The Cost of Production Lecture 9: The Cost of Production Readings: Chapters 11.

Lecture 9: The Cost of ProductionThe 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.


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)


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.

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 total product

curve is similar to

the PPF.

It separates

attainable output

levels from

unattainable

output levels in

the short run.


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.



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 = (TP / L)

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

Textbook p. 213

Labour1 2 3 4 5

Output

c

4

15

10

13d

TP

Labour1 2 3 4 5

2

4

6MP

MPL

3

Copyright © 1997 Addison-Wesley Publishers Ltd.

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.



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.


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)


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


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.


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, AP when MP < AP, AP when MP = AP, maximum AP

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 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


Step 2: Multiply the inverted TP curve by w to

give the firm’s total variable cost (TVC) curve


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

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.



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 = TC / Q MC = additional cost from one-unit

increase in outputQ

continued


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.


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 AVC curve is

U-shaped. As

output increases,

average variable

cost falls to a

minimum and then

increases.


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.


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

Textbook p. 218

Cost

Output0 5 10 15

5

10

15MC

AVC

ATC

AFC

Copyright © 1997 Addison-Wesley Publishers Ltd.


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

MP, MC; AP, AVC

Max. AP,Min. MC

MP, MC; AP, AVC

Max. AP,Min. AVC

MP,MC; AP, AVC

Textbook p. 219

Product Curves and Cost Curves

1

MPAP

4

Labour2

AP,MP

Cost

MC

AVC

10 QCopyright © 1997 Addison-Wesley Publishers Ltd.

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.

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


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


Long-Run Cost


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

Economies and Diseconomies of Scale Economies of scale are features of a

firm’s technology that lead to falling long-run average cost as output increases.

Diseconomies of scale are features of a firm’s technology that lead to rising long-run 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.


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 U-shaped, the minimum point identifies the minimum efficient scale output level.



Textbook p. 225

0

LRACSRACa

Q0

Economiesof scale

ATC0

Q1 Q2

Constant returnsto scale

SRACb

Diseconomiesof scale

P

QCopyright © 1997 Addison-Wesley Publishers Ltd.


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

The Cost of Production Lecture 9: The Cost of Production Readings: Chapters 11.

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