# Transfer Pricing

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## Transfer Pricing with No Outside Market

• In general in these problems we will be given $\displaystyle MC_u$ which will be the marginal cost for the upstream firm and $\displaystyle MC_d$ which will be the marginal cost for the downstream firm.
• We also define $\displaystyle P_T$ as the transfer price between the downstream firm and the upstream firm. The downstream firm will be paying the upstream firm this transfer price for every good that he produces.
• To optimize profit, we set $\displaystyle P_T = MC_u$
• Therefore, to find the quantity that maximizes profit we set $\displaystyle MR = MC_u + MC_d$

## Transfer Pricing with Competitive External Market

• In this case, the marginal cost for the activities of the upstream firm is still $\displaystyle MC_u$ but the marginal cost for the supplies of the downstream firm, $\displaystyle MC_d$ , is now the competitive external price of the of the supplies.
• Therefore to optimize profit the downstream firm should set $\displaystyle MR = MC_d + P_c$ where $\displaystyle P_c$ is the price of the upstream goods in a competitive market.
• The downstream firm should set $\displaystyle P_c = MC_u$
• Alternatively, it is possible to maximize profits by calculating $\displaystyle Profit = P_f * Q_f - TC_f - TC_i + P_c * (Q_i - Q_f)$ , where "i" stands for intermediate good and "f" stands for finished good.
• Next we take $\displaystyle \frac{dProfit}{dQ_i}$ and set it equal to zero to find the optimum quantity of intermediate goods.
• Finally, we take $\displaystyle \frac{dProfit}{dQ_f}$ and set it equal to zero to find the optimum quantity of final goods.