## Transfer Pricing with No External Market

Consider how the situation changes if the firm is reorganized into separate manufacturing and distribution division profit centers, and no external market exists for the transferred product. The demand curve facing the distribution division is precisely the same as the firm's output demand curve. Although the total cost function of the firm is unchanged, it can be broken down into the costs of manufacturing and distribution.

Assume that such a breakdown results in the following divisional cost functions:

TCMfg = \$250,000 + \$20Q + \$0.001Q2 MCMfg = ATCMfg/AQ = \$20 + \$0.002Q

TCDistr = \$62,500 + \$5Q + \$0.0005Q2 MCDistr = ATCDistr/AQ = \$5 + \$°.°01Q With divisional operation, the total and marginal cost functions for the firm are

TC = TCMfg + TCDistr MC = MCMfg + MCDistr and precisely the same as before.

To demonstrate the derivation of an appropriate activity level, the net marginal revenue for the distribution division is set equal to the marginal cost of the manufacturing division:

MR - MCDistr = MCMfg

The 15,000-unit output level remains optimal for profit maximization. If the distribution division determines the quantity it will purchase by movement along its marginal revenue curve, and the manufacturing division supplies output along its marginal cost curve, then the market-clearing transfer price is the price that results when MR - MCDistr = MCMfg. At 15,000 units of output, the optimal transfer price is

PT = MCMfg

At a transfer price of PT = \$50, the quantity supplied by the manufacturing division equals 15,000. This is the same quantity demanded by the distribution division at a PT = \$50, because

At a transfer price of PT > \$50, the distribution division will accept fewer units of output than the manufacturing division wants to supply. If PT < \$50, the distribution division will seek to purchase more units than the manufacturing division desires to produce. Only at a \$50 transfer price are supply and demand in balance in the firm's internal market.