7

Costs

Introduction

Chapter Outline 7.1

Costs That Matter for Decision Making: Opportunity Costs

7.2

Costs That Do Not Matter for Decision Making: Sunk Costs

7.3

Costs and Cost Curves

7.4

Average and Marginal Costs

7.5

Short-Run and Long-Run Cost Curves

7.6

Economies in the Production Process

7.7

Conclusion

7

Introduction

7

Costs and the manner in which costs are structured are key to a firm’s production decisions. • How much to produce? • Whether to expand or shrink in response to changing market conditions? • Whether to switch to producing a different product?

We began thinking about costs with the expansion path introduced in the last chapter; now, we examine cost structures more intimately. • Introducing different types of costs • Differentiating between short-run and long-run

Costs That Matter for Decision Making: Opportunity Costs

7.1

Costs are thought about differently in economics than in accounting. • Accounting costs include the direct costs of operating a business, including costs for raw materials. • Economic cost is the sum of a producer’s accounting and opportunity costs. ‒ Opportunity cost is the value of what a producer gives up by using an input.

Inclusion of opportunity cost means an economist’s interpretation of what constitutes profit will generally be different from an accountant’s. • Accounting profit is a firm’s total revenue minus accounting cost. • Economic profit is a firm’s total revenue minus economic cost.

Costs That Matter for Decision Making: Opportunity Costs

7.1

Opportunity costs occur everywhere in a production process • • •

By choosing to start a business, you may give up your salary at your current position. When you invest in building a factory, you give up any other investment opportunities. By choosing to use an office building you own, you cannot rent it to someone else.

Why does this distinction matter? • •

When firms make decisions on the use of inputs, they consider these opportunity costs. Economists try to describe behavior. ‒ It is necessary to understand opportunity costs to know how firms make decisions.

Costs That Do Not Matter for Decision Making: Sunk Costs

7.2

While opportunity costs should be considered when making decisions, sunk costs should be ignored. Sunk costs are a form of fixed costs, or the cost of the firm’s fixed inputs, independent of the quantity of the firm’s output. • Buildings, operating permits, durable equipment ‒ These costs are partially avoidable; some money can be recovered.

Sunk costs cannot be recovered once spent. • •

Licensing fees, long-term lease contracts, etc. Specific capital such as uniforms, menus, signs, etc.

Sunk costs cannot be recouped and therefore should not be considered if a firm is deciding whether or not to close.

Costs That Do Not Matter for Decision Making: Sunk Costs

7.2

Sunk Costs and Decisions Once incurred, sunk costs should not affect decision making

Consider a business deciding whether to close down. • Some of the costs associated with the business are unavoidable (e.g., permits, loss of value in kitchen equipment, uniforms). • Others costs disappear when operations cease (e.g., wages for employees, raw materials, phone bills).  If staying open will generate some revenue, what should the firm do?

‒ Stay open as long as operating revenues exceed operating costs. ‒ Operating revenue is the money a firm earns from selling its output. ‒ Operating cost is the cost a firm incurs in producing its output. If

Costs That Do Not Matter for Decision Making: Sunk Costs

7.2

Sunk Costs and Decisions The sunk cost fallacy refers to the mistake of letting sunk costs affect a firm’s operating decisions. Often people and firms allow sunk costs to influence decisions. • Usually, this means continuing down one path because of a prior investment. Example: Going to a baseball game because you bought season tickets even if the weather is horrible and there is something else you would rather do.

Costs and Cost Curves

7.3

Economic analysis of costs divides operating costs into two categories: 1. Fixed cost (FC ) is the cost of the firm’s fixed inputs, independent of the quantity of the firm’s output (e.g., office lease).

2. Variable cost (VC ) is the cost of inputs that vary with the quantity of the firm’s output (e.g., raw materials). The sum of fixed and variable costs is a firm’s Total Cost.

Costs and Cost Curves

7.3

Flexibility and Fixed versus Variable Costs •

Time horizon is the chief factor determining flexibility of different input levels. ‒ Over short time horizons, many inputs are fixed costs (e.g., in a single day for a restaurant most costs are fixed, including labor and capital). ‒ As the time horizon expands, wait staff can be hired or fired, new capital can be purchased, and space can be expanded.

Other Factors Affecting Flexibility • •

The presence (or lack) of active capital rental and resale markets allow some capital expenditures to become variable (e.g., renting an extra crane). Labor contracts may lead to stickiness in labor inputs; it may be difficult to fire workers, and firms may become reluctant to hire unless absolutely necessary.

Costs and Cost Curves

7.3

Deriving Cost Curves • A cost curve is the mathematical relationship between a firm’s production costs and output. ‒ Curves associated with fixed, variable, and total costs will have different shapes. ‒ Costs can be represented by a table or a graph.

Consider Fleet Foot, a shoe company that produces running shoes.

Costs and Cost Curves

7.3

7.3

Costs and Cost Curves Figure 7.1 Fixed, Variable, and Total Costs Cost ($/week) TC is the sum of VC and FC

$300 250

Total cost (TC )

200

Variable cost (VC ) 150 100 50 0

Fixed cost (FC ) 1

2

3

4

5

6

7

8

9 10 11 12 Quantity of shoes (pairs)

Costs and Cost Curves

7.3

The Fixed Cost Curve is horizontal. •

Costs do not vary with output; they are $50 per week regardless of production.

Variable costs change with the amount of output, and the Variable Cost Curve is therefore not constant. • •

The slope of the variable cost curve is always positive. In this example, the curve becomes flatter as output rises from 0 to 4 pairs, then becomes steeper as the number of pairs produced per week increases.

The Total Cost Curve is the sum of variable cost and fixed cost. •

The total cost curve will have the same shape as the variable cost curve, but it will be shifted up at each level of output by the amount of fixed costs.

Average and Marginal Costs

7.4

Understanding the cost structure of firms is important, but to understand how costs affect production decisions, we must introduce two related measures: Average cost and Marginal cost. Average cost is simply cost divided by output: •

Average Fixed Cost (AFC )

•

Average Variable Cost (AVC )

•

Average Total Cost (ATC )

AFC  FC / Q AVC  VC / Q

ATC  TC / Q  FC  VC / Q  FC / Q  VC / Q  AFC  AVC

Returning to the shoe example:

Average and Marginal Costs

7.4

Average and Marginal Costs Figure 7.2 Average Cost Curves AFC always falls as quantity rises.

Average cost ($/pair)

This is because it is being averaged across more and more units.

$70 60

Average total cost (ATC )

50 Average fixed cost (AFC )

40

30

Average variable cost (AVC )

20 10 0

1

2

3

4

5

6

7

8

9 10 11 12 Quantity of shoes (pairs)

7.4

Average and Marginal Costs

7.4

Marginal cost is another deciding factor in firms’ production decisions • The additional cost of producing an additional unit of output

MC  TC / Q Returning to the previous table:

Average and Marginal Costs

7.4

Average and Marginal Costs Figure 7.3 Marginal Cost Marginal cost ($/pair) $80

MC falls at first because AFC is falling. Eventually MC rises.

70

Marginal cost (MC )

60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9 10 11 12

Quantity of shoes (pairs)

7.4

Average and Marginal Costs

7.4

Relationships Between Average and Marginal Costs • Since fixed costs do not change when a firm expands output, marginal cost only depends on variable cost.

MC  VC / Q  TC / Q

 What happens when marginal cost is less than average total cost?  For example, consider your overall GPA. What happens to your 3.0 average when you get a 2.5 for the semester? ‒ It drops below 3.0.  • The same holds with costs; when marginal cost is less than the average total cost, producing another unit will reduce average total cost, and vice versa. This observation helps to determine when average total costs are minimized. •

Average total costs are minimized when ATC = MC . ‒ This explains why ATC and AVC have a “U” shape.

Average and Marginal Costs

7.4

Figure 7.4 The Relationship Between Average and Marginal Costs MC always crosses AVC and ATC at

Average cost and marginal cost ($/unit)

their minimums.

MC ATC Minimum

AVC

ATC

Minimum

AVC Quantity

Short-Run and Long-Run Cost Curves

7.5

We now analyze how the time horizon affects the cost structure facing a firm. • Remember, in the short run, the amount of capital is assumed to be fixed.

Short-Run Production and Total Cost Curves A firm’s short-run total cost curve describes the total cost of producing various quantities of output when the amount of capital available for use is fixed. • An easy way to see this concept in action is with a graph. • Consider the production of engines.

Short-Run and Long-Run Cost Curves

7.5

Capital and labor are used to produce engines (quantities are per week)

Figure 7.6

Figure 7.5 Capital (K)

Total Cost ($)

C = 360

TCSR TCLR Long-Run Expansion Path

Z′

$360 $300

C = 120

Short-Run Z′ Expansion Path (𝑲 = 𝟔) Q = 30

Z

6

X′ Y X

Q = 20 C = 180

C = 100

0

Q = 10

Z

$180 $120 $100

X′

Y

X

C = 300

Labor(L)

0

10

20

30

Quantity of engines

Short-Run and Long-Run Cost Curves

7.5

Short-Run Versus Long-Run Average Total Cost Curves Figure 7.6 shows that the short-run total cost curve will never fall below the longrun total cost curve. • This further implies that the short-run average total cost curve will never fall below the long-run average total cost curve. • This fact holds true for all short-run average total cost curves. ‒ Each of which corresponds to a different fixed capital level.

This property means that the long-run ATC curve will envelop all of the short-run ATC curves.

Short-Run and Long-Run Cost Curves

7.5

Figure 7.8 The Long-Run Average Total Cost Curve Envelops the Short-Run Average Cost Curves Average total cost ($/unit)

ATCSR,10

ATCSR,30

ATCSR,20

X′

$12

9

0

X

10

ATCLR

Z'

Y

Z

20

30

Quantity of engines

Short-Run and Long-Run Cost Curves

7.5

Short-Run versus Long-Run Marginal Cost Curves Just as with average costs, • Short-run marginal cost is the cost of producing an additional unit of output when capital is fixed. • Long-run marginal cost is the cost of producing an additional unit of output when both capital and labor are variable.  What does this imply for the shape of the marginal cost curves? ‒ In general, the long-run marginal cost curve will be flatter than the short-run marginal cost curve.

Short-Run and Long-Run Cost Curves

7.5

Figure 7.9 Long-Run and Short-Run Marginal Costs ATCSR,10

Average cost and marginal cost ($/unit)

ATCSR,20

MCLR

ATCSR,30

$12

B Y

9

MCSR,10 0

Note that each short run MC curve intersects each ATC curve at its minimum.

A MCSR,20 10

MCSR,30 20

30

Quantity of engines

Economies in the Production Process

7.6

What happens to the long-run ATC curve as a firm grows? • The answer reveals information about economies in the production process. • Similar to returns to scale, but focused on the cost side.

Economies of Scale: Costs rise more slowly than production. Constant economies of Scale: Costs rise at the same rate as output. Diseconomies of Scale: Costs rise more quickly than production.

Economies in the Production Process

7.6

 Given these relationships, what does the common “U-shape” of the long-run ATC curve imply for production? ‒ At first, average cost per unit produced falls (economies of scale).Eventually, as output rises considerably, diseconomies of scale take hold.

 What factors might cause diseconomies of scale to set in? ‒ Overcrowding, overutilization of capital, organizational complexity, etc.

Not the same as returns to scale! • •

Returns to scale describes how production changes when all inputs are changed by a common factor. Economies of scale does not impose this “common factor” rule in input proportions.

Economies in the Production Process

7.6

Economies of Scope A related concept is the idea of economies of scope. • Refers to the simultaneous production of multiple products at a lower cost than if a firm made each separately.

Why might a firm observe economies of scope? 1. Flexible inputs or production processes ‒ For instance, oil refineries can produce many different petroleum products at the same time through distillation at a much lower aggregate cost than if each were produced separately. 2. Expertise is translatable across several products/services ‒ For instance, life and auto insurance

Conclusion

7.7

We have now linked cost to production. • Opportunity costs, fixed costs, variable costs, sunk costs • Marginal and average costs • Short- and long-run costs

In the next chapters, we introduce market conditions to a firm’s production decision. We begin with the case of a perfectly competitive market in Chapter 8.

In-text figure it out Cooke’s Catering is owned by Dan Cooke. For the past year, Cooke’s Catering had the following statement of revenues and costs Revenues Supplies Electricity and water Employee salaries Dan’s salary

$500,000 $150,000 $15,000 $50,000 $60,000

Dan has the option of closing his business and renting out the building he owns for $100,000 per year. In addition, Dan could go work for another catering company for $45,000 per year or for a high end restaurant for $75,000. Answer the following questions: a. What is Cooke’s Catering’s accounting cost? b. What is Cooke’s Catering’s economic cost? c. What is Cooke’s Catering’s economic profit?

In-text figure it out a. Accounting cost is the direct cost of operating a business, including supplies, utilities, and salaries. Accounting cost = $150,0000 + $15,000 + $50,000 + $60,000 = $275,000 1.

b. Economic cost includes the opportunity cost of ownership. In this case, the opportunity costs include the forgone rent ($100,000) and the difference between Cooke’s current salary and what his would earn if he took the restaurant job ($15,000). • Note, the catering offer is irrelevant because opportunity cost measures the value of the next best alternative, which is working at the high end restaurant. ‒ Economic Cost = Accounting cost + Opportunity cost Economic cost = $275,000 + $100,000 + ($75,000 − $60,000) = $390,000

In-text figure it out c. Economic profit is simply revenues minus economic cost, Economic profit = $500,000 – $390,000 = $110,000

Both accounting and economic profit are positive, so Cooke should continue operating his catering business.

Additional figure it out Jim’s Consulting is owned by James Smith. For the past year, Jim’s Consulting had the following revenues and costs

Revenues Supplies Electricity and water Employee salaries James’s salary

$600,000 $20,000 $10,000 $300,000 $250,000

James has the option of shutting down and renting out the building he owns for $60,000 per year. Additionally, James could go work for a larger consulting house for $275,000 per year. Answer the following questions: a. What is Jim’s Consulting’s accounting cost? b. What is Jim’s Consulting’s economic cost? c. What is Jim’s Consulting’s economic profit?

Additional figure it out a. Accounting cost is the direct cost of operating a business, including supplies, utilities, and salaries. Accounting cost = $20,000 + $10,000 + $300,000 + $250,000 = $580,000 1.

b. Economic cost includes the opportunity cost of ownership. In this case, the opportunity costs include the forgone rent ($60,000) and the difference between James’s current salary and what he would earn if he took another job ($25,000) Economic cost = $580,000 + $60,000 + $25,000 = $665,000

c. Economic profit is simply revenues minus economic cost, Economic profit = $600,000 – $665,000 = –$65,000

While accounting profit is positive, economic profit is negative, and James could do better by shutting down his business and taking his outside opportunities.

In-text figure it out Fields Forever is a small farm that grows strawberries to sell to local farmers. It produces strawberries using 5 acres of land that it rents for $200 per week. They can hire labor at a price of $250 per week per worker. The table below shows how the output of strawberries (measured in truckloads) varies with the number of workers hired: Labor

Strawberries

(Workers per Week)

(Truckloads)

0

0

1

1

3

2

7

3

12

4

18

5

Calculate the marginal cost of 1 to 5 truckloads of strawberries for Fields Forever (assume labor to be the only variable cost).

In-text figure it out The simplest way to solve this is to add several columns to the previous table representing fixed, variable, and total costs. Marginal cost is simply 𝑀𝐶 = ∆𝑇𝐶/∆𝑄output and is measured in dollars

Labor

Strawberries

(Workers per Week)

Total Marginal Cost Cost

Variable Cost

(Truckloads)

Fixed Cost

0

0

$200

$250 × 0 = $0

$200

—

1

1

$200

$250 ×1 = $250

$450

$250

3

2

$200

$250 × 3 = $750

$950

7

3

$200

$250 × 7 = $1,750

$1,950

12

4

$200

$250 × 12 = $3,000

$3,200

18

5

$500 $1,000

$1,250 $200

$250 × 18 = $4,700

$4,700

$1,500

Additional figure it out Frame de Art is an art framing shop in a small town. Frame de Art has one storefront ($500 per week), and can hire workers for $300 per week per worker. The table below shows how output of framed art (in hundreds-per-week) varies with the number of workers.

Labor

Framed Art

(Workers per Week)

(Hundreds per Week)

0

0

1

1

3

2

6

3

11

4

20

5

Calculate the marginal cost of 100 to 500 framing jobs for Frame de Art (assume labor to be the only variable cost).

Additional figure it out The simplest way to solve this is to add several columns to the previous table representing fixed, variable, and total costs. Marginal cost is simply 𝑀𝐶 = ∆𝑇𝐶/∆𝑄output and is measured in dollars.

Labor

Framed Art

Fixed Cost

Variable Cost

Total Cost

Marginal Cost

(Workers per Week)

(Hundreds per Week)

0

0

$500

$300 × 0 = $0

$500

—

1

1

$500

$300×1 = $300

$800

$300

3

2

$500

$300 × 3 = $900

$1,400

$600

6

3

$500

$300 × 6 =$1,800

$2,300

$900

11

4

$500

$300 × 11 = $3,300

$3,800

$1,500

20

5

$500

$300 × 20 = $6,000

$6,500

$2,700

In-text figure it out 2 Suppose a firm’s total cost curve is TC  15Q  8Q  45

and marginal cost

MC  30Q  8

Answer the following questions: a. Find expressions for the firm’s fixed cost, variable cost, average total cost, and average variable cost.

b. Find the output level that minimizes average total cost. c. Find the output level that minimizes average variable cost.

In-text figure it out a. Find the firm’s fixed cost, variable cost, average total cost, and average variable cost. Fixed cost does not vary with output, so solve for total cost when output equals zero. 2

TC  150  80  45  45  FC  45

Variable cost is the portion that does vary with output: Fixed  2 TC  15Q  8Q  45  VC  15Q 2  8Q

Average total cost is simply total cost divided by output:

15Q 2  8Q  45 45 ATC   ATC  15Q  8  Q Q And the same applies to Average variable cost: 15Q 2  8Q AVC   AVC  15Q  8 Q

In-text figure it out b. Minimum average total cost occurs when marginal cost is equal to average total cost. 15Q 2  8Q  45 ATC  MC   30Q  8 Q

45 45  30Q  8  15Q   30Q  Q Q 15Q 2  45  Q  1.732

15Q  8 

45  15Q Q

So, ATC is minimized when Q = 1.732.

c. Finally, average variable cost is minimized when marginal cost is equal to average variable cost. 15Q 2  8Q AVC  MC   30Q  8  15Q  0  Q

And AVC is minimized when production ceases.

Q0

Additional figure it out Suppose a firm’s total cost curve is

and marginal cost

TC  10Q 2  6Q  60

MC = 20Q + 6

Answer the following questions:

a. Find expressions for the firm’s fixed cost, variable cost, average total cost, and average variable cost. b. Find the output level that minimizes average total cost. c. Find the output level that minimizes average variable cost.

Additional figure it out a. Find the firm’s fixed cost, variable cost, average total cost, and average variable cost. Fixed cost does not vary with output, so solve for total cost when output equals zero.

TC  1002  60  60  60  FC  60

Variable cost is the portion that does vary with output.

 TC  10Q  6Q  60  VC  10Q 2  6Q Fixed

2

Average total cost is simply total cost divided by output. 2

ATC 

10Q  6Q  60 60  ATC  10Q  6  Q Q

And the same applies to Average variable cost, 10Q 2  6Q

AVC 

Q

 AVC  10Q  6

Additional figure it out b. Minimum average total cost occurs when marginal cost is equal to average total cost. 10Q 2  6Q  60 ATC  MC   20Q  6 Q 10Q 2  6Q  60  20Q 2  6Q  10Q 2  60

 Q  6  2.45 So, ATC is minimized when Q = 2.45.

c. Finally, average variable cost is minimized when marginal cost is equal to average variable cost, 10Q 2  6Q AVC  MC   20Q  6  Q  0 Q

and AVC is minimized when production ceases.

In-text figure it out Steve and Sons Solar Panels has a production function:

Q  4 KL; MPL  4 K ; MPK  4 L The wage rate (w) is $8 per hour, and the rental rate on capital (r) is $10 per hour. Answer the following questions: a. In the short run, capital is fixed at 𝐾 = 10. What is the cost of producing 200 solar panels? b. What will the firm wish to do in the long run to minimize the cost of producing Q = 200 solar panels? How much will the firm save? ‒ Find the cost minimizing combination of K and L (hint, review Chapter 6). ‒ Show what this combination will cost and compare it to the short run cost.

In-text figure it out a. If capital is fixed at 10 units, the amount of labor needed to produce 200 solar panels is found by plugging in 10 for K and solving for L:

200  4(10) L 

L5

Total cost is therefore given by

TC  rK  wL  $10  10  $8  5  $140 b. From Chapter 6, we know that costs are minimized when the MRTS of labor for capital is equal to the ratio of the costs of labor to capital, W MPL 4 K K W 8 MRTS LK     ;  R MPK 4 L L R 10 3

K 8  L 10

or

8 K  L  0.8 L 10

The ratio of capital to labor that should be used to minimize costs should be 0.8, or for every 1 worker they employ they should employ 0.8 unit of capital.

In-text figure it out To solve for the cost minimizing combination of capital and labor, substitute the expression for K into the production function. This yields:

8 2  8  Q  200  4 L  L  200  L  10  10 

L  7.91

To minimize the cost of producing 200 solar panels, the firm should employ 7.91 units of labor.

Solving for the amount of capital used yields:

K

8 8 L (7.91)  10 10

K  6.33

To minimize the cost of producing 200 solar panels, the firm should employ 6.33 units of capital. Finally, total costs are given by

TC  rK  wL  $10  6.33  $8  7.91  $126.58

Cost is $13.42 ($140 − $126.58) less in the long run than the short run. This is obtained by utilizing less units of capital and more units of labor.

Additional figure it out Suppose a wind turbine producer faces a production function

Q  0.25KL; MPL  0.25K ; MPK  0.25L The wage rate (w) is $12 per hour, and the rental rate on capital (r) is $22 per hour. Answer the following questions: a. In the short run, capital is fixed at 8. What is the cost of producing 200 turbines? b. What should the firm do in the long run to minimize the cost of producing 200 turbines? ‒ Find the cost minimizing combination of K and L. ‒ Show what this combination will cost and compare it to the short run cost. Are the costs of producing 200 turbines in long run more or less than in the short run?

Additional figure it out a. If capital is fixed at 8 units, the amount of labor needed to produce 200 turbines is found by plugging in 8 for K and solving for L.

200  0.25 8 L  L  100 Total cost is therefore given by

TC  rK  wL  $22  8  $12  100  $1,376 b. From Chapter 6, we know that costs are minimized when the MRTS of labor for capital is equal to the ratio of the costs of labor to capital, MRTS LK 

W  R

MPL 0.25K K W 12   ;  MPK 0.25L L R 22

K 12  L 22

or

K

12 L 22

The ratio of capital to labor that should be used to minimize costs 𝟏𝟐 should be 𝟐𝟐, or for every 1 worker they employ they should employ 0.545 units of capital.

Additional figure it out To solve for the cost minimizing combination of capital and labor, substitute the expression for K into the production function. This yields:

3 2  12  Q  200  0.25 L  L  200  L  L  38.3 22 22   To minimize the cost of producing 200 turbines, the firm should employ 38.3 workers. Solving for the amount of capital used yields:

K

12 12 L (38.3)  22 22

K  20.89

To minimize the cost of producing 200 turbines, the firm should employ 20.89 units of capital.

TC  rK  wL  $22  20.89  $12  38.3  $9

Finally, total costs are given by

Cost is $456.82 ($1,376 − $919.18) less in the long run than the short run. This is obtained by utilizing more machines and less workers.

In-text figure it out

Suppose the long-run total cost function for a firm is 𝐿𝑇𝐶 = 32,000𝑄 − 250𝑄2 + 𝑄3 , and its long-run marginal cost function is 𝐿𝑀𝐶 = 32,000 − 500𝑄 + 3𝑄2 . Answer the following question: a. At what levels of output will the firm face economies of scale? Diseconomies of scale? ‒ Hint: these cost functions yield a typical U-shaped long-run average cost curve.

In-text figure it out a. We know that when LMC < LATC, long-run average total cost is falling, and when LMC = LATC, long-run average total costs are minimized. First, derive the equation for LATC

LTC 32,000Q  250Q 2  Q 3 LATC    32,000  250Q  Q 2 Q Q Set LMC = LATC to find the quantity that minimizes the LATC: 32,000  250Q  Q 2  32,000  500Q  3Q 2 250Q  2Q 2 Q  125 Long-run average total cost is minimized at 125 units of output. Therefore, at output levels below 125, the firm is experiencing economies of scale, and output above 125 they are experiencing diseconomies of scale.

Additional figure it out Suppose the long-run total cost function for a firm is LTC = 15,000Q – 200Q2 + Q3 and its long-run marginal cost function is LMC = 15,000 – 400Q + 3Q2.

Answer the following question: a. At what levels of output will the firm face economies of scale? Diseconomies of scale? ‒ Hint: these cost functions yield a typical U-shaped long-run average cost curve.

Additional figure it out a. We know that when LMC < LATC, long-run average total cost is falling, and when LMC = LATC, long-run average total costs are minimized. First, derive the equation for LATC:

LTC 15,000Q  200Q 2  Q 3 LATC    15,000  200Q  Q 2 Q Q Set LMC = LATC to find the quantity that minimizes the LATC:

15, 000 - 200Q + Q 2 = 15, 000 - 400Q + 3Q 2 200Q = 2Q 2 Q = 100 Long-run average total cost is minimized at 100 units of output. Therefore, at output levels below 100, the firm is experiencing economies of scale, and at output above 100 they are experiencing diseconomies of scale.