Chapter 12 Pricing Practices

# When marginal revenue is above 120 only the marginal

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below 120. When marginal revenue is above 120, only the marginal revenue function for market A is relevant. Setting the firm's marginal cost function equal to MRS yields: MRS = 160 – 0.5 Q = 20 + 0.20 Q = MC so Q = 200 and MRS = 60 Substituting MRS = 60 into the marginal revenue function for the two markets yields Q A = 140 and Q B = 60. Page 20

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Substituting these quantities into the demand functions yields P A = 130 and P B = 90. 90.(i) In the absence of an external market, production is determined by vertically summing the two marginal cost functions and setting the sum ( MCS ) equal to marginal revenue: P = 600 – 5 Q so MR = 600 – 10 Q MCS = MC P + MC M = 100 + 6 Q + 4 Q = 100 + 10 Q MR = 600 – 10 Q = 100 + 10 Q = MCS so Q = 25 at P = 475 The transfer price is set equal to the marginal cost of manufacturing the optimal level of output: P T = MC P = 100 + (6)(25) = 250 (ii) The production division should manufacture the quantity that sets its marginal cost equal to the competitive price: P = 292 = 100 + 6 Q so Q P = 32 The transfer price is equal to the competitive market price and so: MCS = P T + MC M = 292 + 4 Q Finally, MCS is set equal to marginal revenue to determine the number of units that will be purchased by the marketing division and the price at which they will be sold: MR = 600 – 10 Q = 292 + 4 Q = MCS and Q M = 22 at P = 490 91.(i) In the absence of an external market, production is determined by vertically summing the two marginal cost functions and setting the sum ( MCS ) equal to marginal revenue: P = 100 – Q so MR = 100 – 2 Q MCS = MC P + MC M = 2 Q + Q = 3 Q MR = 100 – 2 Q = 3 Q = MCS so Q = 20 at P = 80 The transfer price is set equal to the marginal cost of manufacturing the optimal level of output: P T = MC P = (2)(20) = 40 Page 21
(ii) The production division should manufacture the quantity that sets its marginal cost equal to the competitive price: P = 52 = 2 Q so Q P = 26 The transfer price is equal to the competitive market price and so MCS = P T + MC M = 52 + Q Finally, MCS is set equal to marginal revenue to determine the number of units that will be purchased by the marketing division and the price at which they will be sold: MR = 100 – 2 Q = 52 + Q = MCS and Q M = 16 at P = 84 Page 22
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