Unit V

Production Costs (Chapter 12)

In this chapter, look for the answers to these questions:

What is a production function? What is marginal product? How are they related?

What are the various costs, and how are they related to each other and to output?

How are costs different in the short run vs. the long run?

What are “economies of scale”?

Short Run and Long run

• The Short Run: Fixed Plant– The short run is a time frame in which the

quantities of some resources are fixed. – In the short run, a firm can usually change the

quantity of labor it uses but not the quantity of capital.

• The Long Run: Variable Plant– The long run is a time frame in which the

quantities of all resources can be changed.– A sunk cost is irrelevant to the firm’s decisions.

Short Run Production

• To increase output with a fixed plant, a firm must increase the quantity of labor it uses.

• We describe the relationship between output and the quantity of labor by using three related concepts:

– Total product

– Marginal product

– Average product

The Production Function

• A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good.

• It can be represented by a table, equation, or graph.

• Example:– Farmer Jack grows wheat. – He has 5 acres of land. – He can hire as many workers as he wants.

The Production Function

• Total Product

– Total product (TP) is the total quantity of a good produced in a given period.

– Total product is an output rate—the number of units produced per unit of time.

– Total product increases as the quantity of labor employed increases.

The Production Function• The figure shows

the total product and the total product curve.

• Points A through H on the curve correspond to the columns of the table.

• The TP curve is like the PPF: It separates attainable points and unattainable points.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qu

anti

ty o

f o

utp

ut

EXAMPLE: Farmer Jack’s Production Function

30005

28004

24003

18002

10001

00

Q (bushels

of wheat)

L

(no. of workers)

Marginal Product• Marginal product is the change in total product

that results from a one-unit increase in the quantity of labor employed. – Marginal product tells us the contribution to total product

of adding one more worker. – E.g., if Farmer Jack hires one more worker,

his output rises by the marginal product of labor. – Notation:

∆ (delta) = “change in…”– Examples:

∆Q = change in output, ∆L = change in labor – Marginal product of labor (MPL) = ∆Q

∆L

Marginal Product

• The figure shows total product and marginal product.

• We can illustrate marginal productas the orange bars that form steps along the total product curve.

• The height of each step represents marginal product.

Marginal Product

• The table calculates marginal product and the orange bars in part (b) illustrate it.

• Notice that the steeper the slope of the TP curve, the greater is marginal product.

Marginal Product• The total product

and marginal product curves in this figure incorporate a feature of all production processes:– Increasing

marginal returns initially

– Decreasing marginal returns eventually

– Negative marginal returns

30005

28004

24003

18002

10001

00

Q

(bushels of wheat)

L

(no. of workers)

EXAMPLE: Total & Marginal Product

200

400

600

800

1000

MPL

∆Q = 1000∆L = 1

∆Q = 800∆L = 1

∆Q = 600∆L = 1

∆Q = 400∆L = 1

∆Q = 200∆L = 1

MPL equals the slope of the production function.

Notice that MPL diminishes as L increases.

This explains why the production function gets flatter as L increases.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5

No. of workers

Qu

anti

ty o

f o

utp

ut

EXAMPLE: MPL = Slope of Prod Function

30005200

28004400

24003600

18002800

100011000

00

MPL

Q

(bushels of wheat)

L

(no. of workers)

Why MPL Is Important• Rational people think at the margin.• When Farmer Jack hires an extra worker,

– his costs rise by the wage he pays the worker– his output rises by MPL

• Comparing them helps Jack decide whether he would benefit from hiring the worker.

Increasing Marginal Returns

• Increasing marginal returns occur when the marginal product of an additional worker exceeds the marginal product of the previous worker.

• Increasing marginal returns occur when a small number of workers are employed and arise from increased specialization and division of labor in the production process.

Why MPL Diminishes• Decreasing marginal returns occur when

the marginal product of an additional worker is less than the marginal product of the previous worker.

– E.g., Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why?

– If Jack increases workers but not land, the average worker has less land to work with, so will be less productive.

• In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).

Why MPL Diminishes• Decreasing marginal returns are so pervasive that

they qualify for the status of a law:• The law of decreasing returns states that:

As a firm uses more of a variable input, with a given

quantity of fixed inputs, the marginal product of the

variable input eventually decreases.

SHORT-RUN PRODUCTION

The figure graphs the average product against the quantity of labor employed.

The average product curve is AP.

When marginal product exceeds average product, average product is increasing.

SHORT-RUN PRODUCTION

When marginal product is less than average product, average product is decreasing.

When marginal product equals average product, average product is at its maximum.

SHORT-RUN COST

• To produce more output in the short run, a firm employs more labor, which means the firm must increase its costs.

• We describe the relationship between output and cost using three cost concepts: – Total cost– Marginal cost– Average cost

SHORT-RUN COST

• Total Cost

– A firm’s total cost (TC) is the cost of all the factors of production the firm uses.

• Total Cost divides into two parts:– Fixed cost (FC) is the cost of a firm’s fixed

factors of production used by a firm—the cost of land, capital, and entrepreneurship. o Fixed costs don’t change as output changes.

SHORT-RUN COST

– Variable cost (VC) is the cost of the variable factor of production used by a firm—the cost of labor. o To change its output in the short run, a firm must

change the quantity of labor it employs, so total variable cost changes as output changes.

o Total cost is the sum of total fixed cost and total variable cost. That is,

TC = FC + VC

SHORT-RUN COST

Fixed cost (FC) is constant—it graphs as a horizontal line.

Total cost (TC) also increases as output increases.

Variable cost (VC) increases as output increases.

SHORT-RUN COST

The vertical distance between the total cost curve and the total variable cost curve is total fixed cost, as illustrated by the two arrows.

Marginal Cost

• Marginal Cost (MC) is the increase in Total Cost from producing one more unit:

∆TC∆Q

MC =

Marginal cost tells us how total cost changes as total product changes.

Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:

Usually, MC rises as Q rises, due to diminishing marginal product.

Sometimes (as here), MC falls before rising.

(In other examples, MC may be constant.)

EXAMPLE: Marginal Cost

6207

4806

3805

3104

2603

2202

1701

$1000

MCTCQ

140

100

70

50

40

50

$70

∆TC∆Q

MC =

SHORT-RUN COST

• Average Cost– There are three average cost concepts:– Average fixed cost (AFC) is total fixed

cost per unit of output. – Average variable cost (AVC) is total

variable cost per unit of output. – Average total cost (ATC) is total cost per

unit of output.

SHORT-RUN COST

•The average cost concepts are calculated from the total cost concepts as follows:

TC = TFC + TVC

•Divide each total cost term by the quantity produced, Q, to give

ATC = AFC + AVC

Q Q QTC = TFC + TVC

or,

A C T I V E L E A R N I N G 1: Costs Fill in the blank spaces of

this table.

210

150

100

30

10

VC

43.33358.332606

305

37.5012.501504

36.672016.673

802

$60.00$101

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

30

$10

Use AFC = FC/QUse AVC = VC/QUse relationship between MC and TCUse ATC = TC/Q

First, deduce FC = $50 and use FC + VC = TC.

A C T I V E L E A R N I N G 1: Answers

210

150

100

60

30

10

$0

VC

43.33358.332606

40.003010.002005

37.502512.501504

36.672016.671103

40.001525.00802

$60.00$10$50.00601

n.a.n.a.n.a.$500

MCATCAVCAFCTCQ

60

50

40

30

20

$10

EXAMPLE: Average Fixed Cost

1007

1006

1005

1004

1003

1002

1001

14.29

16.67

20

25

33.33

50

$100

n.a.$1000

AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output:

AFC = FC/Q

Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.

EXAMPLE: Average Variable Cost

5207

3806

2805

2104

1603

1202

701

74.29

63.33

56.00

52.50

53.33

60

$70

n.a.$00

AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output:

AVC = VC/Q

As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.

EXAMPLE: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

n.a.

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

74.2914.29

63.3316.67

56.0020

52.5025

53.3333.33

6050

$70$100

n.a.n.a.

AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:

ATC = TC/Q

Also,

ATC = AFC + AVC

Usually, as in this example, the ATC curve is U-shaped.

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE: Average Total Cost

88.57

80

76

77.50

86.67

110

$170

n.a.

ATC

6207

4806

3805

3104

2603

2202

1701

$1000

TCQ

EXAMPLE: The Various Cost Curves Together

AFCAVCATC

MC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

SHORT-RUN COST

REMEMBER -- The marginal cost curve (MC) intersects the average variable cost curve and the average total cost curve at their minimum points.

The vertical distance between these two curves is equal to average fixed cost, as illustrated by the two arrows.

SHORT-RUN COST

• Why the Average Total Cost Curve Is U-Shaped

– Average total cost, ATC, is the sum of average fixed cost, AFC, and average variable cost, AVC. –The shape of the ATC curve combines the shapes of the AFC and AVC curves. –The U shape of the average total cost curve arises from the influence of two opposing forces:

o Spreading total fixed cost over a larger outputo Decreasing marginal returns

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

EXAMPLE: Why ATC Is Usually U-shaped

As Q rises:

Initially, falling AFC pulls ATC down.

Eventually, rising AVC pulls ATC up.

EXAMPLE: ATC and MC

ATCMC

$0

$25

$50

$75

$100

$125

$150

$175

$200

0 1 2 3 4 5 6 7

Q

Co

sts

When MC < ATC,

ATC is falling.

When MC > ATC,

ATC is rising.

The MC curve crosses the ATC curve at the ATC curve’s minimum.

SHORT-RUN COST

• Cost Curves and Product Curves– The technology that a firm uses determines its

costs.– At low levels of employment and output, as the

firm hires more labor, marginal product and average product rise, and marginal cost and average variable cost fall.

– Then, at the point of maximum marginal product, marginal cost is a minimum.

– As the firm hires more labor, marginal product decreases and marginal cost increases.

SHORT-RUN COST

– But average product continues to rises, and average variable cost continues to fall.

– Then, at the point of maximum average product, average variable cost is a minimum.

– As the firm hires even more labor, average product decreases and average variable cost increases.

SHORT-RUN COST

This figure illustrates the relationship between the product curves and cost curves.

A firm’s marginal cost curve is linked to its marginal product curve.If marginal product rises, marginal cost falls.

If marginal product is a maximum, marginal cost is a minimum.

SHORT-RUN COST

A firm’s average variable cost curve is linked to its average product curve.

If average product rises, average variable cost falls.

If average product is a maximum, average variable cost is a minimum.

SHORT-RUN COST

At small outputs, MP and AP rise and MC and AVC fall.

At intermediate outputs,MP falls and MC rises andAP rises and AVC falls.

At large outputs,MP and AP fall andMC and AVC rise.

SHORT-RUN COST

• Shifts in Cost CurvesTechnology– A technological change that increases

productivity shifts the total product curve upward. It also shifts the marginal product curve and the average product curve upward.

– With a better technology, the same inputs can produce more output, so an advance in technology lowers the average and marginal costs and shifts the short-run cost curves downward.

SHORT-RUN COST

Prices of Factors of Production–An increase in the price of a factor of production

increases costs and shifts the cost curves.–But how the curves shift depends on which

resource price changes.An increase in rent or another component of fixed cost

–Shifts the fixed cost curves (TFC and AFC) upward.–Shifts the total cost curve (TC) upward.–Leaves the variable cost curves (AVC and TVC)

and the marginal cost curve (MC) unchanged.

SHORT-RUN COST

• An increase in the wage rate or another component of variable cost – Shifts the variable curves (TVC and AVC)

upward.– Shifts the marginal cost curve (MC) upward.– Leaves the fixed cost curves (AFC and TFC)

unchanged.

• Plant Size and Cost– When a firm changes its plant size, its cost of

producing a given output changes.– Will the average total cost of producing a

gallon of smoothie fall, rise, or remain the same?

– Each of these three outcomes arise because when a firm changes the size of its plant, it might experience:o Economies of scaleo Diseconomies of scaleo Constant returns to scale

LONG-RUN COST

• Economies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a larger percentage and average total cost decreases.– The main source of economies of scale is

greater specialization of both labor and capital.

Economies of Scale

• Diseconomies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a smaller percentage and average total cost increases.– Diseconomies of scale arise from the difficulty

of coordinating and controlling a large enterprise.

– Eventually, management complexity brings rising average total cost.

Diseconomies of Scale

• Constant returns to scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by the same percentage and average total cost remains constant.– Constant returns to scale occur when a firm is

able to replicate its existing production facility including its management system.

Constant Returns to Scale

•The Long-Run Average Cost Curve–The long-run average cost curve shows

the lowest average cost at which it is

possible to produce each output when the

firm has had sufficient time to change both

its plant size and labor employed.

LONG-RUN COST

EXAMPLE: LRATC with 3 Factory Sizes

ATCS ATCM ATCL

Q

AvgTotalCost

Firm can choose from 3 factory sizes: S, M, L.

Each size has its own SRATC curve.

The firm can change to a different factory size in the long run, but not in the short run.

EXAMPLE: LRATC with 3 Factory Sizes

ATCSATCM ATCL

Q

AvgTotalCost

QA QB

LRATC

To produce less than QA, firm will

choose size S in the long run.

To produce between QA

and QB, firm will

choose size M in the long run.

To produce more than QB, firm will

choose size L in the long run.

A Typical LRATC Curve

Q

ATCIn the real world, factories come in many sizes, each with its own SRATC curve.

So a typical LRATC curve looks like this:

LRATC

How ATC Changes as the Scale of Production ChangesEconomies of scale: ATC falls as Q increases.

Constant returns to scale: ATC stays the same as Q increases.

Diseconomies of scale: ATC rises as Q increases.

LRATC

Q

ATC

CONCLUSION

• Costs are critically important to many business decisions, including production, pricing, and hiring.

• This chapter has introduced the various cost concepts.

• The following chapters will show how firms use these concepts to maximize profits in various market structures.

CHAPTER SUMMARY Implicit costs do not involve a cash outlay,

yet are just as important as explicit costs to firms’ decisions.

The production function shows the relationship between output and inputs.

The marginal product of labor is the increase in output from a one-unit increase in labor, holding other inputs constant. The marginal products of other inputs are defined similarly.

Marginal product usually diminishes as the input increases. Thus, as output rises, the production function becomes flatter, and the total cost curve becomes steeper.

CHAPTER SUMMARY Variable costs vary with output; fixed costs do

not. Marginal cost is the increase in total cost from an

extra unit of production. The MC curve is usually upward-sloping.

Average variable cost is variable cost divided by output.

Average fixed cost is fixed cost divided by output. AFC always falls as output increases.

Average total cost (sometimes called “cost per unit”) is total cost divided by the quantity of output. The ATC curve is usually U-shaped.

CHAPTER SUMMARY The MC curve intersects the ATC curve

at minimum average total cost. When MC < ATC, ATC falls as Q rises. When MC > ATC, ATC rises as Q rises.

In the long run, all costs are variable.

Economies of scale: ATC falls as Q rises. Diseconomies of scale: ATC rises as Q rises. Constant returns to scale: ATC remains constant as Q rises.