Chapter 20: Production and Costs

Chapter 20: Production and CostsChapter 20: Production and Costs

• economic costs & profits • short run • long run

big picturebig picture

• understand behavior of firm• understand & measure

production costs

I. economic costs & profitsI. economic costs & profits

• firm’s goal:maximize profit

• look at factors that affect firm’s decision

economic costseconomic costs

• opportunity cost of resources used• explicit costs

paid in money wages, rent, material, etc.

• implicit costs opportunity cost of resources used

example: smoothie shopexample: smoothie shop

• explicit costs: wages interest on loan rent on store fruit, blenders

• implicit costs forgone interest on funds used to

buy capital owner’s forgone wages owner’s forgone profit from other

venture

accounting profitaccounting profit

• total revenue – explicit costs• ignores opportunity cost

economic profiteconomic profit

• includes opp. costs= total revenue - total costs= (price)(quantity)

- (explicit + implicit costs)

normal profitnormal profit

• occurs when• amount of accounting profit

= opportunity costs of resources• if earning a normal profit,

economic profit = 0

Short Run vs. Long RunShort Run vs. Long Run

• Short Run (SR) time frame where some resources

are fixed-- plants, equipment

some inputs variable-- labor

SR decisions are reversible

• Long Run (LR) time frame where all inputs are

variable--build a bigger plant

LR decisions are hard to reverse-- cannot easily get rid of capital

-- sunk cost

II. SR ProductionII. SR Production

• measures of output total product marginal product average product

total product (TP)total product (TP)

• total quantity of good producedin a given period

• at first, increases with labor,then falls

TP: gal. of smoothies per hourTP: gal. of smoothies per hour# workers TP

01234567

01368998

TP

# workers5 6

9

marginal product (MP)marginal product (MP)

• change in TP due to one more worker

=change in TP

change in labor

At first MP rises with workersAt first MP rises with workers

• add more workers• greater specialization• MP of each worker added is larger

than previous worker• increasing marginal returns

then, MP falls with more workersthen, MP falls with more workers

• keep adding workers• but same amount of capital• so eventually get in the way• MP of more workers smaller than

MP of previous workers• decreasing marginal returns

TP, MP: gal. of smoothiesTP, MP: gal. of smoothies# workers TP

01234567

01368998

MP

123

-1012

MP

Q = # workers

0

3

3

law of decreasing returnslaw of decreasing returns

• As firm uses more labor with capital fixed, MP of labor will eventually fall

Average Product (AP)Average Product (AP)

=TP

labor

= productivity

# workers TP

01234567

01368998

MP

123

-1012

AP

11.5221.81.51.1

MP

# workers

0

3

3

AP

MP & APMP & AP• MP intersects AP at max of AP• why?• MP > AP

AP is rising• MP < AP

AP is falling

III. SR costIII. SR cost

• measure cost 3 ways: total cost marginal cost average cost

Total Cost (TC)Total Cost (TC)

• cost of all factors used• total fixed cost (TFC)

cost of land, capital, etc. does not change in SR

• total variable cost (TVC) cost of labor changes in SR

• TC = TFC + TVC

example : yogurtexample : yogurt

• labor = $6/ hour• TFC = $10/ hour

workers TP TFC TVC TC

0 0 10 0 101 1 10 6 161.6 2 10 9.6 19.62 3 10 12 22

45

89

1010

2430

3440

Q = output

TC

TFC10

TC

TVC

Marginal CostMarginal Cost

• change in TC due to one-unit increase in output (Q)

=change in TCchange in Q

TP TFC TVC TC

0 10 0 101 10 6 162 10 9.6 19.63 10 12 22

89

1010

2430

3440

MC

63.62.4

6

Average Cost (ATC)Average Cost (ATC)

• = TC/Q• average fixed cost (AFC)

(TFC/Q)• average variable cost (AVC)

(TVC/Q)• ATC = AFC + AVC

TP TFC TVC TC

0 10 0 101 10 6 162 10 9.6 19.63 10 12 22

89

1010

2430

3440

AFC AVC AC

10 6 165 4.8 9.8 3.33 4 7.33

1.25 3 4.251.11 3.33 4.44

Q = output

AC, MC

AFC

ATCAVC

MC

MC & ACMC & AC

• MC intersects AC at its minimum• MC < AC

AC is falling• MC > AC

AC is rising

AC is U-shapedAC is U-shaped

• why?• AFC falls with Q• AVC falls then rises

decreasing marginal returns• so ATC falls, then rises

cost & product curvescost & product curves

• when MP is at maximum,MC is at minimum

• when AP is at maximum,AVC is at minimum

what shifts cost curves?what shifts cost curves?

• technology make more with same inputs shifts TP, MP, AP up changes ATC curve

• changes in factor prices increase fixed costs

-- TFC, AFC shift up-- TC shift up

increase wages (variable)-- TVC, AVC, MC shift up-- TC shift up

IV. LR costsIV. LR costs

• all inputs (and costs) are variable• what happens if increase plant

AND labor by 10%? ATC fall? ATC rise? ATC stay same?

Economies of scaleEconomies of scale

• increase inputs 10% output increase > 10% ATC falls

• why? gains from specialization

-- labor-- capital

Diseconomies of scaleDiseconomies of scale

• increase inputs 10% output increase < 10% ATC rises

• why? too hard to control large firm

Constant returns to scaleConstant returns to scale

• increase inputs 10% output increase = 10% ATC stays same

LR Average Cost (LRAC)LR Average Cost (LRAC)

• lowest average cost when all inputs are variable

• SRAC curves from different plant sizes

Q = output

ACATC1 ATC2

ATC3ATC4

LRAC

Q = output

ACATC1 ATC2

ATC3ATC4

economiesof scale

constantreturnsto scale

diseconomiesof scale

summary:summary:

• costs = implicit + explicit• SR, only labor variable• LR, all inputs variable• Production & costs

total, marginal, average fixed, variable

The importance of the firm’s production function, the relationship between quantity of inputs and quantity of output

Why production is often subject to diminishing returns to inputs

The various types of costs a firm faces and how they generate the firm’s marginal and average cost curves

Why a firm’s costs may differ in the short run versus the long run

How the firm’s technology of production can generate increasing returns to scale

The Production FunctionThe Production Function

• A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces.

• A fixed input is an input whose quantity is fixed for a period of time and cannot be varied.

• A variable input is an input whose quantity the firm can vary at any time.

Inputs and OutputInputs and Output

• The long run is the time period in which all inputs can be varied.

• The short run is the time period in which at least one input is fixed.

• The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given quantity of the fixed input.

Production Function and TP Curve forGeorge and Martha’s Farm

012345678

1917151311975

01936516475849196

Quantity of labor

L(worker)

Quantity of wheat

Q(bushels)

MP of laborMPL =Q/L

(bushels per worker)

7 86543210

100

80

60

40

20

Quantity of wheat (bushels)

Quantity of labor (workers)

Total product, TP

Adding a 7th worker leads to an increase in output of only 7 bushels

Adding a 2nd worker leads to an increase in output of only 17 bushels

The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.

Marginal Product of Labor

Diminishing Returns to an InputDiminishing Returns to an Input

• There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input.

Marginal Product of Labor Curve

Marginal product of labor, MPL

7 86543210

1917151311975

Marginal product of

labor (bushels per

worker)

Quantity of labor (workers)

There are diminishing returns to labor.

(a) Total Product Curves (b) Marginal Product Curves

Marginal product of labor

(bushels per worker)


7 86543210

30252015105

7 86543210

16014012010080604020

TP20

TP10

MPL20MPL10

Quantity of labor (workers)Quantity of labor (workers)

Total Product, Marginal Product, and the Fixed Input

From the Production Function to Cost From the Production Function to Cost CurvesCurves

• A fixed cost is a cost that does not depend on the quantity of output produced. It is the cost of the fixed input.

• A variable cost is a cost that depends on the quantity of output produced. It is the cost of the variable input.

Total Cost CurveTotal Cost Curve

• The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output.

TC = FC + VC

• The total cost curve becomes steeper as more output is produced due to diminishing returns.

Total Cost Curve for George and Martha’s Total Cost Curve for George and Martha’s FarmFarm

19 36 51 64 75 84 91 960

$2,0001,8001,6001,4001,2001,000

800600400200

Cost


AB

CD

EF

G

Total cost, TC

HI

ABCDEFGHI

Point on graph

012345678

$400400400400400400400400400

O200400600800

1,0001,2001,4001,600

400600800

1,0001,2001,4001,6001,8002,000

01936516475849196

Variable cost(VC)

Total cost

(TC = FC + VC)

$ $

Quantity of labor L

(worker)

Quantity of wheat Q(bushels)

Fixed Cost

(FC)

The Mythical Man-Month

Quantity of labor (programmers)

TP

MPL

0

0

Quantity of labor (programmers)

Marginal product of labor (lines per

programmer)

Quantity of software code

(lines)

Beyond a certain point, an additional

programmer is counterproductive.

Two Key Concepts: Marginal Cost and Average Two Key Concepts: Marginal Cost and Average CostCost

As in the case of marginal product, marginal cost is equal to “rise” (the increase in total cost) divided by “run” (the increase in the quantity of output).

Costs at Selena’s Gourmet SalsasCosts at Selena’s Gourmet Salsas

Total Cost and Marginal Cost Curves for Total Cost and Marginal Cost Curves for Selena’s Gourmet SalsasSelena’s Gourmet Salsas

$250

200

150

100

50

Cost of case

7 8 9 106543210

$1,400

1,200

1,000

800

600

400

200

Cost

Quantity of salsa (cases)7 8 9 106543210

(b) Marginal Cost(a) Total Cost

TC MC

Quantity of salsa (cases)

8th case of salsa increases total cost by $180.

2nd case of salsa

increases total cost by

$36.

Why is the Marginal Cost Curve Upward Why is the Marginal Cost Curve Upward Sloping?Sloping?

• Because there are diminishing returns to inputs in this example. As output increases, the marginal product of the variable input declines.

• This implies that more and more of the variable input must be used to produce each additional unit of output as the amount of output already produced rises.

• And since each unit of the variable input must be paid for, the cost per additional unit of output also rises.

Average CostAverage Cost• Average total cost, often referred to simply as average cost,

is total cost divided by quantity of output produced.

ATC = TC/Q = (Total Cost) / (Quantity of Output)

• A U-shaped average total cost curve falls at low levels of output, then rises at higher levels.

• Average fixed cost is the fixed cost per unit of output.

AFC = FC/Q = (Fixed Cost) / (Quantity of Output)

Average CostAverage Cost

•Average variable cost is the variable cost per unit of output.

AVC = VC/Q= (Variable Cost) / (Quantity of Output)

Average Total Cost CurveAverage Total Cost Curve

•Increasing output has two opposing effects on average total cost:

The spreading effect: the larger the output, the greater the quantity of output over which fixed cost is spread, leading to lower the average fixed cost.

The diminishing returns effect: the larger the output, the greater the amount of variable input required to produce additional units leading to higher average variable cost.

Average Costs for Selena’s Gourmet Average Costs for Selena’s Gourmet SalsasSalsas

Average Total Cost Curve for Selena’s Average Total Cost Curve for Selena’s Gourmet SalsasGourmet Salsas

Average total cost, ATC

M

7 8 9 106543210

$140

120

100

80

60

40

20

Minimum average total cost

Minimum-cost output

Cost of case


Putting the Four Cost Curves Putting the Four Cost Curves TogetherTogether

Note that:1. Marginal cost is upward sloping due to diminishing

returns.2. Average variable cost also is upward sloping but is flatter

than the marginal cost curve. 3. Average fixed cost is downward sloping because of the

spreading effect.4. The marginal cost curve intersects the average total cost

curve from below, crossing it at its lowest point. This last feature is our next subject of study.

Marginal Cost and Average Cost Curves for Marginal Cost and Average Cost Curves for Selena’s Gourmet SalsasSelena’s Gourmet Salsas

$250

200

150

100

50

7 8 9 10654321

M

0

MC

ATCAVC

AFC

Minimum-cost output

Cost of case


General Principles That Are Always True About a General Principles That Are Always True About a Firm’s Marginal and Average Total Cost CurvesFirm’s Marginal and Average Total Cost Curves

• The minimum-cost output is the quantity of output at which average total cost is lowest—the bottom of the U-shaped average total cost curve.

At the minimum-cost output, average total cost is equal to marginal cost.

At output less than the minimum-cost output, marginal cost is less than average total cost and average total cost is falling.

And at output greater than the minimum-cost output, marginal cost is greater than average total cost and average total cost is rising.

The Relationship Between the Average The Relationship Between the Average Total Cost and the Marginal Cost CurvesTotal Cost and the Marginal Cost Curves

Cost of unit

Quantity

MC

ATC

MC L

MC H

A1 B1A2

B2

M

If marginal cost is above average total cost, average total cost is rising.

If marginal cost is below average total cost, average total cost is falling.

Does the Marginal Cost Curve Always Slope Does the Marginal Cost Curve Always Slope Upward?Upward?

• In practice, marginal cost curves often slope downward as a firm increases its production from zero up to some low level, sloping upward only at higher levels of production.

• This initial downward slope occurs because a firm that employs only a few workers often cannot reap the benefits of specialization of labor. This specialization can lead to increasing returns at first, and so to a downward-sloping marginal cost curve.

• Once there are enough workers to permit specialization, however, diminishing returns set in.

More Realistic Cost CurvesMore Realistic Cost CurvesMC

ATC

AVC

Cost of unit

Quantity

2. … but diminishing returns set in once the benefits from specialization are exhausted and marginal cost rises.

1. Increasing specialization leads to lower marginal cost…

Short-Run versus Long-Run Short-Run versus Long-Run CostsCosts•In the short run, fixed cost is completely outside the control of a firm. But all inputs are variable in the long run.

•The firm will choose its fixed cost in the long run based on the level of output it expects to produce.

Choosing the Level of Fixed Cost of Selena’s Gourmet Salsas

ATC1

1248

108192300432588768972

1,200

$ 120156216300408540696876

1,0801,308

Total cost$

ATC2

6245496

150216294384486600

$ $222240270312366432510600702816

Low fixed cost (FC = $108) High fixed cost (FC = $216)

$120.0078.0072.0075.0081.6090.0099.43

109.50120.00130.80

$222.00120.0090.0078.0073.2072.0072.8675.0078.0081.60

123456789

10

Average total cost of case

Quantity of

salsa(salsa)High

variable cost

Low variable cost

Total cost

Average total cost of case

$250

200

150

100

50

Cost of case

Quantity of salsa (cases)7 8 9 106543210

High fixed cost

Low fixed cost

ATC2

ATC1

At low output levels, low fixed cost yields lower average total cost

At high output levels, high fixed cost yields lower average total cost

•The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output.

The Long-run Average Total Cost Curve

Short-Run and Long-Run Average Total Short-Run and Long-Run Average Total Cost CurvesCost Curves

B

ATC6 ATC9ATC3 LRATC

3 5 84 70 6 9

Increasing returns to scale Decreasing returns to scaleConstant returns to scale

C XA

Y

Cost of case


Returns to ScaleReturns to Scale

• There are increasing returns to scale (economies of scale) when long-run average total cost declines as output increases.

• There are decreasing returns to scale (diseconomies of scale) when long-run average total cost increases as output increases.

• There are constant returns to scale when long-run average total cost is constant as output increases.

1. The relationship between inputs and output is a producer’s production function. In the short run, the quantity of a fixed input cannot be varied but the quantity of a variable input can. In the long run, the quantities of all inputs can be varied. For a given amount of the fixed input, the total product curve shows how the quantity of output changes as the quantity of the variable input changes.

2. There are diminishing returns to an input when its marginal product declines as more of the input is used, holding the quantity of all other inputs fixed.

3. Total cost is equal to the sum of fixed cost, which does not depend on output, and variable cost, which does depend on output.

4. Average total cost, total cost divided by quantity of output, is the cost of the average unit of output, and marginal cost is the cost of one more unit produced. U-shaped average total cost curves are typical, because average total cost consists of two parts: average fixed cost, which falls when output increases (the spreading effect), and average variable cost, which rises with output (the diminishing returns effect).

5. When average total cost is U-shaped, the bottom of the U is the level of output at which average total cost is minimized, the point of minimum-cost output. This is also the point at which the marginal cost curve crosses the average total cost curve from below.

6. In the long run, a producer can change its fixed input and its level of fixed cost. The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost at each level of output.

7. As output increases, there are increasing returns to scale if long-run average total cost declines; decreasing returns to scale if it increases; and constant returns to scale if it remains constant. Scale effects depend on the technology of production.

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Chapter 20: Production and Costs