Transcript ATC

Next Week
• Complete Homework 8 on Homework
advantage by Sunday, October 1 at
11:55 pm.
• Read Chapter 9, Perfect Competition
and the Supply Curve
Chapter 8
Behind the Supply
Curve: Inputs and Costs
September 28, 2006
Motivation: Why study the relationship
between inputs and costs?
(In answering this question, assume the
perspective of a producer or firm.)
• Our ultimate goal is to understand how a profitmaximizing firm chooses the quantity of output it will
supply at different prices (supply curve), and how it
decides whether to enter or exit the market (industry)
for that good.
• This understanding depends understanding the cost
relationships between input and output.
Motivation, cont.
Profit maximization and the output decision
•
•
The rule for determining whether a firm is profitable depends
on a comparison of the market price (P) of the good to the
firm’s break even price.
A firm’s break even price is its minimum average total cost
(ATC):
–
–
–
•
If P > ATC, the firm earns a profit
If P = ATC, the firm breaks even
If P < ATC, the firms incurs a loss
The proof of the pudding (the rule) is reserved for Chapter 9.
From Chapter 8 we can get answers to the questions on the
next slide.
Today’s focus
• How can a firm identify its minimum average
total cost ATC?
• Why does it matter if the firm makes its
production decisions in the long run rather
than the short run, and vice versa?
– Short run: a time period in which at least one
input is fixed
– Long run: a time period in which all inputs are
variable (their quantity can be adjusted).
Preview of conclusions:
identifying minimum ATC
1.
Most firms have U-shaped average total cost (ATC)
curves because average total cost consists of two
parts:
–
–
2.
3.
Average fixed cost which falls as output rises (the
spreading effect)
Average variable cost which rises with output
(diminishing returns effect).
When ATC is U-shaped, the bottom of the U is the
level of output at which average total cost in
minimized.
Moreover, the marginal cost (MC) curve crosses
the ATC curve from below at the point of minimumcost output.
Primary conclusions:
Costs in the long run
1. A firm’s costs may be different in the long
run than in the short run because in the long
run, a firm may choose its level of fixed input
and hence its fixed cost. In contrast, fixed
cost is taken as a given in the short run.
2. A firm chooses its fixed cost in the long-run
on the basis of the level of output it expects
to produce.
identifying minimum ATC
• Step 1: Know the production function
Production function: the relationship
between the quantity of inputs a firm uses
and the quantity of output it produces.
• Step 2: Use the price of inputs to translate the
relationship between input and output into the
relationship between output and costs.
identifying minimum ATC
• Step 3: Identify FC, VC
• fixed cost (FC): a cost that does not depend on the quantity of
output produced. It is the cost of the fixed input.
• variable cost (VC): a cost that depends on the quantity of
output produced. It is the cost of the variable input.
• Step 4: Calculate total costs (TC)
• total cost: the sum of the fixed cost and the variable cost of
producing a specific quantity of output:
TC = FC + VC
Discrete Example of fixed and variable costs of
production for a toy manufacturing company
Q
0
1
2
3
4
5
6
VC*
0
$10
25
45
70
100
135
FC
$30
30
30
30
30
30
30
* Labor needed to produce Q x price of labor
TC
$30
40
55
75
100
130
165
Notes about toy manufacturing
• The variable input is labor. As more toys are
produced, variable costs rise as more labor is
hired. The marginal product of labor falls with
each additional unit of labor.
• Because labor is paid an hourly wage, we
measure FC per hour.
• Note that total cost always rises as more toys
are produced.
identifying minimum ATC
• Step 5: Calculate AFC, AVC, ATC
• average total cost: total cost divided by quantity of
output produced.
ATC = TC/Q
• average fixed cost: the fixed cost per unit of output.
AFC = FC/Q
• average variable cost: the variable cost per unit of
output.
AVC = VC/Q
Example of fixed and variable costs of
production for a toy manufacturing
company
TC
AVC
AFC
ATC
Q
VC
FC
(1000s)
0
1
2
3
4
5
6
0
$10
25
45
70
100
135
(per hour)
(VC+FC)
(VC/Q)
(FC/Q)
(TC/Q)
$30
30
30
30
30
30
30
$30
40
55
75
100
130
165
-10
12.5
15
17.5
20
22.5
-30
15
10
7.5
6
5
-40
27.5
25
25
26
27.5
Questions about the costs
of toy manufacturing
• At what rate of production (Q) is ATC at a
minimum?
• Why is it important for a company to know
what its average total cost per item is?
• Why does average fixed cost always fall?
Answers
• At what rate of production (Q) is ATC at a
minimum?
– Between 3000 and 4000 toys
• Why is it important for a company to know
what its ATC per item is?
– Because firms calculate their profit per unit from their
ATC in relation to market ATC.
• Why does average fixed cost always fall?
– Mathematically, because you are dividing a fixed dollar
amount by an increasing quantity. In terms of economic
intuition, you are spreading the fixed cost over more
more toys produced.
identifying minimum ATC
Corresponding Graph
1.
45
40
35
30
Most firms have U-shaped
average total cost (ATC)
curves because average total
cost consists of two parts:
–
ATC
AVC
AFC
25
20
15
10
–
2.
5
0
1 2 3 4 5 6
Average fixed cost (AFC)
which falls as output rises
(the spreading effect)
Average variable cost (AVC)
which rises with output
(diminishing returns effect).
When ATC is U-shaped, the
bottom of the U is the level of
output at which average total
cost in minimized.
identifying minimum ATC
Adding MC to the picture
•
Definition of Marginal cost (MC): the change in total
cost generated by a change in the quantity of output-i.e., the slope of the total cost curve as output
increases by one unit: the “rise” (∆TC) divided by the
“run” (∆Q).
MC = ∆TC/∆Q
identifying minimum ATC
Adding MC to the picture
Q
(1000s)
TC
(VC + FC)
0
$30
MC
(∆TC/∆Q)
$10
1
40
15
2
55
20
3
75
25
4
100
30
5
130
35
6
165
identifying minimum ATC
Adding MC to the picture
Q
ATC
0
--
MC
$10
1
$40
15
2
3
4
20
2. Over what range of production
does the diminishing returns
effect dominate?
25
3. Now what is the minimum-cost
output level?
27.5
25
25
30
5
26
35
6
27.5
1. Over what range of toy
production does the spreading
effect dominate?
4. What is the relationship
between ATC and MC at this
level?
identifying minimum ATC
Adding MC to the picture
Q
ATC
0
--
MC
$10
1
$40
15
2
27.5
20
3
4
5
25
3. Now what is the minimum-cost
output level? 3000 to 4000
30
4. What is the relationship
between ATC and MC at this
level? ATC = MC
25
26
27.5
2. Over what range of production
does the diminishing returns
effect dominate? 4000 to
6000
25
35
6
1. Over what range of toy
production does the spreading
effect dominate? 1000 to
3000
identifying minimum ATC
Q
ATC
0
--
1
2
3
4
5
MC
$10
45
40
15
35
30
20
25
20
25
15
10
30
5
0
$40
27.5
25
25
1 2 3 4 5 6
26
35
6
27.5
ATC
MC
identifying minimum ATC
3.
45
40
35
30
25
20
15
10
5
0
ATC
MC
1
2
3
4
5
6
Moreover, the marginal cost
(MC) curve crosses the ATC
curve from below at the point
of minimum-cost output.
– If MC is less than ATC,
ACT is falling. Increasing
Q will reduce ATC.
– If MC is greater than ATC,
ATC is rising. Decreasing
Q will lower ATC.
FC versus VC
Example Problem
• Consider the following
costs that an airline
company faces:
–
–
–
–
–
–
–
Administrative salaries
Cost of jets
Food
jet fuel
Landing fees
Marketing costs
Salaries of pilots and
crew
– Web site maintenance
• Which of these costs
are variable costs?
• Which costs stay the
same even if they fly
the plane (fixed costs)?
FC versus VC:
Example Problem
• Consider the following costs
that an airline company
faces:
–
–
–
–
–
–
–
–
Administrative salaries
Cost of jets
Food
jet fuel
Landing fees
Marketing costs
Salaries of pilots and crew
Web site maintenance
• Which of these costs
are variable costs?
• Which costs stay the
same even if they fly
the plane (fixed costs)?
ATC versus MC
• Consider the following costs
that an airline company
faces:
– Administrative salaries
– Cost of jets
– Food
– jet fuel
– Landing fees
– Marketing costs
– Salaries of pilots and
crew
– Web site maintenance
• Now consider the airline’s
decision to fly the next flight.
Which costs are relevant to
that decision? The sum of
these costs is the MC of the
next flight. ATC or MC?
• How would you calculate the
average total costs (the cost
per passenger mile)?
ATC versus MC
• Consider the following costs
that an airline company
faces:
– Administrative salaries
– Cost of jets
– Food
– jet fuel
– Landing fees
– Marketing costs
– Salaries of pilots and
crew
– Web site maintenance
•
Now consider the airline’s
decision to fly the next flight.
Which costs are relevant to that
decision? ATC or MC
– MC are the relevant costs
because they are the only
costs incurred by
authorizing the flight.
•
How would you calculate the
average total costs (the cost per
passenger mile)?
– Divide the total costs of
flying a fixed number of
miles by that fixed
number.
Why does it matter if the firm makes
its production decisions in the long
run rather than the short run?
A firm’s costs may be different in the long
run than in the short run because in the
long run, a firm may choose its level of
fixed input and hence its fixed cost. In
contrast, fixed cost is taken as a given in the
short run.
costs in the long run
• A firm chooses its
fixed cost in the
long-run on the
basis of the level of
output it expects to
produce.
• There is a tradeoff
between higher
fixed cost and lower
variable cost for any
given level of output,
and vice versa.
costs in the long run
•
For each output level,
there is some choice
of fixed cost that
minimizes a firm’s
average total cost for
that output level.
•
The locus of these
points is the firm’s
long-run average cost
curve (LRATC).
costs in the long run
• The firm will always try to
produce at some point on the
LRATC. If demand conditions
move it off the LRATC curve,
it moves along its short-run
average total cost curve until
it can adjust its fixed input to
the new output level. The
adjustment will return it to its
LRATC curve.
Costs in the long run
The shape of a firm’s LRATC curve is determined
by the presence of scale effects in production.
There are:
5.
–
–
–
•
economies of scale when LRATC decreases as output
increases
Constant returns to scale when if LRATC do not change
as output increases
diseconomies of scale when LRATC increases as output
increases.
The presence of scale effects depends on
technology.