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1. A firm faces the following demand and total cost schedules, with all quantities listed on a per- month basis. Suppose that it is required to produce a whole number of items each month. Demand Total Cost P Q Q TC \$20 1 1 \$5 18 2 2 15 15 3 3 30 12 4 4 50 8 5 5 75 a. How much does the firm produce, and at what price? How do you know? Demand Total Cost P Q TR MR Q TC MC 20 1 20 20 1 5 5 18 2 36 16 2 15 10 15 3 45 9 3 30 15 12 4 48 3 4 50 20 8 5 40 -8 5 75 25 MR doesn’t equal MC at any output level, so use this rule instead: Produce another unit of output if the revenue it brings (MR) is greater than its cost to the firm (MC). If a unit costs more than the revenue it brings in (MC>MR), then don’t produce that unit. Therefore, produce a quantity of 2. Then TR = 36, TC = 15, and so profit = 21. b. Suppose that the firm is subject to an excise tax of \$5 per item sold. How much does it produce, and at what price? How do you know? Demand Total Cost P Q TR MR Q TC MC 20 1 20 20 1 10 10 18 2 36 16 2 25 15 15 3 45 9 3 45 20 12 4 48 3 4 70 25 8 5 40 -8 5 100 30 Produce a quantity of 2. Then TR = 36, TC = 25, and profit = 11. 1

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c. Suppose, instead, that the firm is subject to a tax of \$20 per month, regardless of how much it produces. How much does it produce, and at what price? How do you know? Demand Total Cost P Q TR MR Q TC MC 0 0 0 20 20 1 20 20 1 25 5 18 2 36 16 2 35 10 15 3 45 9 3 50 15 12 4 48 3 4 75 20 8 5 40 -8 5 95 25 Produce a quantity of 2. Then TR = 36, TC = 35, and profit = 1. d. Suppose, instead, that the firm is subject to a tax of \$25 per month, regardless of how much ir produces. How much does it produce, and at what price? How do you know? Demand Total Cost P Q TR MR Q TC MC 0 0 0 25 20 1 20 20 1 30 5 18 2 36 16 2 40 10 15 3 45 9 3 55 15 12 4 48 3 4 75 20 8 5 40 -8 5 100 25 If the firm can avoid paying the tax, then it will produce nothing (Q=0) and owe nothing. If they have to pay the tax even if they produce nothing, then they will produce 2 units since a loss of \$4 at Q=2 is better than a loss of \$25 at Q=0. (HINT: You have to figure out MR and MC before you can answer these questions. MC may or may not change between parts a, b, c, and d.) 2
2. On the graph below, label the points where: i. marginal product is highest ii. AP = MP iii. MP = 0 3. Amalgamated SteelWorks has the following production function: Q = (0.25×K×L) 1/2 (which can be written equivalently as Q = 0.25 1/2 ×K 1/2 ×L 1/2 ) (note: X 1/2 = X ) The wage rate is \$60 and the rental rate of capital is \$200. In the short run, the firm has rented 400 units of capital.

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