Chapter 13
13
THE COSTS OF PRODUCTION
Problems and Applications 1.
a. opportunity cost; b. average total cost; c. fixed cost; d. variable cost; e. total cost; f. marginal cost.
2.
a.
The opportunity cost of something is what must be forgone to acquire it.
b.
The opportunity cost of running the hardware store is $550,000, consisting of $500,000 to rent the store and buy the stock and a $50,000 opportunity cost, since your aunt would quit her job as an accountant to run the store. Since the total opportunity cost of $550,000 exceeds revenue of $510,000, your aunt should not open the store, as her profit would be negativeshe would lose money.
a.
The lump sum tax is a fixed cost for any producer who chooses to remain in business for the year. The average fixed cost and average total cost curves shift. Figure 7 shows these changes.
3.
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Chapter 13/The Costs of Production
Costs
ATC2 ATC1
AFC2 AFC1 Quantity of Hamburgers Figure 7 b.
The per-unit tax increases both marginal and average variable costs. Figure 8 shows the shifts in the two curves.
Chapter 13/The Costs of Production
Costs MC2
AVC2
MC1 AVC1 $1
Quantity of Hamburgers Figure 8 4.
a. Hours 0 1 2 3 4 5 b.
The following table shows the marginal product of each hour spent fishing: Fish 0 10 18 24 28 30
Fixed Cost $10 10 10 10 10 10
Variable Cost $0 5 10 15 20 25
Total Cost $10 15 20 25 30 25
Marginal Product --10 8 6 4 2
Figure 9 graphs the fisherman's production function. The production function becomes flatter as the number of hours spent fishing increases, illustrating diminishing marginal product.
Figure 9
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Chapter 13/The Costs of Production c.
The table shows the fixed cost, variable cost, and total cost of fishing. Figure 10 shows the fisherman's total-cost curve. It slopes up because catching additional fish takes additional time. The curve is convex because there are diminishing returns to fishing timeeach additional hour spent fishing yields fewer additional fish.
Figure 10 5.
Here is the table of costs: Workers
Output
0 1 2 3 4 5 6 7
0 20 50 90 120 140 150 155
Marginal Product --20 30 40 30 20 10 5
Total Cost $200 300 400 500 600 700 800 900
Average Total Cost --$15.00 8.00 5.56 5.00 5.00 5.33 5.81
Marginal Cost --$5.00 3.33 2.50 3.33 5.00 10.00 20.00
a.
See table for marginal product. Marginal product rises at first, then declines because of diminishing marginal product.
b.
See table for total cost.
c.
See table for average total cost. Average total cost is U-shaped. When quantity is low, average total cost declines as quantity rises; when quantity is high, average total cost rises as quantity rises.
d.
See table for marginal cost. Marginal cost is also U-shaped, but rises steeply as output increases. This is due to diminishing marginal product.
e.
When marginal product is rising, marginal cost is falling, and vice versa.
f.
When marginal cost is less than average total cost, average total cost is falling; the cost of the last unit produced pulls the average down. When marginal cost is greater than average total cost, average total cost is rising; the cost of the last unit produced
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pushes the average up. Marginal cost equals average total cost at minimum average total cost. 6.
a.
See table for total cost. Since average variable cost = 5Q, total variable cost = 5Q2. Total cost = $100 + 5Q2. Output
Total Fixed Cost $100 100 100 100 100 100 100 100 100 100 100
0 1 2 3 4 5 6 7 8 9 10 b.
Total Variable Cost
Total Cost
$0 5 20 45 80 125 180 245 320 405 500
$100 105 120 145 180 225 280 345 420 505 600
Average Total Cost $105 60 48.3 45 45 46.7 49.3 52.5 56.1 60
Marginal Cost $5 15 25 35 45 55 65 75 85 95
See figure 11.
Figure 11
7.
c.
Marginal cost increases with Q. The firm faces diminishing marginal product in its productive process.
a.
The fixed cost is $300, since fixed cost equals total cost minus variable cost.
b. Quantity 0 1
Total Cost $300 350
Variable Cost $0 50
Marginal Cost (using total cost) --$50
Marginal Cost (using variable cost) --$50
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Chapter 13/The Costs of Production 2 3 4 5 6
390 420 450 490 540
90 120 150 190 240
40 30 30 40 50
40 30 30 40 50
Marginal cost equals the change in total cost or the change in variable cost. That is because total cost equals variable cost plus fixed cost and fixed cost does not change as the quantity changes. So as quantity increases, the increase in total cost equals the increase in variable cost and both are equal to marginal cost.
Chapter 13/The Costs of Production 8.
a.
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242
The fixed cost of setting up the lemonade stand is $200. The variable cost per cup is 50 cents.
Figure 12 b.
The following table shows total cost, average total cost, and marginal cost. These are plotted in Figure 12. Quantity 0 1 2 3 4 5 6 7 8 9 10
9.
Total Cost $200 208 216 224 232 240 248 256 264 272 280
Average Total Cost --$208 108 74.7 58 48 41.3 36.6 33 30.2 28
Marginal Cost --$8 8 8 8 8 8 8 8 8 8
The following table illustrates average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC) for each quantity. The efficient scale is 4 houses per month, since that minimizes average total cost. Quantity 0 1 2 3 4 5 6 7
Variable Cost $0 10 20 40 80 160 320 640
Fixed Cost $200 200 200 200 200 200 200 200
Total Cost $200 210 220 240 280 360 520 840
Average Fixed Cost --$200 100 66.7 50 40 33.3 28.6
Average Variable Cost --$10 10 13.3 20 32 53.3 91.4
Average Total Cost --$210 110 80 70 72 86.7 120
243 10
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Chapter 13/The Costs of Production The following table shows average variable cost (AVC), average total cost (ATC), and marginal cost (MC) for each quantity.
a.
Quantity 0 1 2 3 4 5 6 b.
Variable Cost $0 10 25 45 70 100 135
Total Cost $30 40 55 75 100 130 165
Average Variable Cost --$10 12.5 15 17.5 20 22.5
Average Total Cost --$40 27.5 25 25 26 27.5
Marginal Cost --$10 15 20 25 30 35
Figure 13 graphs the three curves. The marginal cost curve is below the average total cost curve when output is less than 4, as average total cost is declining. The marginal cost curve is above the average total cost curve when output is above 4, as average total cost is rising. The marginal cost curve lies above the average variable cost curve.
Figure 13 11.
The following table shows quantity (Q), total cost (TC), and average total cost (ATC) for the three firms:
Quantity 1 2 3 4 5 6 7
Firm A TC ATC 60 60 70 35 80 26.7 90 22.5 100 20 110 18.3 120 17.1
Firm B TC ATC 11 11 24 12 39 13 56 14 75 15 96 16 119 17
Firm C TC ATC 21 21 34 17 49 16.3 66 16.5 85 17 106 17.7 129 18.4
Chapter 13/The Costs of Production
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Firm A has economies of scale since average total cost declines as output increases. Firm B has diseconomies of scale since average total cost rises as output rises. Firm C has economies of scale for output from 1 to 3, then diseconomies of scale for greater levels of output. 12.
The total cost of producing 600 players is 600×$300=$180,000; the total cost of producing 601 players is 601×$301=$180,901. Hence, the marginal cost of producing one more player is $901, which is greater than what the client offers. The offer should not be accepted because it reduces total profit.
THE COSTS OF PRODUCTION
Problems and Applications 1.
a. opportunity cost; b. average total cost; c. fixed cost; d. variable cost; e. total cost; f. marginal cost.
2.
a.
The opportunity cost of something is what must be forgone to acquire it.
b.
The opportunity cost of running the hardware store is $550,000, consisting of $500,000 to rent the store and buy the stock and a $50,000 opportunity cost, since your aunt would quit her job as an accountant to run the store. Since the total opportunity cost of $550,000 exceeds revenue of $510,000, your aunt should not open the store, as her profit would be negativeshe would lose money.
a.
The lump sum tax is a fixed cost for any producer who chooses to remain in business for the year. The average fixed cost and average total cost curves shift. Figure 7 shows these changes.
3.
236
237
✦
Chapter 13/The Costs of Production
Costs
ATC2 ATC1
AFC2 AFC1 Quantity of Hamburgers Figure 7 b.
The per-unit tax increases both marginal and average variable costs. Figure 8 shows the shifts in the two curves.
Chapter 13/The Costs of Production
Costs MC2
AVC2
MC1 AVC1 $1
Quantity of Hamburgers Figure 8 4.
a. Hours 0 1 2 3 4 5 b.
The following table shows the marginal product of each hour spent fishing: Fish 0 10 18 24 28 30
Fixed Cost $10 10 10 10 10 10
Variable Cost $0 5 10 15 20 25
Total Cost $10 15 20 25 30 25
Marginal Product --10 8 6 4 2
Figure 9 graphs the fisherman's production function. The production function becomes flatter as the number of hours spent fishing increases, illustrating diminishing marginal product.
Figure 9
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238
239
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Chapter 13/The Costs of Production c.
The table shows the fixed cost, variable cost, and total cost of fishing. Figure 10 shows the fisherman's total-cost curve. It slopes up because catching additional fish takes additional time. The curve is convex because there are diminishing returns to fishing timeeach additional hour spent fishing yields fewer additional fish.
Figure 10 5.
Here is the table of costs: Workers
Output
0 1 2 3 4 5 6 7
0 20 50 90 120 140 150 155
Marginal Product --20 30 40 30 20 10 5
Total Cost $200 300 400 500 600 700 800 900
Average Total Cost --$15.00 8.00 5.56 5.00 5.00 5.33 5.81
Marginal Cost --$5.00 3.33 2.50 3.33 5.00 10.00 20.00
a.
See table for marginal product. Marginal product rises at first, then declines because of diminishing marginal product.
b.
See table for total cost.
c.
See table for average total cost. Average total cost is U-shaped. When quantity is low, average total cost declines as quantity rises; when quantity is high, average total cost rises as quantity rises.
d.
See table for marginal cost. Marginal cost is also U-shaped, but rises steeply as output increases. This is due to diminishing marginal product.
e.
When marginal product is rising, marginal cost is falling, and vice versa.
f.
When marginal cost is less than average total cost, average total cost is falling; the cost of the last unit produced pulls the average down. When marginal cost is greater than average total cost, average total cost is rising; the cost of the last unit produced
Chapter 13/The Costs of Production
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240
pushes the average up. Marginal cost equals average total cost at minimum average total cost. 6.
a.
See table for total cost. Since average variable cost = 5Q, total variable cost = 5Q2. Total cost = $100 + 5Q2. Output
Total Fixed Cost $100 100 100 100 100 100 100 100 100 100 100
0 1 2 3 4 5 6 7 8 9 10 b.
Total Variable Cost
Total Cost
$0 5 20 45 80 125 180 245 320 405 500
$100 105 120 145 180 225 280 345 420 505 600
Average Total Cost $105 60 48.3 45 45 46.7 49.3 52.5 56.1 60
Marginal Cost $5 15 25 35 45 55 65 75 85 95
See figure 11.
Figure 11
7.
c.
Marginal cost increases with Q. The firm faces diminishing marginal product in its productive process.
a.
The fixed cost is $300, since fixed cost equals total cost minus variable cost.
b. Quantity 0 1
Total Cost $300 350
Variable Cost $0 50
Marginal Cost (using total cost) --$50
Marginal Cost (using variable cost) --$50
241
✦
Chapter 13/The Costs of Production 2 3 4 5 6
390 420 450 490 540
90 120 150 190 240
40 30 30 40 50
40 30 30 40 50
Marginal cost equals the change in total cost or the change in variable cost. That is because total cost equals variable cost plus fixed cost and fixed cost does not change as the quantity changes. So as quantity increases, the increase in total cost equals the increase in variable cost and both are equal to marginal cost.
Chapter 13/The Costs of Production 8.
a.
✦
242
The fixed cost of setting up the lemonade stand is $200. The variable cost per cup is 50 cents.
Figure 12 b.
The following table shows total cost, average total cost, and marginal cost. These are plotted in Figure 12. Quantity 0 1 2 3 4 5 6 7 8 9 10
9.
Total Cost $200 208 216 224 232 240 248 256 264 272 280
Average Total Cost --$208 108 74.7 58 48 41.3 36.6 33 30.2 28
Marginal Cost --$8 8 8 8 8 8 8 8 8 8
The following table illustrates average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC) for each quantity. The efficient scale is 4 houses per month, since that minimizes average total cost. Quantity 0 1 2 3 4 5 6 7
Variable Cost $0 10 20 40 80 160 320 640
Fixed Cost $200 200 200 200 200 200 200 200
Total Cost $200 210 220 240 280 360 520 840
Average Fixed Cost --$200 100 66.7 50 40 33.3 28.6
Average Variable Cost --$10 10 13.3 20 32 53.3 91.4
Average Total Cost --$210 110 80 70 72 86.7 120
243 10
✦
Chapter 13/The Costs of Production The following table shows average variable cost (AVC), average total cost (ATC), and marginal cost (MC) for each quantity.
a.
Quantity 0 1 2 3 4 5 6 b.
Variable Cost $0 10 25 45 70 100 135
Total Cost $30 40 55 75 100 130 165
Average Variable Cost --$10 12.5 15 17.5 20 22.5
Average Total Cost --$40 27.5 25 25 26 27.5
Marginal Cost --$10 15 20 25 30 35
Figure 13 graphs the three curves. The marginal cost curve is below the average total cost curve when output is less than 4, as average total cost is declining. The marginal cost curve is above the average total cost curve when output is above 4, as average total cost is rising. The marginal cost curve lies above the average variable cost curve.
Figure 13 11.
The following table shows quantity (Q), total cost (TC), and average total cost (ATC) for the three firms:
Quantity 1 2 3 4 5 6 7
Firm A TC ATC 60 60 70 35 80 26.7 90 22.5 100 20 110 18.3 120 17.1
Firm B TC ATC 11 11 24 12 39 13 56 14 75 15 96 16 119 17
Firm C TC ATC 21 21 34 17 49 16.3 66 16.5 85 17 106 17.7 129 18.4
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Firm A has economies of scale since average total cost declines as output increases. Firm B has diseconomies of scale since average total cost rises as output rises. Firm C has economies of scale for output from 1 to 3, then diseconomies of scale for greater levels of output. 12.
The total cost of producing 600 players is 600×$300=$180,000; the total cost of producing 601 players is 601×$301=$180,901. Hence, the marginal cost of producing one more player is $901, which is greater than what the client offers. The offer should not be accepted because it reduces total profit.
