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**12 >> CHECK YOUR UNDERSTANDING Behind the Supply Curve:**

Inputs and Costs >> Krugman/Wells CHECK YOUR UNDERSTANDING

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**Check Your Understanding 12-1 Question 1**

Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity. The quantity of output, measured in terms of pounds of ice, is given in this table:

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1ai) Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity. The 10-ton machine is a _____ input. fixed variable The 10-ton machine is the fixed input because it doesn’t change with output.

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1aii) Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity. The electricity is a _____ input. fixed variable The electricity is the variable input because it changes with output.

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**1bi) Calculate the marginal product of the third unit of the variable input.**

1000 900 800 600 The marginal product is the increase in output that occurs when the third kilowatt hour is used. Output increases from 1800 pounds to 2400 pounds with the addition of the 3rd kilowatt hour, so its marginal product is 600 pounds.

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1bii) The calculation of all of the marginal products reveals that there are _______ returns to the input. increasing diminishing The production function exhibits decreasing returns to the variable input because each kilowatt adds a smaller amount of ice to the total output.

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**6 kilowatts of electricity**

1ci) Bernie’s ice-making company produces ice cubes using a 10-ton machine and electricity. Suppose a 50% increase in the size of the fixed input increases output by 100% for any given amount of the variable input. What is the fixed input now? the 10 ton machine the 15 ton machine the 20 ton machine 6 kilowatts of electricity If the 10-ton machine increases by 50%, it will be replaced by a 15-ton machine.

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1cii) Suppose a 50% increase in the size of the fixed input increases output by 100% for any given amount of the variable input. Given the original production function, the quantity of ice that can be produced using 2 units of the variable input is _____. 900 1800 2700 3600 If the larger machine increases output by 100%, the output for 2 kilowatts is 3600 (1800x2).

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**Check Your Understanding 12-2 Question 1***

Suppose that the fixed cost of making 10 game day t-shirts is $25, and the variable cost is $50.

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1*) Suppose that the fixed cost of making 10 game day t-shirts is $25, and the variable cost is $50. Calculate average variable cost. $75 $25 $7.50 $5.00 Average variable cost is variable cost ($50) divided by output (10), which is $5.

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1*) Suppose that the fixed cost of making 10 game day t-shirts is $25, and the variable cost is $50. Calculate average total cost. $75 $25 $7.50 $5.00 Average total cost is total cost ($25 + $50) divided by output (10), which is $7.50.

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1*) Suppose that the fixed cost of making 10 game day t-shirts is $25, and the variable cost is $50. Calculate average fixed cost. $25 $2.50 $7.50 $5.00 Average fixed cost is fixed cost ($25) divided by output (10), which is $2.50.

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**Check Your Understanding 12-2 Question 1**

Alicia’s Apple Pies is a roadside business. Alicia must pay $9 in rent each day. In addition, it costs her $1.00 to produce the first pie of the day, and each subsequent pie costs 50% more to produce than the one before. For example, the second pie costs $1.00 × 1.5 = $1.50 to produce, and so on.

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**1ai) Alicia must pay $9 in rent each day. In addition, it costs her $1**

1ai) Alicia must pay $9 in rent each day. In addition, it costs her $1.00 to produce the first pie of the day, and each subsequent pie costs 50% more to produce than the one before. For example, the second pie costs $1.00 × 1.5 = $1.50 to produce, and so on. Calculate Alicia’s marginal cost of the 3rd pie. $1.00 $1.25 $2.25 $3.00 Since each subsequent pie costs 50% more, the third pie costs $2.25 = ($1.50)x(1.5)

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1aii) Calculate Alicia’s variable cost of producing 3 pies (Hint: The variable cost of two pies is just the marginal cost of the first, plus the marginal cost of the second pie, and so on.) $1.58 $3.25 $4.10 $4.75 The variable cost of the third pie is the sum of the marginal cost of the first three pies $1 + $1.50 +$2.25 = $4.75.

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**1aiii) Alicia must pay $9 in rent each day**

1aiii) Alicia must pay $9 in rent each day. In addition, it costs her $1.00 to produce the first pie of the day, and each subsequent pie costs 50% more to produce than the one before. Calculate Alicia’s average fixed cost of producing 3 pies. $1.00 $1.25 $2.25 $3.00 Average fixed cost is fixed cost ($9) divided by output (3).

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**1aiv) Calculate Alicia’s average variable cost of producing 3 pies.**

$1.58 $3.25 $4.10 $4.75 Average variable cost is variable cost divided by output, $4.75/3 = $1.58

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**1av) Calculate Alicia’s average total cost of producing 3 pies.**

$1.58 $3.25 $4.10 $4.58 Average total cost is average fixed cost ($3.00) plus average variable cost ($1.58) = $4.58

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**1bi) The spreading effect dominates the range of output from _____ .**

4.28 0 to 3 1 to 4 2 to 5 5 to 6 The spreading effect dominates the diminishing returns effect when average total cost is falling; the falling AFC dominates the rise in AVC for pies 1 to 4. 4

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**1bii) The diminishing returns effect dominates the range of output from _____ .**

4.28 0 to 3 1 to 4 2 to 5 5 to 6 The diminishing returns effect dominates when average total cost is rising; the rise in AVC dominates the fall in AFC for pies 5 and 6.

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**1ci) What is Alicia’s minimum cost output?**

4.28 4 1 pie 2 pies 4 pies 5 pies The minimum cost output is where average total cost is a minimum, at $4.28 when 4 pies are produced.

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1cii) Making one more pie raises average total cost when output is greater than 4 pies because the marginal cost of the 5th pie is less than the average total cost of the first four pies. 4.28 4 True False Average total cost increases because the marginal cost of the fifth pie ($5.06) is greater than the average cost of the first four pies.

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**Check Your Understanding 12-3 Question 1**

The table below shows three combinations of fixed and average variables cost. Use it to answer the following questions.

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**1ai) For Choice 1 what is the average total cost of producing 12,000 units?**

$1.80 $1.67 $1.00 Average total cost is average fixed cost ($8000/$12,000) = $0.67 plus average variable cost ($1) = $1.67

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**1aii) Which choice leads to the lowest average total cost of producing 12,000 units?**

The average total cost of producing 12,000 units is lowest for choice 1 at $1.67.

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**1aiii) Which choice leads to the lowest average total cost of producing 22,000 units?**

The minimum average total cost for 22,000 units is $1.30, choice 2.

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**1aiv) Which choice leads to the lowest average total cost of producing 30,000 units?**

Choice 3 is the lowest average total cost for 30,000 at $1.05.

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**1bi) Suppose that a firm has the choices 1, 2, and 3**

1bi) Suppose that a firm has the choices 1, 2, and 3. Historically they have produced 12,000 units. Suddenly, demand increases sharply leading to a permanent change in production for the firm from 12,000 units to 22,000 units. In the short run we expect that the firm will produce using ______. Choice 1 Choice 2 Choice 3 If the firm was producing 12,000 units, it would be using choice 1, which has the lowest average total cost, $ If output increases to 22,000, in the short run there isn’t enough time to increase the fixed input.

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**1bii) Suppose that a firm has the choices 1, 2, and 3**

1bii) Suppose that a firm has the choices 1, 2, and 3. Historically they have produced 12,000 units. Suddenly, demand increases sharply leading to a permanent change in production for the firm from 12,000 units to 22,000 units. The average cost of production in the short run is _______. $1.67 $1.75 $1.36 $1.30 In the short-run, the fixed input can’t be changed, so the firm has to use choice 1, which has an average total cost of $1.36 for 22,000 units.

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**1biii) Suppose that a firm has the choices 1, 2, and 3**

1biii) Suppose that a firm has the choices 1, 2, and 3. Historically they have produced 12,000 units. Suddenly, demand increases sharply leading to a permanent change in production for the firm from 12,000 units to 22,000 units. In the long run we expect that the firm will produce using ______. Choice 1 Choice 2 Choice 3 In the long run, the firm can change the fixed input and would use choice 2 where average total cost is $1.30 for 22,000 units.

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**1biv) Suppose that a firm has the choices 1, 2, and 3**

1biv) Suppose that a firm has the choices 1, 2, and 3. Historically they have produced 12,000 units. Suddenly, demand increases sharply leading to a permanent change in production for the firm from 12,000 units to 22,000 units. The average cost of production in the long run is _______. $1.67 $1.75 $1.36 $1.30 In the long run, the firm can change the fixed input and would use choice 2 where average total cost is $1.30 for 22,000 units.

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**Check Your Understanding 12-3 Question 2**

For the following cases, choose the kind of scale effects you would expect.

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**constant returns to scale**

2a) A telemarketing firm in which employees make sales calls using computers and telephones. diseconomies of scale economies of scale constant returns to scale To increase output the firm must hire more workers, purchase more computers, and pay additional telephone charges. Because these inputs are easily available, their long-run average cost is unlikely to change as output increases.

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**constant returns to scale**

2b) An interior design firm in which design projects are based on the expertise of the firm’s owner. diseconomies of scale economies of scale constant returns to scale This firm will experience decreasing returns to scale. As the firm takes on more projects, the costs of communication and coordination required to implement the expertise of the firm’s owner are likely to increase.

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**2c) A diamond-mining company**

diseconomies of scale economies of scale constant returns to scale This firm is likely to experience increasing returns to scale. Because diamond mining requires a large initial set-up cost for excavation equipment, long-run average total cost will fall as output increases.

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