Costs
7
Introduction 7
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
7Introduction
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
Costs and Cost Curves 7.3
Figure 7.1 Fixed, Variable, and Total Costs
Cost($/week)
$300
250Total cost (TC )
200Variable cost (VC )
150
100
50Fixed cost (FC )
0 1 2 3 4 5 6 7 8
Quantity of shoes (pairs)
9 10 11 12
TC is the sum of VC and FC
Costs and Cost Curves 7.3
The Fixed Cost Curve is horizontal.
• Costs do not vary with output; they are $50 per week regardless of production.
Variable costs change with the amount of output, and the Variable Cost Curve
is therefore not constant.
• The slope of the variable cost curve is always positive.
• In this example, the curve becomes flatter as output rises from 0 to 4 pairs, then
becomes steeper as the number of pairs produced per week increases.
The Total Cost Curve is the sum of variable cost and fixed cost.
• The total cost curve will have the same shape as the variable cost curve, but it will
be shifted up at each level of output by the amount of fixed costs.
Average and Marginal Costs 7.4
Understanding the cost structure of firms is important, but to understand
how costs affect production decisions, we must introduce two related
measures: Average cost and Marginal cost.
Average cost is simply cost divided by output:
• Average Fixed Cost (AFC )
• Average Variable Cost (AVC )
• Average Total Cost (ATC )
Returning to the shoe example:
QFCAFC /
QVCAVC /
QVCFCQTCATC //
AVCAFCQVCQFC //
Average and Marginal Costs 7.4
Average and Marginal Costs 7.4
Figure 7.2 Average Cost Curves
Average cost($/pair)
$70
60 Average total cost (ATC )
50
Average fixed cost (AFC )40
30Average variable cost (AVC )
20
10
0 1 2 3 4 5 6 7 8
Quantity of shoes (pairs)
9 10 11 12
AFC always falls as quantity rises. This is because it is being averaged
across more and more units.
Average and Marginal Costs 7.4
Marginal cost is another deciding factor in firms’ production decisions
• The additional cost of producing an additional unit of output
Returning to the previous table:
QTCMC /
Average and Marginal Costs 7.4
Average and Marginal Costs 7.4
Figure 7.3 Marginal Cost
Marginal cost($/pair)
$80
70Marginal cost (MC )
60
50
40
30
20
10
0 1 2 3 4 5 6 7 8
Quantity of shoes (pairs)
9 10 11 12
MC falls at first because AFC is falling. Eventually MC rises.
Average and Marginal Costs 7.4
Relationships Between Average and Marginal Costs
• Since fixed costs do not change when a firm expands output, marginal cost
only depends on variable cost.
What happens when marginal cost is less than average total cost?
For example, consider your overall GPA. What happens to your 3.0
average when you get a 2.5 for the semester?
‒ It drops below 3.0.
• The same holds with costs; when marginal cost is less than the average total
cost, producing another unit will reduce average total cost, and vice versa.
This observation helps to determine when average total costs are
minimized.
• Average total costs are minimized when ATC = MC .
‒ This explains why ATC and AVC have a “U” shape.
QTCQVCMC / /
Average and Marginal Costs 7.4
Figure 7.4 The Relationship Between Average and Marginal
Costs
Average costand marginalcost ($/unit)
MCATC
Minimum AVCATC
MinimumAVC
Quantity
MC always crosses AVC and ATC at their minimums.
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
0Labor(L)
Capital (K)
XQ = 20
C = 100
0Quantity of engines
Total Cost ($)
$100
Q = 10C = 180 C = 300
Q = 30
Long-Run Expansion Path
10 20 30
TCLR
Capital and labor are used to produce engines (quantities are per week)
Y
Z
X′ Z′
C = 120
C = 360
Short-Run Expansion Path
( 𝑲 = 𝟔)6
$300
$180
X
X′$120
$360
Y
Z
Z′
TCSR
Figure 7.6Figure 7.5
Short-Run and Long-Run Cost
Curves 7.5
Short-Run Versus Long-Run Average Total Cost Curves
Figure 7.6 shows that the short-run total cost curve will never fall below the long-
run total cost curve.
• This further implies that the short-run average total cost curve will never fall
below the long-run average total cost curve.
• This fact holds true for all short-run average total cost curves.
‒ Each of which corresponds to a different fixed capital level.
This property means that the long-run ATC curve will envelop all of the
short-run ATC curves.
Short-Run and Long-Run Cost
Curves 7.5
Figure 7.8 The Long-Run Average Total Cost Curve
Envelops the Short-Run Average Cost Curves
Average ATCSR,10 ATCSR,30total cost($/unit) ATCSR,20 ATCLR
X′ Z'$12
X Y Z9
0 Quantity10 20 30of engines
Short-Run and Long-Run Cost
Curves 7.5
Short-Run versus Long-Run Marginal Cost Curves
Just as with average costs,
• Short-run marginal cost is the cost of producing an additional unit of
output when capital is fixed.
• Long-run marginal cost is the cost of producing an additional unit of
output when both capital and labor are variable.
What does this imply for the shape of the marginal cost curves?
‒ In general, the long-run marginal cost curve will be flatter than
the short-run marginal cost curve.
Short-Run and Long-Run Cost
Curves 7.5
Figure 7.9 Long-Run and Short-Run Marginal Costs
Average cost ATCSR,10 MCLRATCSR,30and marginalATCSR,20cost ($/unit)
$12
B
Y9
A
MCSR,10 MCSR,30MCSR,20
0 Quantity10 20 30of engines
Note that each short run MC curve
intersects each ATCcurve at its minimum.
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 $500,000
Supplies $150,000
Electricity and water $15,000
Employee salaries $50,000
Dan’s salary $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 $600,000
Supplies $20,000
Electricity and water $10,000
Employee salaries $300,000
James’s salary $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 = $580,0001.
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:
Calculate the marginal cost of 1 to 5 truckloads of strawberries for
Fields Forever (assume labor to be the only variable cost).
Labor(Workers per Week)
Strawberries(Truckloads)
0 0
1 1
3 2
7 3
12 4
18 5
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
Fixed
Cost
Variable Cost Total
Cost
$200 $250 × 0 = $0 $200
$200 $250 ×1 = $250 $450
$200 $250 × 3 = $750 $950
$200 $250 × 7 = $1,750 $1,950
$200 $250 × 12 = $3,000 $3,200
$200 $250 × 18 = $4,700 $4,700
Marginal
Cost
—
$250
$500
$1,000
$1,250
$1,500
Labor(Workers per
Week)
Strawberries(Truckloads)
0 0
1 1
3 2
7 3
12 4
18 5
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.
Calculate the marginal cost of 100 to 500 framing jobs for Frame
de Art (assume labor to be the only variable cost).
Labor(Workers per
Week)
Framed Art(Hundreds per Week)
0 0
1 1
3 2
6 3
11 4
20 5
Additional
figure it out
Labor(Workers per
Week)
Framed Art(Hundreds per
Week)
0 0
1 1
3 2
6 3
11 4
20 5
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.
Fixed
Cost
Variable Cost Total
Cost
$500 $300 × 0 = $0 $500
$500 $300×1 = $300 $800
$500 $300 × 3 = $900 $1,400
$500 $300 × 6 =$1,800 $2,300
$500 $300 × 11 = $3,300 $3,800
$500 $300 × 20 = $6,000 $6,500
Marginal
Cost
—
$300
$600
$900
$1,500
$2,700
In-text
figure it out
Suppose a firm’s total cost curve is
and marginal cost
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.
45815 2 QQTC
830 QMC
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.
Variable cost is the portion that does vary with output:
Average total cost is simply total cost divided by output:
And the same applies to Average variable cost:
45454508015 2 FCTC
QQVCQQTC 81545815 2
Fixed2
QQATC
Q
QQATC
45815
45815 2
815815 2
QAVCQ
QQAVC
In-text
figure it out
b. Minimum average total cost occurs when marginal cost is
equal to average total cost.
So, ATC is minimized when Q = 1.732.
c. Finally, average variable cost is minimized when marginal
cost is equal to average variable cost.
And AVC is minimized when production ceases.
83045815 2
QQMCATC
0015830815 2
QQQQ
QQMCAVC
QQQ
Q 1545
3045
1583045
815
732.14515 2 QQ
Additional
figure it out
Suppose a firm’s total cost curve is
and marginal cost
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.
60610 2 QQTC
MC = 20Q+6
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.
Variable cost is the portion that does vary with output.
Average total cost is simply total cost divided by output.
And the same applies to Average variable cost,
60606006010 2 FCTC
QQVCQQTC 61060610 2
Fixed
2
QQATC
Q
QQATC
60610
60610 2
610610 2
QAVCQ
QQAVC
Additional
figure it out
b. Minimum average total cost occurs when marginal cost is
equal to average total cost.
So, ATC is minimized when Q = 2.45.
c. Finally, average variable cost is minimized when marginal
cost is equal to average variable cost,
and AVC is minimized when production ceases.
62060610 2
QQMCATC
0620610 2
QQQ
QQMCAVC
45.26
601062060610 222
Q
QQQQQ
In-text
figure it out
Steve and Sons Solar Panels has a production function:
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.
LMPKMPKLQ KL 4 ;4 ;4
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:
Total cost is therefore given by
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,
3
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.
10
8;
4
4
R
W
L
K
L
K
MP
MP
R
WMRTS
K
LLK
LLKorL
K8.0
10
8
10
8
140$58$1010$ wLrKTC
5)10(4200 LL
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:
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:
To minimize the cost of producing 200 solar panels, the firm should
employ 6.33 units of capital.
Finally, total costs are given by
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.
91.710
8200
10
84200 2
LLLLQ
33.6)91.7(10
8
10
8 KLK
58.126$91.78$33.610$ wLrKTC
Additional
figure it out
Suppose a wind turbine producer faces a production function
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?
LMPKMPKLQ KL 25.0 ;25.0 ;25.0
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.
Total cost is therefore given by
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,
The ratio of capital to labor that should be used to minimize costs
should be 𝟏𝟐
𝟐𝟐, or for every 1 worker they employ they should employ
0.545 units of capital.
200 0.25 8 100L L
22
12;
25.0
25.0
R
W
L
K
L
K
MP
MP
R
WMRTS
K
LLK
LKorL
K
22
12
22
12
376,1$10012$822$ wLrKTC
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:
To minimize the cost of producing 200 turbines, the firm should
employ 38.3 workers.
Solving for the amount of capital used yields:
To minimize the cost of producing 200 turbines, the firm should
employ 20.89 units of capital.
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.
3.3822
3200
22
1225.0200 2
LLLLQ
89.20)3.38(22
12
22
12 KLK
18.919$3.3812$89.2022$ wLrKTC
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
Set LMC = LATC to find the quantity that minimizes the LATC:
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.
232
250000,32250000,32
QQQ
QQQ
Q
LTCLATC
125
2250
3500000,32250000,32
2
22
Q
QQQQ
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:
Set LMC = LATC to find the quantity that minimizes the LATC:
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.
232
200000,15200000,15
QQQ
QQQ
Q
LTCLATC
15,000 - 200Q+Q2 =15,000 - 400Q+3Q2
200Q = 2Q2
Q =100