Although the transfer pricing concept can be introduced conceptually through the use of graphic analysis, most real-world applications are complex and must be solved algebraically. For this reason, examination of a detailed numerical example can be fruitful.
Profit Maximization for an Integrated Firm
Josiah Bartlet & Sons, Inc., is a small integrated domestic manufacturer of material handling equipment. Demand and marginal revenue curves for the firm are
P = $100 – $0.001Q
MR = ΔTR/ΔQ = $100 – $0.002Q
Relevant total cost, marginal cost, and profit functions are
TC = $312,500 + $25Q + $0.0015Q2
MC = ΔTC/ΔQ = $25 + $0.003Q
π = TR – TC
= $100Q – $0.001Q2 – $312,500 – $25Q – $0.0015Q2
= –$0.0025Q2 + $75Q – $312,500
Profit maximization occurs at the point where MR = MC, so the optimal output level is
MR = MC
$100 – $0.002Q = $25 + $0.003Q
75 = 0.005Q
Q = 15,000
This implies that
P = $100 – $0.001(15,000)
π = TR – TC
= –$0.0025(15,0002) + $75(15,000) – $312,500
Therefore, the optimal price/output combination is $85 and 15,000 units for this integrated firm, and profits total $250,000. To be optimal, transfer prices must ensure operation at these levels.
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:
With divisional operation, the total and marginal cost functions for the firm are
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:
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
= $20 + $0.002(15,000)
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.
Competitive External Market with Excess Internal Demand
To consider the effects of an external market for the transferred product, assume that the company is able to buy an unlimited quantity of a comparable product from a foreign supplier at a price of $35. The product supplied by the foreign manufacturer meets the exact same specifications as that produced by Josiah Bartlet & Sons. Because an unlimited quantity can be purchased for $35, a perfectly competitive external market exists for the transferred product, and the optimal transfer price equals the external market price. For PT = $35, the quantity demanded by the distribution division is
whereas the quantity supplied by the manufacturing division is
In this case of excess internal demand, the distribution division will purchase all 7,500 units produced internally plus an additional 12,500 units from the foreign supplier. The price impact for customers and the profit impact for Josiah Bartlet & Sons are dramatic. Domestic customer prices and total profits are now calculated as
P = $100 – $0.001(20,000)
Josiah Bartlet & Sons’ domestic customers benefit from the increased availability of goods, 20,000 versus 15,000 units, and lower prices, $80 versus $85 per unit. The opportunity to purchase goods at a price of $35 from a foreign supplier benefits the company because profits grow from $250,000 to $343,750. The firm now manufactures only 7,500 of the units sold to customers and has become much more of a distributor than an integrated manufacturer and distributor.
Josiah Bartlet & Sons has been able to make its business and profits grow by focusing efforts on distribution, where it enjoys a comparative advantage.
Competitive External Market with Excess Internal Supply
It is interesting to contrast these results with those achieved under somewhat different circumstances. For example, assume that Josiah Bartlet & Sons is able to sell an unlimited quantity of its goods to a foreign distributor at a price of $80. For simplicity, also assume that sales to this new market have no impact on the firm’s ability to sell to current domestic customers and that this market can be supplied under the same cost conditions as previously. If PT = $80, the quantity demanded by the distribution division is
whereas the quantity supplied by the manufacturing division is
In this instance of excess internal supply, the distribution division will purchase all 5,000 units desired internally, while the manufacturing division will offer an additional 25,000 units to the new foreign distributor. Again, the price impact for customers and the profit impact for Josiah Bartlet & Sons are dramatic. Domestic customer prices and total profits are now as follows:
P = $100 – $0.001(5,000)
Under this scenario, Josiah Bartlet & Sons’ domestic market shrinks from an initial 15,000 to 5,000 units, and prices rise somewhat from $85 to $95 per unit. At the same time, foreign customers benefit from the increased availability of goods, 25,000 versus none previously, and the attractive purchase price of $80 per unit. The opportunity to sell at a price of $80 to a foreign distributor has also benefited the company, because profits grew from $250,000 to $625,000.
The company now distributes only 5,000 of 30,000 units sold to customers and has become much more of a manufacturer than a distributor. By emphasizing manufacturing, Josiah Bartlet & Sons makes its business and profits grow by focusing efforts on what it does best.
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