Transfer Pricing

Suppose a firm manufactures bicycles in Hong Kong and distribute it in America.
In consumer market, this firm is monopoly.

As shown below, there's an internal price. If the firm set the internal price differ from the optimal one, it can adjust the profit proportion between manufacture department and sales department, which locate in different areas. In this way, it can reduce total taxes due to different tax rates on profit in the two places.

MMC
marginal manufacture cost
MDC
marginal distribution cost
NMR
net marginal revenue
Pi
internal price

Case 1, no external market for manufacture department

transfer_pricing_no_external_mkt.png

Case 2, competitive external market for manufacture department

External purchases

transfer_pricing_external_mkt.png

External sales

transfer_princing_external_mkt_2.png

Case 3, monopolized external market for manufacture department

transfer_princing_mono_external_mkt.png

Core idea

To maximize profit, the firm in whole should produce at

(1)
\begin{align} marginal\; cost =marginal\; revenue \end{align}
$cost$
money out from the firm
$revenue$
money into the firm

Case 1

Optimal condition $MMC+MDC=MR$

Case 2

Optimal condition $Pe+MDC=MR$

Case 3

Firm faces two markets, domestic market and foreign market.

In domestic market, the firm faces domestic demand curve, and distribute by sales department, so we have the net marginal revenue
${NMR}_{d}={MR}_{d}-MDC$

In foreign market, the firm faces foreign distributor's demand curve. And it has a foreign marginal revenue curve ${MR}_{external}$

Totally, ${NMR}_{d}$ curve plus ${MR}_{external}$ horizontally, the firm has a total demand curve. MMC curve cross this total demand curve, we get optimal point.

Note: for the two curves plus or minus vertically, we can interpret as different marginal costs and/or revenues plus or minus, because we always assume basing on the same product amount. But in the case of plus or minus curves horizontally, we cannot simply interpret marginal costs or revenues plus or minus.

Curves caculation

Curve1 : Q=aP
Curve2 : Q=bP
Curve1 + Curve2 vertically: P=Q/a+Q/b (assume Q stay, Q/a and Q/b represent their old P values, so the new P value is the olds sum)
Curve1 + Curve2 horizontally: Q=aP+bP (P stays, Q is the old Qs sum)

Further study

In case 2 external sales, you may ask, while we assume the firm is monopoly in consumer market, why there's external sales?

The graphs in this page are from the study materials from my microeconomics professor at usc.

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