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Appendix to Chapter 6 Transfer Pricing 275

in the firm’s final products. (We relax this assumption in the following section.)

What transfer price per unit should the chip division charge the copier (or any

other) division?

The answer to this question is that the firm should set the internal transfer price

for the microchip exactly equal to its marginal cost of production.Figure 6A.1 sum-

marizes the demand and cost conditions associated with the production of

copiers. The key point about the figure is understanding the “full” marginal

cost of producing copiers. Managers of the copier division are well aware of

the direct costs they incur in assembly. This marginal cost is shown as the

upward-sloping MCAcurve in the figure. In addition, we must consider the

marginal cost of producing the chips that are used in the copier. In Figure 6A.1,

this marginal cost (labeled MCM) is superimposed on the MCAcurve. The total

marginal cost of producing copiers is the sum of the chip cost and the assem-

bly cost. In the figure, this total marginal cost curve is denoted by MCTMCA

MCMand is drawn as the vertical sum of the two curves. (Note that MCMis

depicted as slightly upward sloping; that is, the gap between MCAand MCT

steadily increases as output rises.)

The firm maximizes the total profit it earns on copiers by setting the quan-

tity such that marginal revenue equals total marginal cost, MR MCT. In

Figure 6A.1, the optimal quantity occurs at Q*, and the associated optimal sell-

ing price for the copier is P*. What transfer price for chips will lead to this out-

come? The appropriate transfer price should be set at PTMCM. By paying

this transfer price, the copier division incurs an additional cost of MCAPT

MCAMCMfor each extra copier it produces. By taking into account the true

“full” cost of producing additional output, the copier division automatically

maximizes the firm’s total profit.

A MARKET FOR CHIPS If there is an external market in which microchips can

be bought and sold, the profit-maximizing analysis must be modified. In this

case, the firm should set the internal transfer price for the microchip equal to the pre-

vailing market price.The reasoning is straightforward. Let Pdenote the pre-

vailing market price. Obviously, the chip division cannot charge the copier

division a transfer price that exceeds P; the copier division would simply opt

to buy chips from the outside market. Nor would the chip division be satisfied

with a transfer price below P; it would prefer to produce and sell chips exclu-

sively for the outside market. Consequently, PTPis the only price at which

internal transfers will occur.

Here is another way to arrive at this conclusion. The correct price to

impute to internally produced chips should reflect the firm’s true opportu-

nity cost. Each chip that goes into the “guts” of the firm’s copiers is a chip that

could have been sold on the outside market at price P. Since it is this mar-

ket price that the firm gives up, the internal transfer price should be set

accordingly.

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