Short-Run Costs
and Output Decisions
Chapter 8
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Decisions Facing Firms
DECISIONS
INFORMATION
are based on
1. The quantity of output to
supply
1. The price of output
2. How to produce that
output (which technique
to use)
2. Techniques of
production available*
3. The quantity of each
input to demand
3. The price of inputs*
*Determines production costs
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Costs in the Short Run
•
•
The short run is a period of time for which two
conditions hold:
1.
The firm is operating under a fixed scale (fixed
factor) of production, and
2.
Firms can neither enter nor exit an industry.
In the short run, all firms have costs that they
must bear regardless of their output. These
kinds of costs are called fixed costs
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Costs in the Short Run
• Fixed cost is any cost that does not depend on the
firm’s level of output. These costs are incurred even if
the firm is producing nothing, i.e., output=0.
• Variable cost is a cost that depends on the level of
production chosen.
TC  TFC  TVC
Total Cost = Total Fixed + Total Variable
Cost
Cost
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Total Fixed Costs and Average Fixed Costs
• Total fixed costs are also called overheads
• Firms have no control over fixed costs in the short
run. For this reason, fixed costs are sometimes
called sunk costs.
• Average fixed cost (AFC) is the total fixed cost (TFC)
divided by the number of units of output (q):
TFC
AFC 
q
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Short-Run Fixed Cost (Total and
Average) of a Hypothetical Firm
(1)
q (output)
(2)
TFC
(3)
AFC =(TFC/q)
$ --
0
$1,000
1
1,000
1,000
2
1,000
500
3
1,000
333
4
1,000
250
5
1,000
200
• AFC falls as output rises; a
phenomenon sometimes
called spreading overhead.
• AFC never reaches zero
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Variable Costs
• The total variable cost curve is a graph
that shows the relationship between total
variable cost and the level of a firm’s output.
The total variable
cost depends on:
1.Technique of production and
2. input prices.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Derivation of Total Variable Cost Schedule
from Technology and Factor Prices
PRODUCT
USING
TECHNIQUE
UNITS OF
INPUT REQUIRED
(PRODUCTION FUNCTION)
K
L
TOTAL VARIABLE
COST ASSUMING
PK = $2, PL = $1
TVC = (K x PK) + (L x PL)
1 Units of
output
A
B
4
2
4
6
(4 x $2) + (4 x $1) = $12
(2 x $2) + (6 x $1) = $10
2 Units of
output
A
B
7
4
6
10
(7 x $2) + (6 x $1) = $20
(4 x $2) + (10 x $1) = $18
3 Units of
output
A
B
9
6
6
14
(9 x $2) + (6 x $1) = $24
(6 x $2) + (14 x $1) = $26
•
The total variable cost curve shows the cost of production using the best
available technique at each output level, given current factor prices
•
Here, K denotes variable capital in the short run
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Marginal Cost
• Marginal cost (MC) is the increase in total cost that
results from producing one more unit of output.
• Marginal cost reflects changes in variable costs
(fixed costs do not change when output changes,
hence the only relevant cost here is the variable
cost)
 TC  TFC  TVC
MC 


Q
Q
Q
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Derivation of Marginal Cost from
Total Variable Cost
UNITS OF OUTPUT
TOTAL VARIABLE COSTS
($)
MARGINAL COSTS
($)
0
1
0
10
0
10
2
18
8
3
24
6
• Marginal cost measures the additional cost
of inputs required to produce each successive
unit of output (refer to previous table)
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
The Shape of the Marginal Cost Curve in
the Short Run
•
The fact that in the short run every firm is
constrained by some fixed input means that:
1.
The firm faces diminishing returns to variable inputs, and
2.
The firm has limited capacity to produce output.
•
As a firm approaches that capacity, it becomes
increasingly costly to produce successively higher
levels of output.
•
Hence diminishing returns or decreasing marginal
product imply increasing marginal cost
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
The Shape of the Marginal Cost Curve
in the Short Run
•
Marginal costs ultimately increases with
output in the short run.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Graphing Total Variable Costs and
Marginal Costs
• Total variable costs always
increases with output-slope
always positive.
• The marginal cost curve
shows how total variable cost
changes with single unit
increases in total output.
• Below 100 units of output,
TVC increases at a
decreasing rate. Beyond 100
units of output, TVC
increases at an increasing
rate.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Average Variable Cost
• Average variable cost (AVC) is the total
variable cost divided by the number of units of
output. (AVC =TVC/q)
• Marginal cost is the cost of one additional unit.
Average variable cost is the average variable
cost per unit of all the units being produced.
• Average variable cost follows marginal cost, but
lags behind.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Relationship Between Average Variable
Cost and Marginal Cost
• When marginal cost is below
average cost, average cost is
declining.
• When marginal cost is above
average cost, average cost is
increasing.
• Rising marginal cost
intersects average
• At 200 units of output, AVC
variable cost at the
is minimum, and MC = AVC.
minimum point of AVC.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Short-Run Costs of a Hypothetical Firm
(1)
q
(3)
MC
( TVC)
(2)
TVC
(4)
AVC
(TVC/q)
(5)
TFC
(6)
TC
(TVC + TFC)
-
$1,000
$ 1,000
(7)
AFC
(TFC/q)
0
$ -
1
10
10
10
1,000
1,010
1,000
1,010
2
18
8
9
1,000
1,018
500
509
3
24
6
8
1,000
1,024
333
341
4
32
8
8
1,000
1,032
250
258
5
42
10
8.4
1,000
1,042
200
208.4
0
$
$
$
-
(8)
ATC
(TC/q or AFC + AVC)
$
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
500
8,000
20
16
1,000
9,000
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
2
Karl Case, Ray Fair
18
Total Costs
• Adding TFC to TVC
means adding the same
amount of total fixed cost
to every level of total
variable cost.
TC  TFC  TVC
© 2002 Prentice Hall Business Publishing
• Thus, the total cost curve
has the same shape as
the total variable cost
curve; it is simply higher
by an amount equal to
TFC.
Principles of Economics, 6/e
Karl Case, Ray Fair
Average Total Cost
• Average total cost (ATC)
is total cost divided by
the number of units of
output (q).
ATC  AFC  AVC
TC TFC TVC
ATC 


q
q
q
• Because AFC falls with
output, an ever-declining
amount is added to AVC.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Relationship Between Average Total
Cost and Marginal Cost
• ATC follows the MC curve but
lags behind it
• If marginal cost is below
average total cost, average
total cost will decline toward
marginal cost.
• If marginal cost is above
average total cost, average
total cost will increase.
• Marginal cost intersects
average total cost and average
variable cost curves at their
minimum points.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Output Decisions: Revenues, Costs,
and Profit Maximization
• In the short run, a competitive firm faces a demand
curve that is simply a horizontal line at the market
equilibrium price.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Total Revenue (TR) and
Marginal Revenue (MR)
• Total revenue (TR) is the total amount that a firm
takes in from the sale of its output.
TR  P  q
• Marginal revenue (MR) is the additional revenue
that a firm takes in when it increases output by
one additional unit.
• In perfect competition, P = MR.
 TR P(  q )
MR 
 P

q
q
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Comparing Costs and Revenues to
Maximize Profit
• The profit-maximizing level of output for all
firms is the output level where MR = MC.
• In perfect competition, MR = P, therefore,
the profit-maximizing perfectly competitive
firm will produce up to the point where the
price of its output is just equal to short-run
marginal cost.
• The key idea here is that firms will produce
as long as marginal revenue exceeds
marginal cost.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Profit Analysis for a Simple Firm
(1)
q
(2)
TFC
(3)
TVC
$
0
(4)
MC
$ -
(5)
P = MR
(6)
TR
(P x q)
$ 15
$
0
$ 10
1
10
10
10
15
2
10
15
5
3
10
20
4
10
5
6
$ -10
15
20
-5
15
30
25
5
5
15
45
30
15
30
10
15
60
40
20
10
50
20
15
75
60
15
10
80
30
15
90
90
0
Principles of Economics, 6/e
$
(8)
PROFIT
(TR - TC)
10
© 2002 Prentice Hall Business Publishing
0
(7)
TC
(TFC + TVC)
Karl Case, Ray Fair
The Short-Run Supply Curve
• At any market price, the marginal cost curve shows the output level
that maximizes profit. Thus, the marginal cost curve of a perfectly
competitive profit-maximizing firm is the firm’s short-run supply curve.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair