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Chapter Eight
Costs and the
Changes at
Firms over Time
Total Costs, Fixed Costs, Variable
Costs and Marginal Costs
Review:
• Total Costs – The sum of variable costs
and fixed costs
• Fixed Costs – Costs of production that do
not depend on the quantity of production
• Variable Costs – Costs of production that
vary with the quantity of production
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Total Costs, Fixed Costs, Variable
Costs and Marginal Costs (cont’d)
• Short run: The period of time during which
it is not possible to change all inputs to
production; only some inputs, such as
labor, can be changed
• Long run: The minimum period of time
during which all inputs to production can
be changed
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Total Costs, Fixed Costs, Variable
Costs and Marginal Costs (cont’d)
• Marginal Cost – The change in total costs
due to a one-unit change in quantity
produced
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Total Costs, Fixed Costs, Variable
Costs and Marginal Costs (cont’d)
• Average Total Cost (ATC) – The total costs of
production divided by the quantity produced;
also known as the cost per unit.
• Average Variable Cost (AVC) – The sum of all
variable costs of production divided by the
quantity produced.
• Average Fixed Cost (AFC) – The sum of all fixed
costs of production divided by the quantity
produced.
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Costs for On-The Move
• Table 8.1 illustrates the cost data for a
sample firm which specializes in moving
pianos. Total costs, variable costs and
marginal costs are all presented in the
table.
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Costs for On-The Move (cont’d)
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Costs for On-The Move (cont’d)
From Table 8.1, we can see that:
1) The fixed cost (FC) stays constant (FC = 300)
regardless of the quantity of pianos moved per
day.
2) The Average Fixed Cost (AFC) continuously
declines as the quantity is increased.
3) The Average Variable Cost (AVC) and the
Average Total Cost (ATC) first declines and
then rises as production is increased.
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Costs for On-The Move (cont’d)
From Table 8.1, we can see that:
4) The marginal cost (MC) also drops when
quantity is low, then rises as quantity
increases.
5) Once the firm experiences rising MC (or
ATC or AVC), the firm will continue to see
that cost rise as quantity keeps
increasing in the short run (it will not go
back down).
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Costs for On-The Move (cont’d)
• Figure 8.2 shows the graphical relationship
between the total fixed costs, the total variable
costs and the total costs. The costs are graphed
with quantity of the goods on the x-axis and
dollars on the y – axis.
• Recall that the relationship between the three
variables is captured by the equation:
Total costs = total fixed costs + total variable costs
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Costs for On-The Move (cont’d)
Figure 8.2
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Costs for On-The Move (cont’d)
• From Figure 8.2, we can see that total
fixed costs is a horizontal line, while the
total costs is an upward sloping line. The
vertical distance between the fixed cost
and the total cost at a given quantity is the
variable cost.
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Costs Depend on the Firm’s
Production Function
• According to Table 8.1, the firm incurs a
fixed cost of $300 per day. This
represents payments to the fixed inputs,
which, in this case, is four trucks and two
terminals. Once the contract to rent this
equipment is made, the firm needs to pay
$300 regardless of whether it moves zero
or 10 or 20 pianos.
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Costs Depend on the Firm’s
Production Function (cont’d)
• The variable costs represent the labor costs
incurred by the firm. Table 8.2 brings together
the production function and the labor or
variables costs of production.
• In the table, you can see that since the firm is
working in the short run time horizon, the only
way for it to be able to increase the quantity
produced is to increase the labor input, resulting
in an increase in the labor costs.
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Costs Depend on the Firm’s
Production Function (cont’d)
Table 8.2
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Costs Depend on the Firm’s
Production Function (cont’d)
• Figure 8.3 shows On-The-Move’s
production function in the short run. Note
that as the number of work hours are used
in production, the output increases, but at
a decreasing rate, (after around 50 hours
of work). Diminishing marginal product
kicks in after the third piano moved.
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On-the-Move’s Production Function
Figure 8.3
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Costs Depend on the Firm’s
Production Function (cont’d)
• As we have discussed in chapter 6, as more
labor is used in conjunction with a fixed capital
input, using additional labor results in a
diminishing marginal product of labor and an
increasing marginal cost of production.
• Increasing marginal product of labor →
decreasing marginal cost.
• Decreasing marginal product of labor →
increasing marginal cost.
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Costs Depend on the Firm’s
Production Function (cont’d)
• Average product of labor (APL)– the quantity
produced divided by the amount of labor input.
• The average product of labor is not the same as
the marginal product of labor (MPL).
Q
MPL 
L
Q
APL 
L
Where Q is the quantity of the output produced, L is the quantity of labor input
used and Δ is the symbol for “change in.”
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Average Cost Curves
• The information on the average total cost,
average fixed costs, average variable costs
and marginal costs found in Table 8.1 are
illustrated graphically in Figure 8.4.
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Average Cost Curves (cont’d)
Figure 8.4
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Average Cost Curves (cont’d)
•
With dollars on the y-axis and quantity of
output on the x-axis, Figure 8.4 shows that:
1) The average fixed cost curve is decreasing as
quantity of the output is increased.
2) The average variable cost curve is decreasing
up to the quantity of output =5, then starts to
increase as quantity of output is greater than 5.
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Average and Marginal Cost Curves
3) The average total cost curve is
decreasing up to the quantity of output
=7, then starts to increase as quantity of
output is greater than 8.
4) The marginal cost curve is decreasing up
to the quantity of output =3, then starts to
increase as quantity of output is greater
than 3.
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Average and Marginal Cost Curves
(cont’d)
A closer look at Figure 8.4 reveals:
1) The vertical distance between the ATC
and the AVC is becoming smaller as
quantity is increased. This vertical
distance is the AFC. Hence, since the
AFC can never be zero or negative, the
ATC will always be higher than the AVC,
and both curves will never cross.
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Average and Marginal Cost Curves
(cont’d)
• Proof that AVC + AFC = ATC
TC  TFC TVC
TC TFC TVC


Q
Q
CQ
ATC  AFC  AVC
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Average and Marginal Cost Curves
(cont’d)
2)
3)
The marginal cost curve intersects with the AVC at the
minimum point of the AVC.
The marginal cost curve intersects with the ATC at the
minimum point of the ATC.
This observation is a result of an important rule:
•
When the marginal cost is less than the average total
(or variable) cost, then the average total (or variable)
cost is declining.
•
When the marginal cost is greater than the average
total (or variable) cost, then the average total (or
variable) cost is rising.
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Marginal vs. Average in the Classroom
• To understand the rule of the
relationship between the
marginal cost and the average
costs, we look at class height
as an example. Suppose the
average height of the class is
5 feet 7 inches. If Yao Ming
(the marginal with height equal
to 7 feet 5 inches) walks into
the room, then the average
class height increases.
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Marginal vs. Average Height
in the Classroom
• Similarly, if Verne Troyer (a.k.a. Mini-Me in
Austin Powers movies; height 2 feet 8 inches)
walks into the room instead of Yao Ming, then
the average class height will decrease.
• Suppose instead that Angelina Jolie walks in the
class (height 5 feet 7 inches). The average
class height will not change. In this example,
the marginal equals the average.
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Generic Cost Curves
• Figure 8.5 illustrates how the average total
cost, the average variable cost and the
marginal cost typically behave.
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Generic Cost Curves (cont’d)
Figure 8.5
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Generic Cost Curves (cont’d)
•
Here is a useful checklist to remember when
drawing the ATC, the AVC and the MC
together.
1) Make sure the marginal cost curve cuts
through the average total cost curve and the
average variable cost curve at their minimum
points, and understand the reason for this.
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Generic Cost Curves (cont’d)
2) Make sure the vertical distance between the
average variable cost and the average total
cost gets smaller as you increase the amount
of production.
3) Put a small dip on the left-hand side of the
marginal cost curve before the upward slope
begins. This allows for the possibility of
decreasing marginal cost at very low levels of
production.
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Costs and Production: Short Run
• From Chapter 6, we learned that a profitmaximizing competitive firm will set the
quantity where the price equals the
marginal cost (P = MC). This profitmaximizing rule is shown in Figure 8.6,
where a horizontal line depicting the
market price is drawn, and the intersection
between the marginal cost and the
horizontal line shows the profit-maximizing
quantity.
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Costs and Production: Short Run(cont’d)
Figure 8.6
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Costs and Production: Short Run (cont’d)
• From Figure 8.6, we see that the ATC and
the AVC do not play a role in determining
the profit-maximizing quantity. However,
these two curves play a role in determining
the firm’s total profit and decision to shut
down.
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Costs and Production: Short Run (cont’d)
• Once the profit maximizing quantity is
determined, the firms total profit earned
can be determined by using the ATC
curve. Figure 8.7 shows the firm profit
earned using the cost diagram.
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Costs and Production: Short Run ( cont’d)
Figure 8.7
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Costs and Production: Short Run (cont’d)
• From Figure 8.7, the total revenue generated by
the firm is shown by the rectangle formed with
height = market price and the width = quantity (Q).
• The total cost incurred by the firm for producing Q
is shown by the rectangle formed with height =
ATC and the width = quantity (Q). This rectangle
is depicted by the hash-marked area.
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Costs and Production: Short Run (cont’d)
• From Figure 8.7, the total profits generated by
the firm is shown by the rectangle formed with
height = (market price – ATC) and the width =
quantity (Q). This area in Figure 8.7 is the
shaded area, without the hash-marks.
• Our graph in Figure 8.7 shows a firm that is
generating positive profits. Positive profits are
generated when at the profit maximizing
quantity, the market price is higher than the ATC.
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Costs and Production: Short Run (cont’d)
• If at the profit maximizing quantity (again,
where P = MC) the market price is below
the ATC but above the AVC curve, then the
firm is generating losses, but will not shut
down in the short run.
• This scenario is depicted in Figure 8.8.
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Costs and Production: Short Run (cont’d)
Figure 8.8
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Costs and Production: Short Run (cont’d)
• From Figure 8.8, the total profits
generated by the firm is shown by the
rectangle formed with height = (market
price – ATC) and the width = quantity (Q).
Since the ATC is higher than the price, the
profits are negative, and the firm is
incurring losses.
• The size of the loss is depicted by the
unshaded area with hash-marks.
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The Break Even Point
• The breakeven point – The point at which
the price equals the minimum of the
average total cost. This is also the point
where the price passes through the
intersection between the MC and the ATC
curve.
• The break even point is shown on the
middle graph on Figure 8.9.
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The Break Even Point (cont’d)
Figure 8.9
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The Break Even Point (cont’d)
• The leftmost graph on Figure 8.9 depicts a firm
that is generating positive profits in the short run
(P> ATC at the profit maximizing Q).
• The rightmost graph on Figure 8.9 depicts a firm
that is generating negative profits in the short
run (P < ATC at the profit maximizing Q).
• All three graphs depicted on Figure 8.9 show
firms that will not choose to shut down in the
short run.
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The Shutdown Point
• The shutdown point – The point at which the
price equals the minimum of the average
variable cost. This is also the point where the
price passes through the intersection between
the MC and the AVC.
• If the price equals the minimum of the AVC or
lower, then the firm must shut down. At any
quantity that the firm produces, the revenue that
the firm gets is not even enough to pay for the
variable costs of production.
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The Shutdown Point (cont’d)
• If the price equals the minimum of the ATC or
lower, the firm maximizes profit (or minimizes
losses) when producing at Q=0. The firm’s profit
equals the negative of the firm’s fixed costs.
If the firm shuts down,
Profit = total revenues – total costs
= 0 – total fixed costs
= – total fixed costs
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The Shutdown Point (cont’d)
Figure 8.10
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The Shutdown Point (cont’d)
• The leftmost graph on Figure 8.10 depicts a firm
that is receiving a price above the minimum of
the AVC, but below the minimum of the ATC. In
this case, the firm is losing profits, but must not
shut down.
• The middle graph on Figure 8.10 depicts a firm
that is receiving a price equal to the minimum of
the AVC. This firm is indifferent between shutting
down or producing at quantity = Q. In either
case, the firm’s losses will be the same (which is
the negative of the fixed costs).
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The Shut-Down Point (cont’d)
• The rightmost graph on Figure 8.10 depicts a
firm that is receiving a price below the minimum
of the AVC. In this case, the firm must shut
down to minimize its losses.
• One thing to remember about shutting down is
that having negative profits is a necessary—but
not a sufficient—condition for a firm to shut down
in the short run.
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Zero Profit and Shut Down Points
Two Different Points:
The shutdown point:
P = minimum AVC
The breakeven point
P = minimum ATC
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Costs and Production: Long Run
Recall:
• Long Run – A period of time when it is
possible for a firm to adjust all its inputs of
production.
• The input that we hold fixed in the short
run and allow to vary in the long run is
capital.
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Effect of Capital Expansion on
Total Costs
•
In order to analyze the effect of capital
expansion on total costs, we need to
analyze two effects:
1) The effect of the change in the capital
input on the fixed costs.
2) The effect of the change in the capital
input on the variable costs.
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Effect of Capital Expansion on
Total Costs (cont’d)
• When a firm increases its capital inputs, its
fixed costs increase, and its variable costs
decrease.
• Figure 8.11 illustrates the effects of an
increase in capital input on the fixed and
variable costs in the long run.
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Effect of Capital Expansion on
Total Costs (cont’d)
Figure 8.11
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Effect of Capital Expansion on
Average Costs
• Since the ATC = total costs/Q, then the
effect of capital expansion depends on the
size of the increase in fixed costs, the
decrease in the variable costs, and the
production quantity.
• Figure 8.12 shows the generic effect of an
increase in the capital inputs on the
average total costs.
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Effect of Capital Expansion on
Average Costs (cont’d)
Figure 8.12
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Effect of Capital Expansion on
Average Costs (cont’d)
• In Figure 8.12, ATC1 represents the average total
cost before capital expansion and ATC2
represents the average total cost after capital
expansion.
• As Figure 8.12 shows, ATC2 is higher than ATC1
when the quantity is low. This is because the
increase in the average fixed costs outweigh the
decrease in the average variable costs when Q
is low.
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Effect of Capital Expansion on
Average Costs (cont’d)
• At higher levels of Q (Q>8 in Figure 8.12),
ATC1 is higher than ATC2. This is because
the decrease in the average variable costs
now outweighs the increase in the average
fixed costs when Q is high.
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Effect of Capital Expansion on
Average Costs (cont’d)
• Figure 8.13 shows four different short run
ATCs, corresponding the average total
costs using four different levels of capital
input. ATC1 represents the average total
cost using the least amount of capital
input, while ATC4 represents the average
total cost using the most amount of capital
input.
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Effect of Capital Expansion on
Average Costs (cont’d)
Figure 8.13
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The Long Run Average Variable Cost
• Long Run Average Total Cost – The curve
that traces out the short-run average total
cost curves, showing the lowest average
total cost for each quantity produced as
firms expand in the long run
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The Long Run Average Variable Cost
(cont’d)
• Since firms can adjust capital inputs in the
long run, each firm will increase or
decrease capital inputs in order to produce
the profit maximizing quantity at the lowest
average total cost. The derivation of the
long run average total cost is traced out in
the thicker green line in Figure 8.13.
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Economies of Scale
• Economies of scale – A situation in which the
long run average total cost declines as the
output of a firm is increased.
• Constant Returns to Scale – A situation in which
the long run average total cost is constant as the
output of a firm is increased.
• Diseconomies of Scale – A situation in which the
long run average total cost rises as the output of
a firm is increased.
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Economies of Scale (cont’d)
• Minimum efficient scale – The smallest scale of
production for which the long run average total
cost is at a minimum.
• Figure 8.15 illustrates the typical shape of the
long run average total cost curve. It also shows
the regions corresponding to economies of
scale, diseconomies of scale, constant returns to
scale and the minimum efficient scale.
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Economies of Scale (cont’d)
Figure 8.15
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Economies of Scale (cont’d)
From Figure 8.15, note the following:
1) The declining part of the long run ATC
curve corresponds to the region with
economies of scale.
2) The flat part of the long run ATC curve
corresponds to the region with constant
returns to scale.
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Economies of Scale (cont’d)
3) The increasing part of the long run ATC
curve corresponds to the region with
diseconomies of scale.
4) The quantity where the long run ATC
begins to enter constant returns to scale
is the minimum efficient scale.
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Mergers and Economies of Scope
• Mergers occur because firms try to lower
their costs. When two similar firms merge
to lower costs, they merge to take
advantage of economies of scale. When
two different firms merge to lower costs or
to create new products, their merger is
done to take advantage of economies of
scope.
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Mergers and Economies of Scope (cont’d)
• Table 8.4 lists some of the recent mergers
of large companies. The merger of the
first eight pairs of companies were driven
by economies of scale. The merger of
America Online and Time Warner may be
due to economies of scope.
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Mergers and Economies of Scope (cont’d)
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Key Terms
•
•
•
•
•
•
Short Run vs. Long Run
Average Total Cost (ATC)
Average Variable Cost (AVC)
Average Fixed Cost (AFC)
Average product of labor
Breakeven and shutdown point
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Key Terms (cont’d)
•
•
•
•
•
•
Long run average total cost curve
Economies of scale
Diseconomies of scale
Constant returns to scale
Minimum efficient scale
Economies of scope
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