HW8-solution

# HW8-solution - Econ 501 Homework Assignment 8 No need to...

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Econ 501 Homework Assignment 8 No need to submit 1. BB 11.20 a) Equating the marginal costs at MC T , we have Q = Q 1 + Q 2 + Q 3 = 0.25 MC T + 0.5 MC T – 1 + MC T – 6, which can be rearranged as MC T = (4/7) Q + 4. Setting MR = MC yields 64 – (2/7)* Q = (4/7)* Q + 4 or Q = 70 and P = 54. At this output level, MC T = 44, implying that Q 1 = 11, Q 2 = 21, and Q 3 = 38. b) In this case, using plant 3 is inefficient because its marginal cost is always higher than that of plant 2. Hence, the firm will use only plants 1 and 2. Moreover, the firm will not use plant 1 once its marginal cost rises to MC 2 = 4, so we can immediately see that it will only produce 4 Q 1 = 4 or Q 1 = 1 unit at plant 1. Its total production can be found by setting MR = MC 2 , yielding 64 – (2/7)* Q = 4 or Q = 210 and P = 34. So it produces Q 1 = 1 unit in plant 1 and Q 2 = 209 units in plant 2, while producing no units in plant 3 (i.e. Q 3 = 0). 2. BB 12.6 a) We can represent the marginal willingness to pay for each unit beyond Q 1 = 20 as P = 100 – (20 + Q 2 ) = 80 – Q 2 . The associated marginal revenue is then MR = 80 – 2 Q 2 , so the profit maximizing second block is MR = MC : 80 – 2 Q 2 = 10. Thus Q 2 = 35 and P 2 = 80 – 35 = 45. So the firm sells the first 20 units at a price of \$80 apiece, while the firm sells any quantity above 20 at \$45 apiece. The firm’s total profit will be (80 – 10)*20 + (45 – 10)*35 = \$2625.

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HW8-solution - Econ 501 Homework Assignment 8 No need to...

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