Chapter 12 Pricing Practices

# I mr t 150 150 q 100 q mc implies q 20 since this is

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(i) MR T = 150 – 1.50 Q = 100 + Q = MC implies Q = 20. Since this is less than 50, the firm should produce Q A = Q B = 50. This yields prices of P A = 95 and P B = 40. (ii) MR T = 150 – 1.50 Q = 0.125 Q = MC implies Q = 92.31. Since this is greater than 50, the firm should not produce this level of output. Instead, it should set MR A = MC as follows: MR A = 100 – 0.50 Q = 0.125 Q = MC so Q A = 160 and P A = 60. Q B must also be equal to 160, but the firm should dispose of any output beyond that which results in a marginal revenue from sale of B equal to zero, that is, beyond Q B = 50 and P B = 25. The firm will dispose of 110 units of product B. 87.For levels of output where the marginal revenue for both products is nonnegative, the firm's marginal revenue function is obtained by vertically summing the two individual marginal revenue functions as follows: P A = 150 – 0.05 Q A so MR A = 150 – 0.10 Q A P B = 100 – 0.10 Q B so MR B = 100 – 0.20 Q B MR T = MR A + MR B = 150 – 0.10 Q + 100 – 0.20 Q = 250 – 0.30 Q For levels of output where the marginal revenue for one product is negative, the firm's marginal revenue function is equal to the nonnegative marginal revenue function. If output exceeds Q = 500, then MR B is negative so the firm's marginal revenue function is equal to MR A . (i) MR T = 250 – 0.30 Q = 70 + 0.30 Q = MC implies Q = 300. Since this is less than 500, the firm should produce Q A = Q B = 300. This yields prices of P A = 135 and P B = 70. (ii) MR T = 250 – 0.30 Q = 10 + 0.04 Q = MC implies Q = 705.88. Since this is greater than 500, the firm should not produce this level of output. Instead, it should set MR A = MC as follows: Page 19

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MR A = 150 – 0.10 Q = 10 + 0.04 Q = MC so Q A = 1000 and P A = 100. Q B must also be equal to 1000, but the firm should dispose of any output beyond that which results in a marginal revenue from sale of B equal to zero, that is, beyond Q B = 500 and P B = 50. The firm will dispose of 500 units of product B. 88.The horizontal sum of the marginal revenue functions ( MRS ) for the two markets is calculated as follows: P A = 200 – 2 Q A so MR A = 200 – 4 Q A and Q A = 50 – 0.25 MR A P B = 120 – 2 Q B so MR B = 120 – 4 Q B and Q B = 30 – 0.25 MR B Q = Q A + Q B = 50 – 0.25 MRS + 30 – 0.25 MRS = 80 – 0.50 MRS MRS = 160 – 2 Q This horizontally summed marginal revenue function applies when marginal revenue is 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 – 2 Q = 20 + 0.80 Q = MC so Q = 50 and MRS = 60 Substituting MRS = 60 into the marginal revenue function for the two markets yields Q A = 35 and Q B = 15. Substituting these quantities into the demand functions yields P A = 130 and P B = 90. 89.The horizontal sum of the marginal revenue functions ( MRS ) for the two markets is calculated as follows: P A = 200 – 0.50 Q A so MR A = 200 – Q A and Q A = 200 – MR A P B = 120 – 0.50 Q B so MR B = 120 – Q B and Q B = 120 – MR B Q = Q A + Q B = 200 – MRS + 120 – MRS = 320 – 2 MRS MRS = 160 – 0.50 Q This horizontally summed marginal revenue function applies when marginal revenue is below 120. When marginal revenue is above 120, only the marginal revenue function for
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