactures bicycles in Hong Kong and distributes them in America. The manufacturing division and the distribution division are distinct units, even though they are owned by the same firm. When bicycles are transferred from the manufacturing division to the distribution division, there will normally be an internal price that the manufacturing division charges to the distribution division. If this price is set too low, then the manufacturing division will not produce enough bicycles. If it is set too high, the manufacturing division will be motivated to produce too much. The proper internal price is the one that maximizes the profit of the firm as a whole. This requires setting the internal price equal to marginal manufacturing cost MMC.
Figure 11.i.1 shows the case of a monopoly firm that has no external market for the manufactured good. This means that it manufactures all of the goods that it distributes, so the quantity manufactured, Qm, is equal to the quantity distributed, Qd. The firm’s marginal distribution cost is given by the curve MDC. The firm’s overall marginal cost MC is given by the sum of its manufacturing and distribution costs, or MC=MMC+MDC. The profit-maximizing output is found where MC=MR, at the output Qm (=Qd).
While the profit-maximizing output is being determined, the firm must also decide on the internal price Pi. This is set equal to the marginal manufacturing cost of the last unit produced. The distribution division’s perceived marginal cost MC’ is therefore equal to its own marginal distribution cost MDC plus the internal price Pi that it must pay to buy the manufactured good. Note that at the output Qm, the firm’s true marginal cost MC is equal to the distribution division’s perceived marginal cost MC’. Thus the output chosen by the distribution division will be the one that maximizes the firm’s overall profit.
Figure 11.i.1: No External Market. The monopolistic firm’s marginal manufacturing cost MMC and marginal distribution cost MDC are added together vertically to give the firm’s overall marginal cost MC=MMC+MDC. The quantity distributed Qd and the retail price Pr are found by setting MC=MR. The firm then sets an internal price Pi equal to marginal manufacturing cost. This is the profit-maximizing price for the manufacturing division to charge to the distribution division. The perceived marginal cost MC’ of the distribution division is then equal to the sum of its own marginal distribution cost MDC plus the internal price Pe that it must pay to buy the manufactured good. The profit earned by the distribution division is then equal to the upper shaded area (yellow), while the manufacturing division earns the lower shaded area (blue). The two shaded areas combined are equal to the firm’s total profit abcd.
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Assuming the firm has no fixed costs, the profit earned by the manufacturing division is the lower shaded area (blue), which shows the difference between the price charged for each unit and the marginal manufacturing costs MMC. The profit of the distribution division is shown by the upper shaded area (yellow). Profit is equal to the difference between the retail price Pr and the distribution division’s own perceived marginal cost MC’. The sum of the yellow and blue areas is equal to the firm’s total profit. Alternatively, the firm’s total profit is also equal to area abcd.
The sizes of the two profit areas would be of interest to the tax authorities. Suppose, for example, that taxes are much lower in Hong Kong than in America. The firm would want to understate its American profit and overstate its Hong Kong profit in order to reduce its total tax. If the tax authorities are interested in collecting the “correct” tax, then they should calculate the profits of the two divisions based on the assumption that the internal price is set equal to the marginal manufacturing cost. Of course, the tax authorities might not be interested in collecting the correct amount of tax. They might be interested in collecting the maximum amount of tax, at the expense of the firm and the other country. In this case, a neutral third party, like an international court, would be able to determine the correct internal price based on the marginal manufacturing cost.
Case 2: Competitive External Market for the Manufactured Good
When there is a competitive market for the manufactured good, the firm does not choose the internal price, but rather sets it equal to the external price Pe. This price is determined in the open market. The manufacturing division will then produce where Pe=MMC, at an output of Qm. The perceived marginal cost MC’ of the distribution division will then be equal to its own distribution cost MDC plus the external price Pe that it pays to buy the manufactured good. Note that the distribution division will buy (Qd-Qm) units from outside sources, since Pe is less than MMC when out put exceeds Qm. As long as MMC<Pe, the firm will manufacture its own goods. But when MMC>Pe it is cheaper for the firm to buy the good than to manufacture it.
As before, the profit of the distribution division is the upper shaded area (yellow) while the profit of the manufacturing division is the lower shaded area (blue) The two areas combined are equal to total profit.
Figure 11.i.2: Competitive External Market—External Purchases. The external price Pe of the manufactured good is determined in a competitive market and is therefore beyond the firm’s control. The quantity manufactured Qm is found by setting Pe=MMC. The distribution division’s perceived marginal cost MC’ is then equal to the vertical sum of Pe and MDC. Setting MC’=MR yields the quantity distributed Qd. The firm will therefore buy Qd-Qm units of the manufactured good from external sources. The profits of the two divisions are shown by the shaded areas, while the firm’s total profit is equal to the two areas combined.
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Figure 11.i.3 shows a case where the competitive external price of the manufactured good is relatively high. This motivates the manufacturing division to produce the relatively large quantity Qm, which is more than the distribution division can use. The firm will therefore sell (Qm-Qd) units outside of the firm. The perceived marginal cost MC’ of the distribution division is MC’=MDC+Pe, and at the retail price Pr the distribution division earns a profit equal to the upper shaded area (yellow). The manufacturing division’s profit is equal to the lower shaded area (blue). The firm’s total profit is equal to the two shaded areas combined.
Figure 11.i.3. Competitive External Market—External Sales. In this case the competitive external price Pe is relatively high, so the manufacturing division produces more than the distribution division can use and sells goods outside the firm. As before, the distribution division’s perceived marginal cost MC’ is equal to the sum of the external price plus MDC, or MC’=Pe+MDC. The manufacturing division produces the quantity Qm, while the distribution division takes Qd units, leaving (Qm-Qd) for sales outside the firm.
Case 3: Monopolized External Market for the Manufactured Good
Figure 11.i.4. Monopolized External Market for the Manufactured Good. In the top panel, the firm’s distribution division faces a retail demand and marginal revenue curve as shown. The net marginal revenue curve NMR is found by subtracting MR-MDC. (At the vertical intercepts, 110=120-10.) In the lower panel, NMR and MRexternal are horizontally summed to get NMR+MRexternal. The total quantity manufactured, Qtotal, is found where MMC=NMR+MRexternal. The MMC of the last unit produced gives the correct internal price Pinternal. Setting Pinternal equal to NMR yields Qinternal: the quantity sold to the firm’s own distribution division, and following Qinternal up to Dretail in the upper panel yields the retail price of the distributed good Pretail. Setting Pinternal equal to MRexternal yields Qexternal: the quantity sold monopolistically to outside distributors of the good. Following Qexternal up to Dexternal yields Pexternal: the price of the manufactured good to outside distributors.
Figure 11.i.4 shows the situation of a firm that manufactures and sells a good monopolistically in its home market, while selling the manufactured good monopolistically to outside distributors. Those outside distributors would presumably operate in a foreign market, so that they do not compete with the firm in its own home market. This firm faces several questions: How many units to manufacture, how to divide those manufactured units between outside firms and its own distribution division, what external and internal prices to charge for the manufactured good, and finally what retail price to charge for the distributed good.
To answer these questions, we begin by deriving a new curve, net marginal revenue NMR, in the upper panel. This curve is derived by subtracting MR-MDC. Thus NMR shows the marginal revenue received by the manufacturing division when selling to its own distribution division. The NMR curve is summed horizontally with MRexternal in the lower panel to yield NMR+MRexternal. The total quantity manufactured, Qtotal, is found where MMC=NMR+MRexternal.Moving left along the Pinternal line allows us to find the quantities to sell internally and externally. Once these are found, the retail price for the distribution division to charge is found at Pretail in the upper panel, while the price to charge to outside distributors is Pexternal.
There are a few limitations to the above analysis. The above cases ignore fixed cost, and it is possible, for example, that the manufacturing division might find a way to reduce fixed cost without affecting MMC. This would leave the internal price unchanged, with the manufacturing division reaping no benefit from its efforts at cost reduction. Or suppose that some cost reduction lowered MMC. This could leave the internal price lower than before, meaning that even though the firm as a whole gains, the manufacturing division would be penalized for its efforts.
This analysis of internal pricing is of interest not just to firms, but to tax authorities as well. If the firm manufactures in Hong Kong, where taxes are low, and distributes in America, where taxes are high, then the firm could avoid taxes by setting the internal price artificially high. This would inflate profits in Hong Kong and reduce them in America, thereby reducing overall tax payments. Of course, tax authorities have the reverse incentive. American tax authorities would claim the firm should reduce its internal price, thus increasing American tax collections. Meanwhile, Hong Kong tax authorities would claim the firm should increase its internal price, thus increasing Hong Kong tax collections. In this case, the true level of the internal price might best be set by a fair-minded, wise, and virtuous economic consultant.