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Page 88 a. With Process A, total daily costs of employing labour and capital are $400 [= ($80 x 2 workers) + ($40 x 6 machines)]. With Process B, these costs are $360 [= ($80 x 3 workers) + ($40 x 3 machines)]. Because Process B minimizes daily costs and maximizes productive efficiency, it will be chosen by the owner. b. $400 [= ($80 x 3) + ($40 x 3) + $30 + $10] c. $200 [= (.06 x 10 000) - $400]. d. Implicit costs are $180 [= ($150 + $30)]. Economic costs are $580 [= ($400 + $180)] e. $20 [= ($600 - $580)]. f. No, the owner should not consider closing, since the shop is making a positive economic profit. Page 96 1a. Marginal product is 50 [= (50 – 0)] pots for the first worker, 150 [= (200 – 50)] pots for the second worker, 70 [= (270 – 200)] pots for the third worker, 30 [= (300 – 270)] pots for the fourth worker, and -60 [= (240 – 300)] pots for the fifth worker. b. Marginal product rises when the first and second workers are hired. Marginal product falls and is positive when the third and fourth workers are hired. Marginal product is negative when the fifth worker is hired. c. This is because it becomes increasingly difficult for each of these new workers to raise output given the potter’s fixed inputs. d. Average product is 50 [= (50/1)] pots with one worker, 100 [= (200/2)] pots with two workers, 90 [= (270/3)] pots with three workers, 75 [= (300/4)] pots when four workers are employed, and 48 [= (240/5)] pots when five workers are employed. e. Marginal and average product are the same when the first worker is hired. As marginal product is rising (when the second worker is hired), marginal product is greater than average product. As marginal product falls (when the last three workers are hired), marginal product is less than average product. f. g. Marginal product reaches its peak where diminishing marginal returns set in. Total product rises less rapidly and finally becomes negatively sloped once diminishing marginal returns set in. Average product reaches its maximum where it equals marginal product. Then, because of diminishing marginal returns, with marginal product falling and below average product, average product declines. 2a. Variable costs are $0 at a zero output, $100 at an output of 50 pots, $200 at 200 pots, $300 at 270 pots, and $400 at 300 pots. Total cost is $100 [= ($100 + $0)] at 0 pots, $200 [= ($100 + $100)] at 50 pots, $300 [= ($100 + $200)] at 200 pots, $400 [= ($100 + $300)] at 270 pots, and $500 [= ($100 + $400)] at 300 pots. b. Marginal cost is $2.00 [= ($100 - $0)/(50 – 0)] when moving from 0 to 50 pots; $0.67 [= ($200 - $100)/( 200 – 50)] from 50 to 200 pots; $1.43 [= ($300 - $200)/(270 – 200)] from 200 to 270 pots; $3.33 [= ($400 - $300)/(300 – 270)] from 270 to 300 pots. c. Average fixed cost is $2.00 [= ($100/50) at 50 pots, $0.50 [= ($100/200)] at 200 pots, $0.37 [= ($100/270)] at 270 pots, and $0.33 [= ($100/300)] at 300 pots. Average variable cost is $2.00 [= ($100/50)] at 50 pots, $1.00 [= ($200/200)] at 200 pots, $1.11 [= ($300/270)] at 270 pots, and $1.33 [= ($400/300)] at 300 pots. Average cost is $4.00 [= ($200/50)] at 50 pots, $1.50 [= ($300/200)] at 200 pots, $1.48 [= ($400/270)] at 270 pots, and $1.67 [= ($500/300)] at 300 pots. d. e. Yes. The marginal cost and average variable cost curves are J-shaped, and the average cost curve is bowl-shaped, with the minimum points of both average variable cost and average cost occurring at the curves’ intersection with the marginal cost curve. Page 101 a. The percentage increase in the labour input is 50% [= ((9 – 6)/6)) x 100%] and the percentage increase in the capital input is also 50% [= ((3 – 2)/2)) x 100%], while the percentage increase in output is 100% [= (240 – 120)/120]. Because the relative increase in output exceeds the relative increase in each of the inputs, the business is experiencing increasing returns to scale. Long run average cost falls from $5.33 [= ((6 x $100) + (2 x $20))/120] to $4 [= ((9 x $100) + (3 x $20))/240]. b. The percentage increase in output is 50% [= (180 – 120)/120]. Because the relative increase in output equals the relative increase in each of the inputs, the business is experiencing constant returns to scale. Long run average cost at 120 units is $5.33 [= ((6 x $100) + (2 x $20))/120] and at 180 units is also $5.33 [= ((9 x $100) + (3 x $20))/180]. c. The percentage increase in output is 33% [= (160 – 120)/120]. Because the relative increase in output is less than the relative increase in each of the inputs, the business is experiencing decreasing returns to scale. Long run average cost rises from $5.33 [= ((6 x $100) + (2 x $20))/120] to $6 [= ((9 x $100) + (3 x $20))/160]. |