# PRICING WITH MARKET POWER IV

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PRICING WITH MARKET POWER IV

Overview Importance & significance of transfer pricing in vertically integrated M-form of firms Transfer pricing with no outside market (Fig 1) Transfer pricing with a competitive outside market Buying (Fig 2) Selling (Fig 3) Transfer pricing with a non-competitive outside market Buying (monopsonist: Fig 5 not given in text) Selling (monopolist: Fig 4) To do numerical example in class, if time permits

Importance & Significance of Transfer Pricing
Transfer price = Price for inter-divisional transaction in a multi-divisional company, which is a major determinant of the overall financial performance of the company Unless the right transfer price is chosen, the company shall end up having less than maximum profit (can be shown with a simple diagram) Assuming a competitive external market exists for sale/purchase of the intermediate good, choice of any transfer price other than the competitive outside price shall lead to lower profit (can be shown with a simple diagram)

Fig 1: Transfer Pricing When There is No Outside Market
MCA is the marginal cost of assembling cars given the engines. Since one car requires one engine, the marginal product of engines is 1. Therefore the curve (MR – MCA ) is the net marginal revenue curve NMRE for engines. The transfer price PE correctly values the engines used to produce the cars. The same result is obtained if we take intersection point between MR and ∑MC. NMRE ∑MC PA MCE AR PE MCA MR Quantity QA = QE (MR – MCA)

Fig 2: Buying Engines in a Competitive Outside Market
Since the outside market is competitive, the marginal cost of the intermediate good equals the market price of the good, which is the optimal transfer price PE,M. The downstream division uses QE,2 engines for its cars, but buys only QE,1 engines from the upstream division and the rest from the open market. If the firm makes all its engines, then MCE will exceed the market price, increasing the engine division’s profits but lowering the total profit of the firm. The same result is obtained if we take intersection point between MR and ∑MC’ (after adjusting for horizontal MC*E) Q: What’ll happen if external competitive market is ignored? NMRE ∑MC’ PA ∑MC MCE AR MCA PE,M MC*E MR QE,1 QE,2 = QE Quantity Sub-optimum Solution at (MR – MCA)

Fig 3: Selling Engines in a Competitive Outside Market
∑MC ∑MC’ Although engine division produces QE,1 engines, only QE,2 engines are used by the car division, the rest being sold at the price PE,M. Some engines are sold in the market because they will earn higher net revenue than if they were used to manufacture cars. Q: What if external competitive market ignored? NMRE PA MCE PE,M MC*E AR MCA MR QE,2 = QA Sub- optimum solution QE,1 Quantity (MR – MCA)

Fig 4: Monopoly Supply of Engines to the Outside Market
The total net marginal revenue curve NMRE is the sum of MRE,M and (MR – MCA). Optimal transfer price is P*E and the no. of engines is QE,1. QE,2 engines are used to make cars (the quantity at which car division’s MR – MCA is equal to the transfer price P*E) The remaining QE,3 engines are sold in the outside market at the price PE,M. Case similar to that of a discriminating monopolist. NMRE MRE,M ARE,M PA NMRE MCE PE,M P*E AR MCA MR QE,3 QE,2 = QA QE,1 Quantity (MR – MCA)

Fig 5: Monopsony Purchase of Engines from the Outside Market
NMRE MC’E MRE,M ARE,M PA Transfer price (marked green) is above the open market price (in red), because with monopsony power, purchasing additional engine from outside market involves a marginal expenditure MC’E greater than the average price of procurement MCE NMRE MCE AR MCA MR QE,2 = QA QE,1 QE,3 MR-MCA

Numerical Example Demand for automobiles: P = 20,000 – Q
MR for automobiles: MR = 20,000 – 2Q Down-stream’s assembling cost: CA(Q) = 8000Q => MCA = 8000 Up-stream’s cost of production of engines: CE(QE) = 2QE2 => MCE(QE) = 4QE Because of 1-1 correspondence: QE = Q

Numerical Example: Case 1 – No outside market
NMRE = MR – MCA = 20,000 – 2Q – 8,000 = 12,000 – QE NMRE = MCE => 12, QE = 4QE => QE = 2000 PE = MCE = 4QE = \$8,000

Numerical Example: Case 2 – Outside competitive market for engines
Let PE,M = 6000 < Transfer price = 8000 => Buying some engines from outside => NMRE = 6000 => 12, QE = QE = 6000 => QE = 3000 Company produces more cars & buys some engines at lower price, given lower cost of engines in outside market Up-stream production: MCE = 6000 => 4QE =6000 => QE = 1500 => Rest 1500 are bought from market

Numerical Example: Case 3 – Outside non-competitive market for engines
Given PE,M = 10,000 – QE => MRE,M = 10, QE => Draw this line, noting that MRE,M = 10,000 when QE = 0; QE = 5000, when MRE,M = 0 Draw NMRE = 12,000 – 2QE, noting that NMRE = 12,000 when QE = 0; QE = 6,000 when NMRE = 0 Hence, NMRE,total = MRE,M + NMRE for QE > 10,000, when equated to MCE = 4QE gives 11,000 - QE = 4QE => QE = 2200 = total # of engines produced Optimal transfer price = MCE = 4QE = 8800 MRE,M = 10,000 – 2QE = transfer price = 8800 => QE = 600 = # of engines to be sold in market NMRE = 8800 gives 8800 = 12,000 – 2QE => QE = 1600 = # of engines & cars produced in-house

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