Transcript Chapter 7: Short-Run Costs and Output Decisions

Ch. 7: Short-run Costs and Output Decisions
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
7.1
Costs in the Short Run
7.2
The short run is a period of time for which two conditions hold:
1. The firm is operating with at least one factor of production
being fixed.
2. Firms can neither enter nor exit an industry.
There are two types factors of production (inputs) in the short-run:
fixed and variable
 two types of costs: fixed costs and variable costs.
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.
Variable cost is a cost that depends on the level of production
chosen.
Costs in the Short Run
Total Cost (TC) of Production is the sum of Total Fixed
Costs (TFC) and Total Variable Costs (TVC):
TC = TFC + TVC
Total Fixed Costs (TFC): 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
7.3
Short-Run Fixed Cost (Total and Average) for
Widget, Inc.
AFC
0
55
1
55
55.00
2
55
27.50
3
55
18.33
4
55
13.75
5
55
11.00
6
55
9.17
7
55
7.86
8
55
6.88
9
55
6.11
10
55
5.50
AFC falls as output rises; a
phenomenon sometimes
called spreading overhead.
TFC
400
$
TFC
200
0
0
2
4
6
8
10
q: units of output
AFC
$ per unit
q
7.4
60.00
40.00
20.00
0.00
0
2
4
6
q: units of output
8
10
Total Variable Costs
7.5
Total Variable Costs (TVC) depend on the level of production. The
relationship should be positive: as the firm produces more output,
total variable costs will increase. The question is how does it
increase?
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. It measures the
additional cost of inputs required to produce each successive unit
of output.
TC TFC TVC
MC 


q
q
q
TFC
TVC
Because,
by
definition,
0

q
q
Costs of Production Schedule for Widget, Inc.
Q
TVC
TFC
TC
MC=TC/ q
0
0
55
55
---
1
30
55
85
30
2
55
55
110
25
3
75
55
130
4
105
55
160
5
155
55
210
6
225
55
280
7
315
55
370
8
425
55
480
9
555
55
610
10
705
55
760
7.6
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(s)
means that:
1. The firm has limited capacity to produce output
2. The firm faces diminishing marginal product for its variable inputs
(Chapter 6)
As a firm approaches that capacity, it becomes increasingly costly to produce
successively higher levels of output.
Example:
From Ch. 6
L
TP MPL
1
10
2
25
3
35
4
40
5
42
6
42
7.7
The Shape of the Marginal Cost Curve in the
Short Run
Marginal costs ultimately increase with output in the
short run.
7.8
Graphing Total Variable Costs and Marginal
Costs: Widget, Inc.
TVC
Total variable costs always
increase with output. The
marginal cost curve shows
how total variable cost
changes with single unit
increases in total output.
800
$
600
400
200
0
0
2
4
6
8
10
12
q: units of output
For output levels below
q=3, TVC increases at a
decreasing rate. For output
levels above q=3, TVC
increases at an increasing
rate.
$ per unit
MC
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
0
2
4
7.9
6
q: units of output
8
10
12
Graphing Total Variable Costs and Marginal
Costs: The General Case
• Total variable costs always
increase with output.
$
TVC
$ per unit
qo
q
MC
qo
q
7.10
• In general, TVC might initially
increase with q at a decreasing
rate, but will eventually begin
to increase with q at an
increasing rate due to the law of
diminishing marginal product
(diminishing returns)
Average Variable Cost
Average variable cost (AVC) is the total variable cost
divided by the number of units of output.
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.
TVC
AVC 
q
7.11
Complete Cost Schedule for Widget, Inc.
Q
TVC
TFC
TC =
TVC+TFC
MC=
TVC/ q
0
0
55
55
---
1
30
55
85
30
2
55
55
110
25
3
75
55
130
20
4
105
55
160
30
5
155
55
210
50
6
225
55
280
70
7
315
55
370
90
8
425
55
480
110
9
555
55
610
130
10
705
55
760
150
AVC=
TVC/q
AFC=
TFC/q
7.12
ATC=
TC/q
Relationship Between Average Variable Cost and
Marginal Cost: Widget, Inc.
$ per unit
MC and AVC
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
MC
AVC
0
2
4
6
q: units of output
8
10
12
7.13
Relationship Between Average Variable Cost and
Marginal Cost: The General Case
$ per unit
MC
AVC
qo q1
q
For output levels between qo
and q1, MC is rising
(diminishing returns set in) but
MC is still less than AVC, so
AVC continues to fall.
7.14
When marginal cost is below
average cost, average cost is
declining. This occurs for
output levels below q1.
When marginal cost is above
average cost, average cost is
increasing. This occurs for
output levels greater than q1.
Rising marginal cost intersects
average variable cost at the
minimum point of AVC.
Total Costs: The General Case
7.15
Adding TFC to TVC means
adding the same amount of
total fixed cost to every level
of total variable cost.
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.
TC = TVC + TFC
Total Costs: Widget, Inc.
Total Cost Curves
TC
800
$
600
TVC
400
200
TFC
0
0
2
4
6
q: units of output
8
10
7.16
The curvature pf TVC
amd TC is not obvious
in this graph, but an
examination of the
numbers shows us that
rate of increase in total
costs is initially
decreasing and then
begins to increase.
Average Total Cost: The General Case
7.17
Average total cost (ATC) is
total cost divided by the
number of units of output (q).
ATC = AFC + AVC
but also:
TC TFC TVC
ATC 


q
q
q
Because AFC falls with
output, an ever-declining
amount is added to AVC.
Relationship Between Average Total Cost and
Marginal Cost: General Case
7.18
 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.
Average and Marginal Cost Curves: Widget, Inc.
7.19
$ per unit
Graph of MC, ATV, AVC
MC
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
ATC
AVC
0
2
4
6
q: units of output
8
10
12
Interpreting the Numbers
7.20
Pick an output level and examine the numbers: IF our widget manufacturer
produces q = 4 units 
Total costs are TC = $160 where $55 of this cost is fixed and must be paid even
if the firm produces q = 0 units; $105 are total variable costs: the cost of the
variable inputs that were used to produce the 4 units of output.
MC = $30 meaning the 4th unit increased total costs by $30. On the margin, the
4th unit incurred $30 in additional variable costs.
ATC = $ 40 which is $ 40 per unit produced. On average each of the 4 units
cost $ 40 to produce.
AVC = $ 26.25 which is $ 26.25 per unit produced. On average, each of the 4
units incurred $26.25 in variable costs.
AFC = $13.75 which is $ 13.75 per unit produced. On average, each of the 4
units incurred $13.75 in fixed costs.
Output Decisions: Revenues, Costs, and Profit
Maximization
7.21
In the short run, a competitive firm faces a demand curve that is simply a
horizontal line at the market equilibrium price. The firm “looks” to the
market to get the market price. Now it must decide what output level to offer
for sale (its “quantity supplied”).
Widget Firm
Widget Market
S
$70
$70
d
D
Q
q
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. Because a perfectly competitive firm can all it
wants to at the market price, P = MR. (Price and
Marginal Revenue are equivalent concepts)
TR
MR 
P
q
7.22
Comparing Costs and Revenues to Maximize
Profit
7.23
The Profit-Maximizing Rule:
The profit-maximizing level of output (q*) for all firms is the
output level where MR = MC.
• The key idea is that firms will ↑ q long as MR > MC. But as q ↑,
MC ↑ while MR stays flat. The firm will maximize profits at the
output level q where MR = MC. Beyond this output level, the
firm would not want to ↑ q because that would cause MC > MR
and thus lower profits.
• But, in perfect competition, MR ≡ P  the profit-maximizing
perfectly competitive firm will produce up to the point where the
marginal cost of the last unit produced equals the price it
receives from selling this last unit (q* is where P = MC)
Profit Analysis for Widget, Inc.
q
0
1
2
3
4
5
6
7
8
9
TVC
0
30
55
75
105
155
225
315
425
555
TFC
55
55
55
55
55
55
55
55
55
55
TC
55
85
110
130
160
210
280
370
480
610
7.24
MC
MR=P
TR
profits
30
25
20
30
50
70
90
110
130
70
70
70
70
70
70
70
70
70
70
140
210
280
350
420
490
560
630
-15
30
80
120
140
140
120
80
20
Apply the profit-maximizing rule: find q* where P = MC. This occurs at q
= 6. The profit levels for the various output levels are shown in the last
column. It is true that q = 5 yields the same profit as q = 6. This does not
invalidate the rule; the discrepancy is due to the “whole numbers” problem
Graph of Profit-Maximization
Widget Market
7.25
Widget Firm
S
MC
ATC
$70
d
$70
AVC
D
q*=6
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 with one caveat
that we will study in the next chapter.