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OUTPUT AND COSTS

C h a p t e r K e y I d e a sThe ATM is Everywhere!

A. Why are banks replacing teller windows with ATMs?B. Why do auto-makers have unused production capacity while

electric utilities can’t always produce enough to meet demand?C. This chapter studies a firm’s production possibilities and the costs

of production.

O u t l i n eI. Decision Time Frames

A. The firm makes many decisions in order to achieve its main objective: profit maximization.

21. Some decisions are relatively critical to the survival of the firm,

or are irreversible (or very costly to reverse).2. Other decisions are easily reversible or are much less critical to

the survival of the firm (but still influence profitability).B. The Short Run

1. The short run is a time frame in which the quantities of some resources are fixed.

2. Some resources used by the firm are fixed in quantity (such as technology, buildings, capital) in the short run. This set of resources is called the firm’s plant. In the short run, a firm’s plant is fixed.

3. Other resources used by the firm vary with output (such as labor, raw materials, energy). In the short run, to increase output the firm must increase the quantity of variable inputs it uses.

C. The Long Run1. The long run is a time frame in which the quantities of all

resources can be varied. This means that the firm can change its plant size, as well as the quantity of all its other resources in the long run.

2. Long-run decisions are not easily reversed.3. Sunk costs are costs incurred by the firm and cannot be

changed. The firm’s investment in its plant is a sunk cost. Sunk costs are irrelevant to a firm’s decisions.

II. Short-Run Technology ConstraintA. To increase output in the short run, a firm must increase the

quantity of labor employed. B. Product Schedules

Three concepts describe the relationship between output and the quantity of labor employed.1. Total product, which is the maximum output that a given

quantity of labor can produce.2. Marginal product of labor, which is the increase in total

product that results from a one-unit increase in the quantity of labor employed with all other inputs remaining the same.

3. Average product of labor, which equals total product divided by the quantity of labor employed.

4. Table 10.1 shows an example of total product, marginal product, and average product for a firm that produces sweaters.

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W H A T I S E C O N O M I C S ? 3C. Product Curves

Produce curves are graphs of the three product concepts that show how total product, marginal product, and average product change as the quantity of labor employed changes.

D. Total Product Curve The total product curve shows how the total product increases with the level of labor employed. 1. The total product curve is similar to the PPF because it

separates attainable output levels from unattainable output levels in the short run.

2. Figure 10.1 shows a total product curve.

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E. Marginal Product CurveThe marginal product of labor curve shows the change in total product for each unit of labor employed. 1. The total and marginal product curves are related.

a) The height of the marginal product curve is the slope of the total product curve.

b) Figure 10.2 shows the relationship between the marginal product of labor curve and the total product curve.

2. When the marginal product of an additional worker exceeds the marginal product of the previous worker, the marginal product of labor curve rises as the quantity of labor increases. The firm experiences increasing marginal returns.

3. When the marginal product of an additional worker is less than the marginal product of the previous worker, the marginal product of labor curve falls as the quantity of labor increases. The firm experiences diminishing marginal returns, which occurs when the marginal product of an additional worker is less than the marginal product of the previous worker.a) Diminishing marginal returns arises from the fact that

employing additional units of labor means each worker has less access to capital and less space in which to work.

4. The law of diminishing returns states that as a firm uses more of a variable input with a given quantity of fixed inputs, the marginal product of the variable input eventually diminishes.

F. Average Product CurveThe marginal product of labor curve and the average product curve have the relationship shown in Figure 10.3:1. When the marginal product of

labor exceeds the average product of labor, the average product increases when the quantity of labor increases.

2. When the marginal product of labor is less than the average product of labor, the average product decreases when the quantity of labor increases.

3. The marginal product curve intersects the average product curve at the point of maximum average product.

4. The relationship between a student’s marginal class grade and the student’s grade point average (GPA) is similar to that between marginal product and average product. a) If the grade in another class is higher than the student’s GPA,

this marginal grade will pull the student’s GPA up.b) If the grade in another class is less than the student’s GPA, this

marginal grade will pull the student’s GPA down.c) If the grade in another class is the same as the student’s GPA,

the GPA will be unchanged.

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III. Short-Run CostA. To produce more output in the

short run, the firm must employ more labor, which means that it must increase its costs. These costs can be described in a way that relates cost with output.

B. Total Cost1. A firm’s total cost (TC) is

the cost of all the factors of production it uses.

2. Total fixed cost (TFC) is the cost of the firm’s fixed inputs. Fixed costs do not change with output.

3. Total variable cost (TVC) is the cost of the firm’s variable inputs. Variable costs change with output.

4. Total cost equals total fixed cost plus total variable cost, or TC = TFC + TVC.

5. Figure 10.4 shows TFC, TVC and TC curves.

B. Marginal Cost1. Marginal cost (MC) is the

increase in total cost that results from a one-unit increase in output.

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C. Average CostThere are three average cost measures:1. Average total cost (ATC) is total cost per unit of output.2. Average fixed cost (AFC) is total fixed cost per unit of output.3. Average variable cost (AVC) is total variable cost per unit of

output.4. Average total cost equals average fixed cost plus average variable

cost, or ATC = AFC + AVC.5. Table 10.2 provides a complete glossary of cost terms.

6. The value of MC, ATC, and AVC cost measures are related:a) When MC is below AVC, AVC falls as output increases. When MC

is above AVC, AVC rises as output increases. And the MC curve intersects the AVC curve at its lowest point.

b) When MC is below ATC, ATC falls as output increases. When MC is above ATC, ATC rises as output increases. And the MC curve intersects the ATC curve at its lowest point.

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c) Figure 10.5 shows the MC, AFC, AVC, and ATC curves.

D. Why the Average Total Cost Curve is U-Shaped1. ATC is the sum of AFC and AVC. Initially the ATC curve slopes

downward because both the AFC and AVC curves slope downward. Eventually at some level of output, diminishing returns mean that as output increases, AVC increases. When AVC slopes upward enough, it offsets the downward slope of the AFC curve so that the ATC curve slopes upward.

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E. Cost Curves and Product CurvesThe shapes of a firm’s cost curves are determined by the technology it uses.1. Figure 10.6 shows the

relationships between MC and the marginal product of labor and also the relationship between AVC and the average product of labor.

2. When the marginal product curve is at its maximum, the marginal cost is at its minimum. So when the marginal product curve is rising, the MC curve is falling and when the marginal product curve is falling, the MC curve is rising.

3. When the average product of labor is at its maximum, the AVC is at its minimum. So then the average product of labor curve is rising, the AVC curve is falling and when the average product of labor curve is falling, the AVC curve is rising.

F. Shifts in Cost Curves1. Technological change

influences both the productivity curves and the cost curves.a) A technological change that increases productivity shifts the

average and marginal product curves upward and the average and marginal cost curves downward.

b) If a technological advance requires more capital and less labor to be used, fixed costs increase and variable costs decrease. The average total cost increases at low levels of output and decreases at high levels of output.

2. Changes in the prices of resources shift the cost curves.a) An increase in a fixed cost shifts the total cost (TC) curve and

the average total cost (ATC) curve upward but does not shift the marginal cost (MC) curve.

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b) An increase in a variable cost shifts the total cost (TC) curve, the average total cost (ATC) curve, and the marginal cost (MC) curve upward.

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IV. Long-Run CostA. In the long run, all inputs levels are variable, the firm incurs no fixed

cost to production, and all costs are variable. B. The Production Function

1. The behavior of long-run cost depends upon the firm’s production function, which is the relationship between the maximum output attainable and the quantities of both capital and labor.

2. Table 10.3 shows a production function.

3. The marginal product of capital is the change in total product divided by the change in capital when the quantity of labor is constant.a) The amount of capital a

firm employs determines its plant size.

b) Typically, a firm’s production function exhibits diminishing marginal product of labor (for a given plant size) as well as diminishing marginal product of capital (for a given quantity of labor).

c) For each plant size, the diminishing marginal product of labor creates a set of short run, U-shaped costs curves for MC, AVC, and ATC.

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C. Short-Run Cost and Long-Run Cost1. The average cost of producing a given output varies and depends

on the firm’s plant size.a) The larger the plant size, the greater is the output at which ATC

is at a minimum.b) The firm can compare the ATC for each given output at different

plant sizes. Figure 10.7 shows a set of four ATC curves, each representing the four possible plant sizes. Only one plant size delivers the minimum ATC for each output.

2. The long-run average cost curve (LRAC) is the relationship between the lowest attainable ATC and output when both the plant size and labor are varied.a) The LRAC curve is a planning curve; it shows the minimum

possible ATC the firm can attain for any given level of output. So for any level of output the firm may choose to produce, the LRAC tells the plant size and quantity of labor that will minimize cost.

c) Once the firm has chosen its plant size, the firm will incur costs corresponding the ATC curve associated with that plant size.

E. Economies and Diseconomies of Scale1. The long-run average cost curve is influenced by the firm’s

technology.a) Economies of scale are features of a firm’s technology that

lead to falling long-run average cost as output increases. As plant size increases, the minimum attainable ATC falls and the LRAC curve slopes downward. Economies of scale occur when the percentage increase in output exceeds the percentage increase in inputs.

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b) Diseconomies of scale are features of a firm’s technology that lead to rising long-run average cost as output increases. As plant size increases, the minimum attainable ATC rises and the LRAC curve slopes upward. Diseconomies of scale occur when the percentage increase in output is less than the percentage increase in inputs.

c) Constant returns to scale are features of a firm’s technology that lead to constant long-run average cost as output increases. As plant size increases, the minimum attainable ATC remains constant and the LRAC curve is horizontal. Constant returns to scale occur if the percentage increase in output equals the percentage increase in inputs.

2. A firm experiences economies of scale up to some output level. Beyond that output level, it has constant returns to scale which is then followed by diseconomies of scale.a) Minimum efficient scale is the smallest quantity of output at

which the long-run average cost reaches its lowest level.b) If the long-run average cost curve has the typical U shape, the

minimum point identifies the minimum efficient scale output level.

R e a d i n g B e t w e e n t h e L i n e sA news article reveals that banks are closing human teller windows and replacing them with ATMs. An analysis of the short-run and long-run average total cost curves is explored for the two different technologies for supplying teller services.

N e w i n t h e S e v e n t h E d i t i o nThere are no significant changes to this chapter.

Te a c h i n g S u g g e s t i o n s1. The big picture. Stand back from the details of this chapter and be sure

that your students learn two big ideas: A firm’s lowest production costs depend on the manager’s flexibility to

choose the level of all inputs. This flexibility enables firm managers to produce at a lower cost than is possible in the short run when some inputs are fixed.

In the short run, with one or more fixed inputs, production costs vary with output in a predictable way because they are directly linked to measures of input productivity.

2. Lots of definitions and terminology can cloud the primary message. Make good use of the glossary of productivity and cost terms provided in Table 10.2 but don’t get mired down in reciting productivity

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and cost measure definitions! Students must learn the definitions, but they are secondary to the concepts they define and the insights they bring.

3. Focus on why productivity measures and cost measures are useful for decision making: Firm managers must frequently make quick decisions with little information. If managers have knowledge of a useful relationship between input measures (which are relatively easy to get) and production cost measures (which are more difficult to get—especially marginal cost figures) they can use their understanding of this link to make inferences about how production costs might behave when the firm’s output must change to accommodate market changes.

4. The marginal pulls (but cannot not push) the average. Don’t let the students fall into the trap of thinking that if the marginal measure rises (falls) with the level of an activity, then the average measure must also rise (fall). This is a sloppy statement of the relationship between marginal and average measures. Use the tried-and-true grade point average (GPA) example used in the text. Explain that if a student’s GPA is a 3.5 and their next marginal class grade is a C (2.0), followed by a B (3.0), this increasing marginal grade will not be pushing their GPA up at all. Conceptually, the students should understand that the marginal value can’t “push” the average measure higher when it is, itself, lower than the average measure. The marginal measure must be higher (lower) than the average value if the average value is to rise (fall) with the level of activity, thereby “pulling” the average from its position of higher (or lower) than the average.

4. Learn about production by producing. This chapter is one more place where an in-class experiment has a huge payoff in student comprehension. This 30 minute experiment teaches students about product curves and production cost measures. It motivates the students to go beyond memorizing the cost and productivity definitions by getting them directly involved with generating their own data as well as productivity and cost measures. This fun exercise will illustrate the concept of diminishing returns to labor as well as how short-run productivity measures and production cost measures are related. Inputs: Capital: A medium sized table (the class must have an

unobstructed view of it), tear-off scratch pads with about 500 sheets of paper, a fully loaded stapler, a back-up stapler (also fully loaded), a spreadsheet (that you can download from your Parkin Instructor’s Web site). Labor: Provided by your students.

The Task: To produce “widgets.” A widget is a piece of paper, torn from a pad, folded twice very carefully so that the corners of the paper align, and stapled. (The first fold bisects the paper along its long side and the second fold is at right angles to the first.) Once folded, it is stapled to hold the folds in place. A widget is fragile and breaks if it falls off the table.

The Pre-Experiment Stage: Hire a manager from your class and appoint an auditor. (Have some jokes about Enron and Andersen.) Get the manager to hire a quality controller, an accountant, and some workers. Tell the manager that he must produce widgets as efficiently

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as possible and that he can discuss the process with his workers and with the class.

The Experiment: A “work day” lasts for 1 minute. Get the class to keep time. On day 1, have one worker produce widgets. On day 2, have two workers produce widgets, and so on. You’ll probably run for 10 to 12 days before you get to almost zero marginal product. Record the inputs and outputs in a spreadsheet. Have some fun with quality control, shirking, and cheating. The auditor must ensure that old widgets and partly made widgets don’t get used in a subsequent day. Each day must start clean.

The Assignment (Stage 1): Get the students to calculate marginal product and average product from the total product numbers that you’re recorded in the spreadsheet. Get them to make graphs of the total product, marginal product, and average product curves. Get them to describe the curves and to explain their similarities with and differences to the curves for sweater production in the textbook.

The Assignment (Stage 2). Use the data from your widget production experiment and give the students figures for the cost of the capital and the wage rate of a worker. (Make up the numbers—any will do.) Tell the students to calculate total cost, marginal cost, and average cost. Get them to make graphs of the total cost, marginal cost, and average cost curves. Get them to describe the curves and to explain their similarities with and differences to the curves for sweaters in the textbook. (This assignment and the previous one make an outstanding assignment for credit.)

The Experiment Extended. If you have the time, duplicate the capital of the first experiment and repeat all its steps. You should generate a horizontal LRAC. Get the class to think about what would have to happen in the context of this experiment to get economies of scale and diseconomies of scale.

3. Relation between TP and TVC. Make a graph of a TP curve on a transparency. Label the x-axis labor and the y-axis output. Put some actual numbers on the labor axis (use 1, 2, 3, 4, and 5 labor units) and tell the students that the price of a unit of labor $10. Next, change the label on the x-axis to TVC and ask the students to tell you the numbers to put on the x-axis now that it measures TVC (the numbers will now be $10, $20, $30, $40 and $50). Once the students are really clear about what you have done, pick up the transparency, turn it over, and replace it on the display base with what was previously the x-axis (TVC) running vertically. Point out that the students are now looking at a TVC curve. Emphasize that all the product curves can be derived from the TP curve and all the cost curves can be derived from the TVC curve.

4. Short-Run Costs: The Relationships between Productivity and Production Cost. Explain to the students the usefulness of understanding the intuition behind the relationship between productivity measures and production cost measure. For example: If a firm manager knows that average productivity of labor has been

falling with the last additional quantity of labor hired, then she knows

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that the average variable cost (AVC) of production has necessarily been rising as the output from that additional labor has increased.

If she knows that AVC is rising as output increases, then she also knows that the marginal cost (MC) of the additional output has been higher than the AVC (which has been pulling AVC up).

If the firm manager has sold the previous units of output at a small profit, she may be faced with a time-sensitive contractual opportunity that arises within the same short run time period. She may be asked to sell a little more output at the same market price as her previous sales. The manager can quickly infer that the profitability of this potential new contract will not be as high because the marginal cost of producing the extra output will be higher than the last units of output produced. She can infer this through productivity-cost relationships rather than knowing marginal costs directly.

5. Long-Run Costs: The firm’s transition between the short run and long run revolves around the commitments made by the firm. Be sure the students realize that accurate forecasting of market demand for a firm’s product is key to profitability, since it must make the proper long-run commitment to a given plant size. Show the students that if faulty market analysis causes a firm to commit to a plant that is too small (or too large) when the required range of production is actually relatively high (or relatively low), then the firm will suddenly be locked into a much less competitive production cost situation with potentially dire economic consequences.

T h e B i g P i c t u r eWhere we have been:

This chapter has explained how the firm’s output decision affects its costs when the firm allocates its resources efficiently in the short run and in the long run. The student sees how establishing short-run productivity and cost measures and understanding how they are related reveals how a firm can predict how its production costs will change with the level of output. This relationship helps firm managers make profitable output decisions in the short run and make commitments to efficient plant size in the long run.

Where we are going:Chapters 11, 12, and 13 use the productivity and cost relationships to explain how firms make decisions in competitive, monopoly, and other market structures. Chapter 17 uses these same ideas to explain how firms decide how much labor and capital to use.

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O v e r h e a d Tr a n s p a r e n c i e sTransparenc

yText figure Transparency title

59 Figure 10.2 Total Product and Marginal Product60 Figure 10.3 Average Product61 Figure 10.5 Marginal Cost and Average Costs 62 Figure 10.6 Product Curves and Cost Curves63 Figure 10.7 Short-Run Costs of Four Different Plants64 Figure 10.8 Long-Run Average Cost Curve65 Table 10.2 A Compact Glossary of Costs

E l e c t r o n i c S u p p l e m e n t sMyEconLabMyEconLab provides pre- and post-tests for each chapter so that students can assess their own progress. Results on these tests feed an individualized study plan that helps students focus their attention in the areas where they most need help. Instructors can create and assign tests, quizzes, or graded homework assignments that incorporate graphing questions. Questions are automatically graded and results are tracked using an online grade book.

PowerPoint Lecture NotesPowerPoint Electronic Lecture Notes with speaking notes are available and offer a full summary of the chapter.PowerPoint Electronic Lecture Notes for students are available in MyEconLab.

Instructor CD-ROM with Computerized Test BanksThis CD-ROM contains Computerized Test Bank Files, Test Bank, and Instructor’s Manual files in Microsoft Word, and PowerPoint files. All test banks are available in Test Generator Software.

A d d i t i o n a l D i s c u s s i o n Q u e s t i o n s11. Is the law of diminishing returns a result of firms hiring the best

workers first? Students should understand that diminishing returns to labor occur under the assumption of a homogenous work force. Emphasize that diminishing marginal returns occurs due to labor’s increasing inaccessibility to a fixed level of capital.

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2. Do increasing marginal costs result from the rising wages of workers? Students should understand that rising marginal cost in the short run results from diminishing marginal productivity of labor holding the wages for labor constant. Show the students the following thought process: Employing another labor unit increases output, but the extra output is

less than the added output from the previous labor unit (diminishing marginal productivity).

Each labor unit costs the same to employ, so the firm is getting less additional output for the same additional cost (constant cost of labor).

As a result, each additional unit of output is more expensive for the firm to make than the previous units of output (rising marginal cost).

3. Fixating on fixed costs. Students should be aware of how fixed costs affect pricing decisions made by firms: Why are some consumer products cheaper to buy in bulk? The

students should be aware that if packaging costs comprise a significant proportion of the total production cost of an item, then an increase in the ratio of product to packaging lowers the production cost per unit. The firm can be more competitive and still retain profitability if it passes some of the savings on to the customer through a lower unit price.

Why do businesses offer “Buy one, get one for half price” sales when they could just sell each unit separately for 1/3 off the usual sale price? If part of the cost of each sale is fixed (for example, id sales personnel is not correlated with quantity sold), then the firm can spread the fixed costs out over more units, lowering the per-unit cost of production. The firm can be more competitive and still retain profitability if it passes some of these cost savings on to the customer through a lower unit price.

What is the difference between increasing unit costs due to diminishing returns to labor and increasing unit costs due to diseconomies of scale? Students should recognize that a rising unit cost of production could result from managerial constraints arising from short-run situations (diminishing returns due to labor’s decreasing access to capital) or from technological constraints in long-run situations (technology limitations frustrate a firm’s attempts to exploit economies from larger plant sizes).

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A n s w e r s t o t h e R e v i e w Q u i z z e sPage 222

1. Initially, as the quantity of labor is increased, the firm will experience increasing marginal returns. Eventually, the firm will experience diminishing marginal returns.

2. The law of diminishing returns states that, as a firm uses more of a variable input with a given quantity of fixed inputs, the marginal product of the variable input eventually diminishes. Diminishing marginal returns arises from the fact that ever more workers are using the same capital and working in the same space.

3. Initially, as the quantity of labor is increased, the firm will experience increasing returns and the marginal product of labor will increase with labor. Since the marginal product of labor is higher than the average product over this range of labor, the average product of labor will increase with labor. Eventually, diminishing marginal returns causes the marginal product of labor to fall. When the marginal product of labor falls below the average product, and average product will decrease with labor.

Page 2271. The value of marginal cost (MC), average total cost (ATC) and average

variable cost (AVC) are all related in the short run: When the value of MC is lower (higher) than AVC, AVC falls (rises) with

output. This implies that as output increases, the MC curve cuts through the AVC curve at its lowest point.

When the value of MC is lower (higher) than ATC, ATC falls (rises) with output. This implies that as output increases, the MC curve cuts through the ATC curve at its lowest point.

2. Initially, the ratio of increase to output to increase in cost will fall, and marginal cost declines with output. Eventually, the ratio of increase to output to increase in cost will rise, and marginal cost increases with output.

3. Decreasing marginal returns means the additional labor unit employed increases output by less than the previous unit. Since the price per labor unit remains unchanged, the ratio of increased output to increased cost will fall, and marginal cost of the additional output will rise.

4. Average fixed cost (AFC) equals total fixed cost divided by total product. As output increases, the fixed costs (which do not change with output) are spread out over a larger and larger quantity of output, and its value decreases. This makes the AFC curve continually decreasing with output.

5. The average variable cost (AVC), and average total cost (ATC) curves are both U-shaped as output increases.

The marginal cost (MC) curve reflects how total cost changes with output. If the MC curve is below the AVC curve, AVC falls with output. Diminishing marginal returns means that eventually the MC curve

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increases with output. At some point the MC eventually becomes higher than the AVC, after which the AVC rises with output.

ATC is the sum of average fixed cost (AFC) and AVC. Initially the ATC curve will fall with output because the AFC is initially quite large, but drops rapidly as total fixed costs are spread over greater levels of output. However, diminishing returns causes marginal product to fall below the average product, causing the average product to fall with labor. This causes AVC to rise with output. If AVC rises with output more quickly than AFC falls, then the ATC curve will rise with output.

Page 2311. A firm’s production function is the relationship between the maximum

output attainable and the quantities of both capital and labor used to produce it. The total product curve relates how output increases with input, for a given plant size.

2. The marginal product of capital is the change in the total product when adding one more unit of capital, holding the level of labor constant. A given level of labor input will benefit from having access to more capital. Then labor becomes more productive and can increase output. Eventually, labor’s access to ever more units of capital becomes less and less useful, as there are fewer labor units to be combined with any given unit of capital for production. This means each additional unit of capital contributes less and less additional units of output, resulting in diminishing returns to capital.

3. The long-run average cost curve (LRAC) is the relationship between the lowest attainable ATC and output when both plant size and labor are varied. The LRAC curve reflects the minimum possible ATC the firm can attain for any given level of output. For any level of output the firm may choose to produce, the LRAC reflects the lowest possible ATC taken from an ATC curve that corresponds to a particular plant size. Once the firm has chosen that plant size, it will incur production costs corresponding the ATC curve associated with that plant size.

4. Economies of scale are features of a firm’s technology that lead to falling long-run average cost (LRAC) as output increases. As plant size increases, minimum attainable average total cost (ATC) for each plant size falls with output. Diseconomies of scale are features of a firm’s technology that lead to rising LRAC as output increases. As plant size increases, minimum attainable ATC for each plant size rises with output. A firm initially experiences economies of scale up to some output level and over this range of output the LRAC curve falls with output. Beyond that output level, it may move towards diseconomies of scale. When there are diseconomies of scale, the LRAC rises with output, resulting in a U-shaped LRAC curve.

5. Minimum efficient scale is the smallest quantity of output at which the long-run average cost reaches its lowest level. If the long-run average cost curve has the typical U shape, the minimum point of the LRAC identifies the level of output that represents the firm’s minimum efficient scale.

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A n s w e r s t o t h e P r o b l e m s1. a. To draw the total product curve measure labor on the x-axis and output

on the y-axis. The total product curve is upward sloping.b. The average product of labor is equal to total product divided by the

quantity of labor employed. For example, when 3 workers are employed, they produce 6 boats a week, so the average product is 2 boats per worker.The average product curve is upward sloping when the number of workers is between 1 and 8, but it becomes downward sloping when 9 and 10 workers are employed.

c. The marginal product of labor is equal to the increase in total product when an additional worker is employed. For example, when 3 workers are employed, total product is 6 boats a week. When a fourth worker is employed, total product increases to 10 boats a week. The marginal product of going from 3 to 4 workers is 4 boats.The marginal product curve is upward sloping when up to 5.5 workers a week are employed and downward sloping when more than 5.5 workers a week are employed.

d. (i) When Rubber Dinghies produces fewer than 30 boats a week, it employs fewer than 8 workers a week. With fewer than 8 workers a week, marginal product exceeds average product and average product is increasing. Up to an output of 30 boats a week, each additional worker adds more to output than the average. Average product increases.

(ii) When Rubber Dinghies produces more than 30 boats a week, it employs more than 8 workers a week. With more than 8 workers a week, average product exceeds marginal product and average product is decreasing. For outputs greater than 30 boats a week, each additional worker adds less to output than average. Average product decreases.

2. a. To draw the total product curve measure labor on the x-axis and output on the y-axis. The total product curve is upward sloping.

b. The average product of labor is equal to total product divided by the quantity of labor employed. For example, when 2 workers are employed, they produce 100 surfboards a week, so average product is 50 surfboards per worker.The average product curve is upward sloping when up to 2 workers are hired, but average product curve is downward sloping when more than 2 workers are hired.

c. The marginal product of labor is equal to the increase in total product when an additional worker is employed. For example, when 3 workers are employed, total product is 140 surfboards a week. When a fourth worker is employed, total product increases to 170 surfboards a day. The marginal product of going from 3 to 4 workers is 30 surfboards.The marginal product curve is upward sloping when up to 1.5 workers a week and it is downward sloping when more than 1.5 workers a week are employed.

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d. (i) When Sue’s SurfBoards produces fewer than 100 surfboards a week, it employs fewer than 2 workers a week. With fewer than 2 workers a day, marginal product exceeds average product and average product is increasing. Up to an output of 100 surfboards a week, each additional worker adds more to output than the average. Average product increases.

(ii) When Sue’s SurfBoards produces more than 100 surfboards a week, it employs more than 2 workers a week. With more than 2 workers a week, average product exceeds marginal product and average product is decreasing. For outputs greater than 100 surfboards a week, each additional worker adds less to output than average. Average product decreases.

3. a. Total cost is the sum of the costs of all the inputs that Rubber Dinghies uses in production. Total variable cost is the total cost of the variable inputs. Total fixed cost is the total cost of the fixed inputs.For example, the total variable cost of producing 10 boats a week is the total cost of the workers employed, which is 4 workers at $400 a week, which equals $1,600. Total fixed cost is $1,000, so the total cost of producing 10 boats a week is $2,600.To draw the short-run total cost curves, plot output on the x-axis and the total cost on the y-axis. The total fixed cost curve is a horizontal line at $1,000. The total variable cost curve and the total cost curve have shapes similar to those in Fig. 10.4, but the vertical distance between the total variable cost curve and the total cost curve is $1,000.

b. Average fixed cost is total fixed cost per unit of output. Average variable cost is total variable cost per unit of output. Average total cost is the total cost per unit of output.For example, when the firm makes 10 boats a week: Total fixed cost is $1,000, so average fixed cost is $100 per boat; total variable cost is $1,600, so average variable cost is $160 per boat; and total cost is $2,600, so average total cost is $260 per boat.Marginal cost is the increase in total cost divided by the increase in output. For example, when output increases from 3 to 6 boats a week, total cost increases from $1,800 to $2,200, an increase of $400. That is, the increase in output of 3 boats increases total cost by $400. Marginal cost is equal to $400 divided by 3 boats, which is $133.33 a boat. The short-run average and marginal cost curves are similar to those in Fig. 10.5.

c. The table sets out the data to use to draw the curves.

Labor(workers

)

Output(boats)

AP(boats

per worker)

MP(boats

per worker)

TC(dollars)

MC(dollars

per boat)

AVC(dollars

per boat)

1 1 1.00 1,000 400.002.00 200.00

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2 3 1.50 1,400 266.673.00 133.33

3 6 2.00 1,800 200.004.00 100.00

4 10 2.50 2,200 160.005.00 80.00

5 15 3.00 2,600 133.336.00 66.67

6 21 3.50 3,000 142.295.00 80.00

7 26 3.71 3,400 107.694.00 100.00

8 30 3.75 3,800 106.673.00 133.33

9 33 3.67 4,200 109.092.00 200.00

10 35 3.50 4,600 114.29

4. a. Total cost is the sum of the costs of all the inputs that Sue’s SurfBoards employs. Total variable cost is the total cost of the variable inputs. Total fixed cost is the total cost of the fixed inputs.For example, the total variable cost of producing 100 surfboards a week is the total cost of the workers employed, which is 2 workers at $100 a week, which equals $200. Total fixed cost is $200, so the total cost of producing 100 surfboards a week is $300.To draw the short-run total cost curves, plot output on the x-axis and the total cost on the y-axis. The total fixed cost curve is a horizontal line at $200. The total variable cost curve and the total cost curve have shapes similar to those in Fig. 10.4, but the vertical distance between the total variable cost curve and the total cost curve is $200.

b. Average fixed cost is total fixed cost per unit of output. Average variable cost is total variable cost per unit of output. Average total cost is the total cost per unit of output.For example, when the firm makes 100 surfboards a week: Total fixed cost is $200, so average fixed cost is $2 per surfboard; total variable cost is $200, so average variable cost is $2 per surfboard; and total cost is $400, so average total cost is $4 a surfboard.Marginal cost is the increase in total cost divided by the increase in output. For example, when output increases from 100 to 140 surfboards a week, total cost increases from $400 to $500, an increase of $100. That is, the increase in output of 40 surfboards increases total cost by $100. Marginal cost is equal to $100 divided by 40 surfboards, which is $2.50 a surfboard.

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The short-run average and marginal cost curves are similar to those in Fig. 10.5.

c. The following table sets out the data to use to draw the curves.

Labor(worker

s)

Output(boards

)

AP(boards

per worker)

MP(boards

per worker)

TC(dollar

s)

MC(dollars

per board)

AVC(dollars

per board)

0 040.00 7.50

1 40 40.00 300 2.5060.00 1.67

2 100 50.00 400 2.0040.00 2.50

3 140 46.67 500 2.1430.00 3.33

4 170 42.50 600 2.3520.00 5.00

5 190 38.00 700 2.6310.00 10.00

6 200 33.33 800 3.00

5. The increase in total fixed cost increases total cost but does not change total variable cost. Average fixed cost is total fixed cost per unit of output. The average fixed cost curve shifts upward. Average total cost is total cost per unit of output. The average total cost curve shifts upward. Marginal cost and average variable cost do not change.

6. The increase in the price of labor increases total variable cost and total cost but total fixed cost does not change. Average variable cost is total variable cost per unit of output. The average variable cost curve shifts upward. Average total cost is total cost per unit of output. The average total cost curve shifts upward. The marginal cost curve shifts upward. Average fixed cost curve does not change.

7. a. Total cost is the cost of all the inputs. For example, when 3 workers are employed they now produce 12 boats a week. With 3 workers, the total variable cost is $1,200 a week and the total fixed cost is $2,000 a week. The total cost is $3,200 a week. The average total cost of producing 12 boats is $266.67.

b. The long-run average cost curve is made up the lowest parts of the firm’s short-run average total cost curves when the firm operates 1 plant and 2 plants. The long-run average cost curve is similar to Fig. 10.8.

c. It is efficient to operate the number of plants that has the lower average total cost of a boat. It is efficient to operate one plant when

O U T P U T A N D C O S T S 2 4 3

output is less than 27 boats a week, and it is efficient to operate two plants when the output is more than 27 boats a week.Over the output range 1 to 27 boats a week, average total cost is less with one plant than with two, but if output exceeds 27 boats a week, average total cost is less with two plants than with one.

8. a. Total cost is the cost of all the inputs. For example, when 2 workers are employed they now produce 200 surfboards a week. With 2 workers, the total variable cost is $200 a week and the total fixed cost is $400 a week. The total cost is $600 a week. The average total cost of producing 200 surfboards is $6.00 a surfboard.

b. The long-run average cost curve is made up of the lowest parts of the firm's short-run average total cost curves when the firm operates one plant and two plants. The long-run average cost curve is similar to Fig. 10.8.

c. It is efficient to operate the number of plants that has the lower average total cost of a surfboard. It is efficient to operate one plant when output is less than 170 surfboards a week, and it is efficient to operate two plants when the output is more than 170 surfboards a week.Over the output range 1 to 170 surfboards a week, average total cost is less with one plant than with two, but if output exceeds 170 surfboards a week, average total cost is less with two plants than with one.

9. a. For example, the average total cost of producing a balloon ride when Bonnie rents 2 balloons and employs 4 workers equals the total cost ($1,000 rent for the balloons plus $1,000 for the workers) divided by the 20 balloon rides produced. The average total cost equals $2,000/20, which is $100 a ride.The average total cost curve is U-shaped, as in Fig. 10.5.

b. The long-run average cost curve is similar to that in Fig. 10.8.c. Bonnie’s minimum efficient scale is 13 balloon rides when Bonnie rents

1 balloon.The minimum efficient scale is the smallest output at which the long-run average cost is a minimum. To find the minimum efficient scale, plot the average total cost curve for each plant and then check which plant has the lowest minimum average total cost.

d. Bonnie will choose the plant (number of balloons to rent) that gives her minimum average total cost for the normal or average number of balloon rides that people buy.

10. a. For example, the average total cost of producing cakes when Cathy rents 2 ovens and employs 2 workers equals the total cost ($200 rent for the ovens plus $100 for the 2 workers) divided by the 60 cakes produced. The average total cost equals $300/60, which is $5 a cake. The average total cost curve for each plant is U-shaped, as in Fig. 10.5.

b. The long-run average cost curve is similar to that in Fig. 10.8.c. Cathy experiences economies of scale at outputs up to 60 cakes a day,

constant returns to scale from 60 to 90 cakes a day, and diseconomies of scale for outputs exceeding 90 cakes a day.

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When economies of scale are present, the LRAC curve slopes downward. When constant returns to scale are present, the LRAC curve is horizontal. Cathy’s LRAC curve is horizontal at 90 cakes a day. When diseconomies of scale are present, the LRAC curve slopes upward. Cathy’s LRAC curve slopes upward at outputs that exceed 90 cakes a day.

d. Cathy will choose the plant (number of ovens to rent) that gives her minimum average total cost for the normal or average number of cakes that people buy.

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A d d i t i o n a l P r o b l e m s1. Charlie’s Chocolates total product schedule is

Labor Output(workers per day) (boxes per day)

1 122 243 484 845 1216 1927 2408 2769 300

10 312a. Draw the total product curve.b. Calculate the average product of labor and draw the average product

curve.c. Calculate the marginal product of labor and draw the marginal product

curve.d. What is the relationship between the average product and marginal

product when Charlie’s Chocolates produces (i) less than 276 boxes a day and (ii) more than 276 boxes a day?

2. In problem 1, the price of labor is $50 per day, and total fixed costs are $50 per day.a. Calculate total cost, total variable cost, and total fixed costs for each

level of output and draw the short-run total cost curves.b. Calculate average total cost, average fixed cost, average variable cost,

and marginal cost at each level of output and draw the short-run average and marginal cost curves.

3. In problem 2, suppose that the price of labor increases to $70 per day. Explain what changes occur to the short-run average and marginal cost curves?

4. In problem 2, Charlie’s Chocolates buys a second plant and now the total product of each quantity of labor doubles. The total fixed cost of operating each plant is $50 a day. The wage rate is $50 a day.a. Set out the average total cost curve when Charlie’s operates two

plants.b. Draw the long-run average cost curve.c. Over what output range is it efficient to operate one plant and two

plants?

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5. The table below shows the production function of Mario’s Pizza-to-Go. Mario must pay $100 a day for each oven he rents and $75 a day for each kitchen hand he hires.a. Find and graph the average total cost curve for each plant size.b. Draw Mario’s long-run average cost curve.c. Over what output range does Mario experience economies of scale?d. Explain how Mario uses his long-run average cost curve to decide how

many ovens to rent.Labor Output (pizzas per day)

(workers per day) Plant 1 Plant 2 Plant 3 Plant 41 4 8 11 132 8 12 15 173 11 15 18 204 13 17 20 22

Ovens (number) 1 2 3 4

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S o l u t i o n s t o A d d i t i o n a l P r o b l e m s1. a. To draw the total product curve measure labor on the x-axis and output

on the y-axis. The total product curve is upward sloping.b. The average product of labor is equal to total product divided by the

quantity of labor employed. For example, when 3 workers are employed, they produce 48 boxes a day, so average product is 16 boxes per worker.The average product curve is upward sloping when the number of workers is between 1 and 8, but it becomes downward sloping when 9 and 10 workers are employed.

c. The marginal product of labor is equal to the increase in total product when an additional worker is employed. For example, when 3 workers are employed, total product is 48 boxes a day. When a fourth worker is employed, total product increases to 84 boxes a day. The marginal product of going from 3 to 4 workers is 36 boxes.The marginal product curve is upward sloping when the number of workers is between 1 and 6, but it becomes downward sloping when 7 or more workers are employed.

d. (i) When Charlie’s Chocolates produces fewer than 276 boxes a day, it employs fewer than 8 workers a day. With fewer than 8 workers a day, marginal product exceeds average product and average product is increasing. Up to an output of 276 boxes a day, each additional worker adds more to output than the average. Average product increases.

(ii) When Charlie’s Chocolates produces more than 276 boxes a day, it employs more than 8 workers a day. With more than 8 workers a day, average product exceeds marginal product and average product is decreasing. For outputs greater than 276 boxes a day, each additional worker adds less to output than average. Average product decreases.

2. a. Total cost is the sum of the costs of all the inputs that Charlie’s Chocolates uses in production. Total variable cost is the total cost of the variable inputs. Total fixed cost is the total cost of the fixed inputs.For example, the total variable cost of producing 48 boxes a day is the total cost of the workers employed, which is 3 workers at $50 a day, which equals $150. Total fixed cost is $50, so the total cost of producing 48 boxes a day is $200.To draw the short-run total cost curves, plot output on the x-axis and the total cost on the y-axis. The total fixed cost curve is a horizontal line at $50. The total variable cost curve and the total cost curve have shapes similar to those in Fig. 10.4, but the vertical distance between the total variable cost curve and the total cost curve is $50.

b. Average fixed cost is total fixed cost per unit of output. Average variable cost is total variable cost per unit of output. Average total cost is the total cost per unit of output.For example, when the firm makes 48 boxes a day: Total fixed cost is $50, so average fixed cost is $1.04 per box; total variable cost is $150,

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so average variable cost is $3.13 per box; and total cost is $200, so average total cost is $4.17 per box.Marginal cost is the increase in total cost divided by the increase in output. For example, when output increases from 24 to 48 boxes a day, total cost increases from $150 to $200, an increase of $50. That is, the increase in output of 24 boxes increases total cost by $50. Marginal cost is equal to $50 divided by 24 boxes, which is $2.08 a box. The short-run average and marginal cost curves are similar to those in Fig. 10.5.

3. The increase in the price of labor increases total variable cost and total cost but does not change total fixed cost. Average variable cost is total variable cost per unit of output. The average variable cost curve shifts upward. Average total cost is total cost per unit of output. The average total cost curve shifts upward. The marginal cost curve shifts upward. Average fixed cost does not change.

4. a. Total cost is the cost of all the inputs. For example, when 3 workers are employed they now produce 96 boxes a day. With 3 workers, the total variable cost is $150 a day and the total fixed cost is $100 a day. The total cost is $250 a day. The average total cost of producing 96 boxes is $2.60.

b. The long-run average cost curve is made up of the lowest parts of the firm’s short-run average total cost curves when the firm operates one plant and two plants. The long-run average cost curve is similar to Fig. 10.8.

c. It is efficient to operate the number of plants that has the lower average total cost of a box of chocolates. It is efficient to operate one plant when output is less than 48 boxes a day, and it is efficient to operate two plants when the output is more than 48 boxes a day.Over the output range 1 to 48 boxes a week, average total cost is less with one plant than with two, but if output exceeds 48 boxes a day, average total cost is less with two plants than with one.

5. a. For example, the average total cost of producing a pizza when Mario rents 2 ovens and employs 4 workers equals the total cost ($200 rent for the ovens plus $300 for the workers) divided by the 17 pizzas produced. The average total cost equals $500/17, which is $29.41 a pizza. The average total cost curve is U-shaped, as in Fig. 10.5.

b. The long-run average cost curve is similar to that in Fig. 10.8.c. Mario experiences economies of scale at output levels of 4 to 15 pizzas

a day. When economies of scale are present, the LRAC curve slopes downward. Mario’s LRAC curve slopes downward between the output levels of 4 to 15 pizzas a day.

d. Mario will choose the plant (number of ovens to rent) that gives him minimum average total cost for the normal or average number of pizzas that people buy.

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