Chapter 20 production and costs
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Chapter 20: Production and Costs. economic costs & profits short run long run. big picture. understand behavior of firm understand & measure production costs. I. economic costs & profits. firm’s goal: maximize profit look at factors that affect firm’s decision. economic costs.

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Chapter 20: Production and Costs

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Chapter 20 production and costs

Chapter 20: Production and Costs

  • economic costs & profits

  • short run

  • long run


Big picture

big picture

  • understand behavior of firm

  • understand & measure

    • production

    • costs


I economic costs profits

I. economic costs & profits

  • firm’s goal:

    maximize profit

  • look at factors that affect firm’s decision


Economic costs

economic costs

  • opportunity cost of resources used

  • explicit costs

    • paid in money

    • wages, rent, material, etc.

  • implicit costs

    • opportunity cost of resources used


Example smoothie shop

example: smoothie shop

  • explicit costs:

    • wages

    • interest on loan

    • rent on store

    • fruit, blenders


Chapter 20 production and costs

  • implicit costs

    • forgone interest on funds used to buy capital

    • owner’s forgone wages

    • owner’s forgone profit from other venture


Accounting profit

accounting profit

  • total revenue – explicit costs

  • ignores opportunity cost


Economic profit

economic profit

  • includes opp. costs

    = total revenue - total costs

    = (price)(quantity)

    - (explicit + implicit costs)


Normal profit

normal profit

  • occurs when

  • amount of accounting profit

    = opportunity costs of resources

  • if earning a normal profit,

    • economic profit = 0


Short run vs long run

Short Run vs. Long Run

  • Short Run (SR)

    • time frame where some resources are fixed

      -- plants, equipment

    • some inputs variable

      -- labor

    • SR decisions are reversible


Chapter 20 production and costs

  • 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 production

II. SR Production

  • measures of output

    • total product

    • marginal product

    • average product


Total product tp

total product (TP)

  • total quantity of good produced

    in a given period

  • at first, increases with labor,

    then falls


Tp gal of smoothies per hour

TP: gal. of smoothies per hour

# workers

TP

0

1

2

3

4

5

6

7

0

1

3

6

8

9

9

8


Chapter 20 production and costs

9

5 6

TP

# workers


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 workers

At 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 workers

then, 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 smoothies

1

2

3

2

1

0

-1

TP, MP: gal. of smoothies

# workers

TP

MP

0

1

2

3

4

5

6

7

0

1

3

6

8

9

9

8


Chapter 20 production and costs

3

0

3

MP

Q = # workers


Law of decreasing returns

law 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


Chapter 20 production and costs

1

2

3

2

1

0

-1

AP

# workers

TP

MP

0

1

2

3

4

5

6

7

0

1

3

6

8

9

9

8

1

1.5

2

2

1.8

1.5

1.1


Chapter 20 production and costs

3

0

3

MP

AP

# workers


Mp ap

MP & AP

  • MP intersects AP at max of AP

  • why?

  • MP > AP

    • AP is rising

  • MP < AP

    • AP is falling


Iii sr cost

III. 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 yogurt

example : yogurt

  • labor = $6/ hour

  • TFC = $10/ hour


Chapter 20 production and costs

workers

TP

TFC

TVC

TC

0 0 10 0 10

1 1 10 6 16

1.6 2 10 9.6 19.6

2 3 10 12 22

10

10

4

5

8

9

24

30

34

40


Chapter 20 production and costs

TC

TC

TVC

TFC

10

Q = output


Marginal cost

Marginal Cost

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

change in TC

=

change in Q


Chapter 20 production and costs

TP

TFC

TVC

TC

6

3.6

2.4

6

MC

0 10 0 10

1 10 6 16

2 10 9.6 19.6

3 10 12 22

10

10

8

9

24

30

34

40


Average cost atc

Average Cost (ATC)

  • = TC/Q

  • average fixed cost (AFC)

    • (TFC/Q)

  • average variable cost (AVC)

    • (TVC/Q)

  • ATC = AFC + AVC


Chapter 20 production and costs

TP

TFC

TVC

TC

AFC AVC AC

0 10 0 10

1 10 6 16

10 6 16

2 10 9.6 19.6

5 4.8 9.8

3 10 12 22

3.33 4 7.33

10

10

1.25 3 4.25

8

9

24

30

34

40

1.11 3.33 4.44


Chapter 20 production and costs

AC, MC

MC

ATC

AVC

AFC

Q = output


Mc ac

MC & AC

  • MC intersects AC at its minimum

  • MC < AC

    • AC is falling

  • MC > AC

    • AC is rising


Ac is u shaped

AC is U-shaped

  • why?

  • AFC falls with Q

  • AVC falls then rises

    • decreasing marginal returns

  • so ATC falls, then rises


Cost product curves

cost & 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


Chapter 20 production and costs

  • 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 costs

IV. 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 scale

Economies of scale

  • increase inputs 10%

    • output increase > 10%

    • ATC falls

  • why?

    • gains from specialization

      -- labor

      -- capital


Diseconomies of scale

Diseconomies of scale

  • increase inputs 10%

    • output increase < 10%

    • ATC rises

  • why?

    • too hard to control large firm


Constant returns to scale

Constant 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


Chapter 20 production and costs

AC

ATC1

ATC2

ATC3

ATC4

Q = output

LRAC


Chapter 20 production and costs

AC

ATC1

ATC2

ATC3

ATC4

Q = output

diseconomies

of scale

economies

of scale

constant

returns

to

scale


Summary

summary:

  • costs = implicit + explicit

  • SR, only labor variable

  • LR, all inputs variable

  • Production & costs

    • total, marginal, average

    • fixed, variable


Chapter 20 production and costs

  • 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 function

The 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 output

Inputs 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.


Chapter 20 production and costs

Production Function and TP Curve forGeorge and Martha’s Farm

Quantity of wheat (bushels)

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

Quantity of labor L

Quantity

of wheat Q

MP of labor

D

D

MPL

=

Q

/

L

(bushels per worker)

(worker)

(bushels)

0

0

Total product, TP

100

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

19

1

19

17

2

36

80

15

3

51

13

60

4

64

11

5

75

9

40

6

84

7

7

91

20

5

8

96

0

1

2

3

4

5

6

7

8

Quantity of labor (workers)


Chapter 20 production and costs

Marginal Product of Labor

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


Diminishing returns to an input

Diminishing 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.


Chapter 20 production and costs

Marginal Product of Labor Curve

Marginal product of labor (bushels per worker)

There are diminishing returns to labor.

19

17

15

13

11

9

7

5

Marginal product of labor, MPL

0

1

2

3

4

5

6

7

8

Quantity of labor (workers)


Chapter 20 production and costs

Total Product, Marginal Product, and the Fixed Input

(a) Total Product Curves

(b) Marginal Product Curves

Quantity of wheat

(bushels)

Marginal product of labor

(bushels per worker)

160

30

TP

140

20

25

120

20

100

TP

10

80

15

60

10

40

MPL

20

5

20

MPL

10

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

Quantity of labor (workers)

Quantity of labor (workers)


From the production function to cost curves

From the Production Function to Cost Curves

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 curve

Total 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 farm

Total Cost Curve for George and Martha’s Farm

Cost

Total cost, TC

$2,000

I

1,800

H

1,600

G

1,400

F

1,200

E

1,000

D

800

C

600

B

400

A

200

0

19

36

51

64

75

84

91

96

Quantity of wheat (bushels)

Variable cost

(VC)

Quantity of labor L

Quantity of wheat Q

Fixed Cost (FC)

Total cost

Point on graph

(worker)

(bushels)

(TC = FC + VC)

A

0

0

$

O

$400

$

400

B

1

19

200

400

600

C

2

36

400

400

800

D

3

51

600

400

1,000

E

4

64

800

400

1,200

F

5

75

1,000

400

1,400

G

6

84

1,200

400

1,600

H

7

91

1,400

400

1,800

I

8

96

1,600

400

2,000


Chapter 20 production and costs

The Mythical Man-Month

Quantity of software code (lines)

TP

Beyond a certain point, an additional programmer is counterproductive.

0

Quantity of labor (programmers)

Marginal product of labor (lines per programmer)

0

MPL

Quantity of labor (programmers)


Two key concepts marginal cost and average cost

Two Key Concepts: Marginal Cost and Average Cost

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 salsas

Costs at Selena’s Gourmet Salsas


Total cost and marginal cost curves for selena s gourmet salsas

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

(a) Total Cost

(b) Marginal Cost

Cost

Cost of case

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

T

C

$1,400

$250

MC

1,200

200

1,000

2nd case of salsa increases total cost by $36.

150

800

600

100

400

50

200

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

7

8

9

10

Quantity of salsa (cases)

Quantity of salsa (cases)


Why is the marginal cost curve upward sloping

Why is the Marginal Cost Curve Upward 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 cost

Average 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 cost1

Average Cost

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

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


Average total cost curve

Average 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 salsas

Average Costs for Selena’s Gourmet Salsas


Average total cost curve for selena s gourmet salsas

Average Total Cost Curve for Selena’s Gourmet Salsas

Cost of case

$140

Average total cost, ATC

Minimum average total cost

120

100

M

80

60

40

20

0

1

2

3

4

5

6

7

8

9

10

Quantity of salsa (cases)

Minimum-cost output


Putting the four cost curves together

Putting the Four Cost Curves Together

Note that:

Marginal cost is upward sloping due to diminishing returns.

Average variable cost also is upward sloping but is flatter than the marginal cost curve.

Average fixed cost is downward sloping because of the spreading effect.

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 selena s gourmet salsas

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

Cost of case

$250

MC

200

150

A

T

C

A

VC

100

M

50

AFC

0

1

2

3

4

5

6

7

8

9

10

Quantity of salsa (cases)

Minimum-cost output


General principles that are always true about a firm s marginal and average total cost curves

General Principles That Are Always True About a Firm’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 tomarginal cost.

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

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


The relationship between the average total cost and the marginal cost curves

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

Cost of unit

MC

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

A

T

C

MC

H

B

2

A

1

M

B

A

1

2

MC

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

L

Quantity


Does the marginal cost curve always slope upward

Does the Marginal Cost Curve Always Slope 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 curves

More Realistic Cost Curves

Cost of unit

MC

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

A

T

C

A

VC

1. Increasing specialization leads to lower marginal cost…

Quantity


Short run versus long run costs

Short-Run versus Long-Run Costs

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.


Chapter 20 production and costs

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

Low fixed cost (FC = $108)

High fixed cost (FC = $216)

Average total cost of case

Average total cost of case

Quantity of salsa

Low variable cost

High variable cost

Total cost

Total cost

(salsa)

A

T

C

A

T

C

1

2

1

$

12

$

120

$120.00

$

6

$222

$222.00

2

48

156

78.00

24

240

120.00

3

108

216

72.00

54

270

90.00

4

192

300

75.00

96

312

78.00

5

300

408

81.60

150

366

73.20

6

432

540

90.00

216

432

72.00

7

588

696

99.43

294

510

72.86

8

768

876

109.50

384

600

75.00

9

972

1,080

120.00

486

702

78.00

10

1,200

1,308

130.80

600

816

81.60

Cost of case

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

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

$250

200

Low fixed cost

150

A

T

C

1

100

A

T

C

2

High fixed cost

50

0

1

2

3

4

5

6

7

8

9

10

Quantity of salsa (cases)


Chapter 20 production and costs

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 cost curves

Short-Run and Long-Run Average Total Cost Curves

Cost of case

Constant returns to scale

Increasing returns to scale

Decreasing returns to scale

A

T

C

A

T

C

A

T

C

L

R

A

T

C

3

6

9

B

Y

A

X

C

0

3

4

5

6

7

8

9

Quantity of salsa (cases)


Returns to scale

Returns 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.


Chapter 20 production and costs

  • 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 variableinput 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.

  • 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.

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


Chapter 20 production and costs

  • 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-shapedaverage 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).

  • 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.


Chapter 20 production and costs

  • 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.

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


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