Transcript No Slide Title

Lecture 9:
The Cost of Production
Readings: Chapters 11
The Cost of Production
What determines the shape of the firm’s total cost
curve?
 The shape of the total cost curve depends on:

Input prices

Technology
The Cost of Production: the Production Function
Q: How are input prices and technology related to a firm’s
cost curve?

Begin with a model of a firm’s organizational problem in
which the firm is assumed to:

Purchase L units of homogeneous labour in a
competitive labour market for price w.

Have invested K units of homogeneous capital
which earns the competitive capital market price i.

Combine K units of capital and L units of labour to
produce Q units of output, each unit of which is
sold in a competitive output market for price p
The Cost of Production
The Cost of Production : the Production Function
Q: What sort of decision model is this?
 The firm has two planning horizons

short run — at least one fixed input;
other inputs variable

long run — all inputs are variable

This is a short-run decision model in which
the firm’s capital stock is fixed.

The firm can alter its capital stock over the
long-run by altering investment flows.
The Cost of Production : the Production Function
Q: What determines the short-run relationship
between labour input flows and output flows?
 Two things govern this relationship:

1. The amount of capital (K).

2. The technology available to the firm.
Q: How can this relationship be characterized?
 A production function: Q=f(L)
The Cost of Production : the Production Function
Q: What do most production functions look like?
 The graph of most production functions are S
shaped curves called Total Product (TP) curves.
 The TP curve divides the set into an technically
feasible and unfeasible sets.
 The curve itself provides all the technically
efficient plans available to the firm.
The Cost of Production: the Production Function
 Total Product Curve

Figure 11.1 shows
a total product
curve.

The total product
curve shows how
total product
changes with the
quantity of labour
employed.
The Cost of Production: the Production Function
The total product
curve is similar to
the PPF.
It separates
attainable output
levels from
unattainable
output levels in
the short run.
The Cost of Production: Productivity
Marginal Product Curve

Figure 11.2 shows
the marginal product
of labour curve and
how the marginal
product curve relates
to the total product
curve.

The first worker hired
produces 4 units of
output.
The Cost of Production: Productivity

The second worker
hired produces 6
units of output and
total product
becomes 10 units.

The third worker
produces 3 units of
output and total
product becomes
13 units.

And so on.
The Cost of Production: Productivity
 Q: Why does the TP curve for most firms have
this characteristic S shape?
 A: The S shape reflects the common experience
that, for a given plant size, additions of labour
initially cause the Marginal Product of Labour
(MPL) to rise, but eventually the MPL will fall.
 Q: What is the MPL?
 A: The MPL is the addition to TP (output) that an
additional worker would add: MPL = (DTP / DL)
The Cost of Production: Productivity

To make a graph of the
marginal product of
labour, we can stack
the bars in the
previous graph side by
side.

The marginal product
of labour curve
passes through the
mid-points of these
bars.
Deriving Marginal Product From Total Product
Output
15
13
d
10
TP
c
4
1 2 3 4 5
MP
Labour
6
4
3
2
MPL
1 2 3 4 5
Copyright © 1997 Addison-Wesley Publishers Ltd.
Labour
Textbook p. 213
The Cost of Production: Productivity
Diminishing Marginal
Returns Eventually
 When the marginal
product of a worker
is less than the
marginal product of
the previous worker,
the marginal product
of labour decreases.
 The firm experiences
diminishing
marginal returns.
The Cost of Production: Productivity
 Q: Is there a quick way to derive the MPL curve
from the TP curve?
 A: At each level of employment (L), the slope of
the tangent to the TP curve gives the MPL.
 Q: Where is the dividing line between increasing
and decreasing marginal returns to labour?
 A: The inflection point on the TP curve.
The Cost of Production: Productivity
The Cost of Production: Productivity
 Q: Is there a general productivity law implicit in
this model of the production relationship?
 A: The underlying principle is the Law of
diminishing returns: given a certain level of fixed
factor input (K), increases in the variable factor
input (L) will eventually result in diminishing
marginal product of the variable input (MPL)
 Marginal Product can be calculated for any
variable input (ie the MP of chemical fertilizer)
The Cost of Production: Productivity
 Q: Are there other measures of productivity?
 A: Average Product of Labour: APL = (TP / L)
 The APL is the most popular measure of
technical productivity. It is frequently misused as
a measure of efficiency.
 Average Product can be calculated for any
variable input (ie the AP of chemical fertilizer)
 Average Product is not a measure of efficiency
The Cost of Production: Productivity
 Q: Is there a quick way to derive the APL curve
from the TP curve?
 A: At each level of employment (L), the slope of
a line drawn through the TP curve gives the APL
 Q: Where is the dividing line between increasing
and decreasing average returns to labour?
 A: Where a line drawn from the origin just
touches the TP curve as a tangent.
The Cost of Production: Productivity
The Cost of Production: Productivity
Q: Does the declining MPL curve always pass down
through the maximum of the APL curve?
 As L , MP increases, reaches a maximum, and
then declines



when MP > AP,
when MP < AP,
when MP = AP,
AP
AP 
maximum AP
The Cost of Production: Productivity
When marginal product
exceeds average
product, average
product increases.
When marginal product is
below average
product, average
product decreases.
When marginal product
equals average
product, average
product is at its
maximum.
The Cost of Production: Productivity
 The technological productivity of a firm can be
described using the TP, APL, and MPL curves.
Q: Is technological productivity the same as
economic efficiency?
 No a more technologically productive (or
technologically efficient) process will produce
the same output with fewer factor inputs. A more
economically efficient process will produce the
same output at a lower opportunity cost.
The Short-Run Cost of Production
 Q: What is the relationship between the
technological efficiency and the firm’s costs?
 A: Step 1: Invert the TP curve
The Short-Run Cost of Production
 Step 2: Multiply the inverted TP curve by w to
give the firm’s total variable cost (TVC) curve
The Short-Run Cost of Production
 In addition to the variable cost of labour is the
fixed cost of paying for the factory.
 Short-run cost curves

TC = TFC + TVC = Total Cost

TFC = total fixed cost
= cost of fixed inputs

TVC = total variable cost
= cost of variable inputs

In our simple model Total Costs are:

TC = TFC + TVC = iK +wL
continued
The Short-Run Cost of Production
Total fixed cost is the same
at each output level.
Total variable cost increases
as output increases.
Total cost, which is the sum
of TFC and TVC also
increases as output
increases.
The Short-Run Cost of Production
Q: The TP curve had a marginal product and
average product curve associated with it. Does
the TC curve have similar average and marginal
curves associated with it?
 A1: average total cost, ATC = TC/Q = AFC+AVC

average fixed cost = AFC = TFC / Q

average variable cost = AVC = TVC/ Q
 A2: marginal cost, MC = DTC / DQ

MC = additional cost from one-unit
increase in output Q
continued
The Short-Run Cost of Production
Q: What do the ATC and MC curves look like?
A: They can each be derived from the TC curve.

The ATC at each point on the TC curve is
simply the slope of a line drawn from the
origin through that point.

The MC at each point on the TC curve is
simply the slope of a tangent line just
touching the TC at that point.

The inflection point gives the minimum of
the MC curve.
The Short-Run Cost of Production
The Short-Run Cost of Production
Q: What do the AFC and AVC curves look like?
 The shape of these curves can be deduced
using the same process as used to deduce the
shape of the ATC curve.
 With a little thought it is clear that the AVC is
bowl shaped and the AFC is shaped like a
rectangular hyperbole.
The Short-Run Cost of Production
The Short-Run Cost of Production

The AVC curve is
U-shaped. As
output increases,
average variable
cost falls to a
minimum and then
increases.
The Short-Run Cost of Production
The ATC curve is also U-shaped.

The MC curve is very special.

The outputs over which AVC
is falling, MC is below AVC.

The outputs over which AVC
is rising, MC is above AVC.

The output at which AVC is at
the minimum, MC equals AVC.
The Short-Run Cost of Production
 Similarly, the outputs
over which ATC is falling,
MC is below ATC.
 The outputs over which
ATC is rising, MC is
above ATC.
 At the minimum ATC,
MC equals ATC.
Marginal Cost and Average Costs
Cost
15
MC ATC
10
AVC
5
AFC
0
5
Copyright © 1997 Addison-Wesley Publishers Ltd.
10
15
Output
Textbook p. 218
The Short-Run Cost of Production
AVC, ATC, and MC curves are U-shaped
 As Q , MC , reaches minimum, then MC

when MC < ATC,
ATC 

when MC > ATC,
ATC

when MC = ATC,
minimum ATC

same relation between MC and AVC
 The critical result is that the rising MC curve cuts
through the minimum point on the ATC and AVC
curves.
The Short Run Cost of Production and Productivity
Q: What is the relationship between productivity and
the cost of producing?
 The relationship is simple:

The AVC is at a minimum when the APL is
at a maximum

The MC is at a minimum when the MPL is
at a maximum
Product Curves and Cost Curves
AP,
MP
AP
MP
 MP, MC;
AP, AVC
MP, MC;
AP, AVC
Cost
1
Max. AP,
Min. MC
 MP, MC;
 AP, AVC
2
Max. AP,
Min. AVC
Labour
MC
AVC
4
Copyright © 1997 Addison-Wesley Publishers Ltd.
10
Q
Textbook p. 219
The Long-Run Cost of Production
Q: What is the relationship between factor inputs
and output in the Long-run?
 In the long-run, all factors are variable, and there
is no distinction between stocks and flows.

This implies that all costs are variable.

In our simple model this means that capital
(K) is just as variable as labour (L).

The production function describing the
maximum output associated with various
input combinations would be Q = F(K,L)
continued
The Long-Run Cost of Production
Long-Run Cost
The Production Function

The behavior of long-run cost depends
upon the firm’s production function.

The firm’s production function is the
relationship between the maximum output
attainable and the quantities of both
capital and labour.
Long-Run Cost

Table 11.3 shows a firm’s
production function.

As the size of the plant
increases, the output that a
given quantity of labour can
produce increases.

But as the quantity of labour
increases, diminishing
returns occur for each plant.
Long-Run Cost




Diminishing Marginal Product of Capital
The marginal product of capital is the increase
in output resulting from a one-unit increase in
the amount of capital employed, holding
constant the amount of labour employed.
A firm’s production function exhibits diminishing
marginal returns to labour (for a given plant) as
well as diminishing marginal returns to capital
(for a quantity of labour).
For each plant, diminishing marginal product of
labour creates a set of short run, U-shaped
costs curves for MC, AVC, and ATC.
Long-Run Cost
 Short-Run Cost and Long-Run Cost

The average cost of producing a given output
varies and depends on the firm’s plant.

The larger the plant, the greater is the output
at which ATC is at a minimum.

The firm has 4 different plants: 1, 2, 3, or 4
knitting machines.

Each plant has a short-run ATC curve.

The firm can compare the ATC for each
output at different plants.
Long-Run Cost
ATC1 is the ATC curve for a plant with 1 knitting machine.
Long-Run Cost
ATC2 is the ATC curve for a plant with 2 knitting machines.
Long-Run Cost
ATC3 is the ATC curve for a plant with 3 knitting machines.
Long-Run Cost
ATC4 is the ATC curve for a plant with 4 knitting machines.
Long-Run Cost

The long-run average cost curve is made up
from the lowest ATC for each output level.

So, we want to decide which plant has the
lowest cost for producing each output level.

Let’s find the least-cost way of producing a
given output level.

Suppose that the firm wants to produce 13
sweaters a day.
Long-Run Cost
13 sweaters a day cost $7.69 each on ATC1.
Long-Run Cost
13 sweaters a day cost $6.80 each on ATC2.
Long-Run Cost
13 sweaters a day cost $7.69 each on ATC3.
Long-Run Cost
13 sweaters a day cost $9.50 each on ATC4.
Long-Run Cost
13 sweaters a day cost $6.80 each on ATC2.
The least-cost way of producing 13 sweaters a day.
Long-Run Cost
 Long-Run Average Cost Curve



The long-run average cost curve is the
relationship between the lowest attainable
average total cost and output when both the
plant and labour are varied.
The long-run average cost curve is a planning
curve that tells the firm the plant that minimizes
the cost of producing a given output range.
Once the firm has chosen its plant, the firm
incurs the costs that correspond to the ATC
curve for that plant.
Long-Run Cost
Figure 11.8 illustrates the long-run average cost (LRAC) curve.
Long Run Cost and Productivity
 Economies and Diseconomies of Scale

Economies of scale are features of a
firm’s technology that lead to falling longrun average cost as output increases.

Diseconomies of scale are features of a
firm’s technology that lead to rising longrun average cost as output increases.

Constant returns to scale are features of
a firm’s technology that lead to constant
long-run average cost as output increases.
Long Run Cost and Productivity
Figure 11.8 illustrates economies and diseconomies of scale.
Long Run Cost and Productivity
 Minimum Efficient Scale
 A firm experiences economies of scale up
to some output level.
 Beyond that output level, it moves into
constant returns to scale or diseconomies
of scale.
 Minimum efficient scale is the smallest
quantity of output at which the long-run
average cost reaches its lowest level.
 If the long-run average cost curve is Ushaped, the minimum point identifies the
minimum efficient scale output level.
Long Run Cost and Productivity
P
LRAC
SRACa
SRACb
ATC0
Economies
of scale
0
Q0
Constant returns
to scale
Q1
Copyright © 1997 Addison-Wesley Publishers Ltd.
Diseconomies
of scale
Q2
Q
Textbook p. 225
Long Run Cost and Productivity
Q: How is technical efficiency be described in the long-run?

Returns to Scale

constant returns to scale % output = % inputs

increasing returns to scale
(economies of scale)

% output > % inputs
decreasing returns to scale
(diseconomies of scale) % output < % inputs
continued
Long Run Cost
Q: What does the TC, ATC and MC curves look like
in the long-run?
 Very much like the short-run curves. The only
difference is that there are no fixed costs and all
costs are variable costs.
 Assuming that there are economies of scale that
eventually end and are replaced with diminishing
returns to scale, the cost function would have
the standard shape.
Long-Run Cost
 There is no AVC and no AFC because
everything is variable and nothing is fixed.
 Furthermore, the LRTC curve begins at the
origin because of the absence of fixed costs.
End of Lecture 9