production cost and cost firm in the firm 1 © 2012 cengage learning. all rights reserved. may not...

Production and Cost in the Firm

1© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

22

Cost and Profit• Producers: Maximize profit• Opportunity cost

– All resources have an opportunity cost• Explicit costs

– Opportunity cost of resources employed by a firm

– Cash payments– On the accounting statement

© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

33

Cost and Profit• Implicit costs

– A firm’s opportunity cost of using its own resources or those provided by its owners

– Without a corresponding cash payment– Not on the accounting statement


Alternative Measures of Profit• Accounting profit

– Total revenue minus explicit costs• Economic profit

– Total revenue minus all costs (implicit and explicit)• Opportunity cost of all resources

• Normal profit – Accounting profit earned when all resources

earn their opportunity cost


Exhibit 1

5

Wheeler Dealer Accounts, 2012


Production in the Short Run• Variable resources

– Can be varied in the short run to increase or decrease production

• Fixed resources – Cannot be varied in the short run

• Short run– At least one resource is fixed

• Long run – No resource is fixed


Diminishing Marginal Returns• Total product

– A firm’s total output• Production function

– Relationship between amount of resources employed and total product

• Marginal product– Change in total product from an

additional unit of resource– Other things constant


Diminishing Marginal Returns• Increasing marginal returns

– Marginal product increases• Diminishing marginal returns

– Marginal product decreases• Law of diminishing marginal returns

– As more of a variable resource is added to a given amount of another resource

– Marginal product eventually declines• Could become negative


Exhibit 2

9

The Short-Run Relationship Between Units of Labor and Tons of Furniture Moved

Marginal product increases as the firm hires each of the first three workers, reflecting increasing marginal returns. Then marginal product declines, reflecting diminishing marginal returns. Adding more workers may, at some point, actually reduce total product (as occurs here with an eighth worker) because workers start getting in each other’s way.


Exhibit 3

10

The Total and Marginal Product of Labor

5

10

15

Tota

l pro

duct

(to

ns/d

ay)

5 10 Workers per day0

5 10 Workers per day

1

3

5

Mar

gina

l pro

duct

(to

ns/d

ay)

0

2

4

Total

product

Marginal product

Negative

marginal

returns

Diminishing but

positive

marginal returns

Increasing

Marginal

returns

(a) Total product

(b) Marginal product

When marginal product is rising, total product increases by increasing amounts. When marginal product is falling but still positive, total product increases by decreasing amounts.

When marginal product equals 0, total product is at a maximum. When marginal product is negative, total product is falling.


Costs in the Short Run• Fixed cost, FC

– Any production cost that is independent of the firm’s rate of output

• Variable cost, VC – Any production cost that changes as the

rate of output changes• Total cost, TC = FC + VC


Costs in the Short Run• Marginal cost, MC = ∆TC/∆q

– Change in total cost resulting from a one-unit change in output

• Changes in MC– Reflect changes in marginal productivity

• Increasing marginal returns– MC falls

• Diminishing marginal returns– MC increases


Exhibit 4

13

Short-Run Total and Marginal Cost Data for Smoother Mover

Because of increasing marginal returns from the first three workers, marginal cost declines at first, as shown in column (6). Because of diminishing marginal returns beginning with the fourth worker, marginal cost starts increasing.


Costs in the Short Run• Fixed cost curve

– Straight horizontal line• Variable cost curve

– Starts at the origin• Total cost curve

– Fixed cost curve + variable cost curve• Slope of total cost curve

– Marginal cost


Exhibit 5

15

Total and Marginal Cost Curves for Smoother Mover

200

$500

Tota

l dol

lars

25

Cos

t per

ton

$50Marginal cost

9 15 Tons per day0 63 12

Fixed cost

Total cost

Tons per day0 9 1563 12

Variable costFixed

cost

In panel (a), fixed cost is $200 at all levels of output. Variable cost starts from the origin and increases slowly at first as output increases. When the variable resource generates diminishing marginal returns, variable cost begins to increase more rapidly. Total cost is the vertical sum of fixed cost and variable cost. In panel (b), marginal cost first declines, reflecting increasing marginal returns from the variable resource (labor in this example) and then increases, reflecting diminishing marginal returns.


Average Cost in the Short Run• Average variable cost, AVC = VC/q

– Variable cost divided by output• Average fixed cost, AFC = FC/q

– Fixed cost divided by quantity• Average total cost, ATC = TC/q

– Total cost divided by output– ATC = AFC + AVC


Average Cost in the Short Run• When MC < average cost

– The marginal pulls down the average• When MC > average cost

– The marginal pulls up the average• U-shape of average cost curves

– Law of diminishing marginal returns


Exhibit 6

18

Short-Run Total, Marginal, and Average Cost Data for Smoother Mover

Marginal cost first falls then increases because of increasing then diminishing marginal returns from labor. As long as marginal cost is below average cost, average cost declines. Once marginal cost exceeds average cost, average cost increases. Columns (4), (5), and (6) show the relation between marginal and average costs.


Exhibit 7

19

Average and Marginal Cost Curves for Smoother Mover

0 5 10 15 Tons per day

$150

125

100

75

50

25

Cos

t pe

r to

n

ATC

AVC

MC

Average variable cost and average total cost curves first decline, reach low points, and then rise. Overall, they have U shapes. When marginal cost is below average variable cost, average variable cost is falling. When marginal cost equals average variable cost, average variable cost is at its minimum. When marginal cost is above average variable cost, average variable cost is increasing. The same relationship holds between marginal cost and average total cost.


Costs in the Long Run• Long run

– Planning horizon– All resources can be varied

• Firms plan for the long run• Firms produce in the short run


Costs in the Long Run• Economies of scale

– Forces that reduce a firm’s average cost– As the scale of operation increases in the

long run• Diseconomies of scale

– Forces that may eventually increase a firm’s average cost

– As the scale of operation increases in the long run


Costs in the Long Run• Long-run average cost curve

– Indicates the lowest average cost of production• At each rate of output when the scale of the

firm varies

– Planning curve– U-shaped

• Economies of scale• Diseconomies of scale


Exhibit 8

23

Short-Run Average Total Cost Curves Form the Long-Run Average Cost Curve, or Planning Curve

Cos

t pe

r un

it

0 q qa q’ Output per periodqb

S

S’

M M’

L

L’

Curves SS’, MM’, and LL’ show short-run average total costs for small, medium, and large plants, respectively. For output less than qa, average cost is lowest when the plant is small. Between qa and qb, average cost is lowest with a medium-size plant. If output exceeds qb, the large plant offers the lowest average cost. The long-run average-cost curve connects these low cost segments of each curve and is identified as SabL’.

a b


Exhibit 9

24

Many Short-Run Average Total Cost Curves Form a Firm’s

Long-Run Average Cost Curve, or Planning Curve

ATC1

ATC2

0 q q’ Output per period

Cos

t pe

r un

it

$11

10

9

b

ATC3

ATC4

ATC5

ATC6

ATC7

ATC8

ATC9

ATC10

Long-run

average cost

c

a

With many possible plant sizes, the long-run average cost curve is the envelope of portions of the short-run average cost curves. Each short-run curve is tangent to the long-run average cost curve. Each point of tangency represents the least-cost way of producing that rate of output.


Costs in the Long Run• Constant long-run average cost

– Over some range of output– Long-run average cost neither increases

nor decreases with changes in firm size– No economies of scale– No diseconomies of scale


Exhibit 10

26

A Firm’s Long-Run Average Cost CurveC

ost

per

unit

0 A Output per periodB

Economies

of scale

Long-run

average cost

Diseconomies

of scale

Constant

average cost

Up to output level A, long-run average cost falls as the firm experiences economies of scale. Output level A is the minimum efficient scale—the lowest rate of output at which the firm takes full advantage of economies of scale. Between A and B, the average cost is constant. Beyond output level B, long-run average cost increases as the firm experiences diseconomies of scale.


Economies & Diseconomies of Scale

• Plant level– Particular location

• Firm level– Collection of plants


Appendix Production and Cost

• Production function – Identifies the most that can be produced –Per time period –Using various combinations of resources–For a given state of technology

• Technologically efficient production –Producing the maximum possible output

given the combination of resources used• That same output could not be produced

with fewer resources


Exhibit 11

29

A Firm’s Production Function Using Labor and Capital: Production per Month



• Isoquant–All technologically efficient combinations

of two resources• That produce a certain (constant) rate of

output

• Properties of isoquants–Farther from origin: greater output rates–Negative slope–Don’t intersect–Convex to the origin


Exhibit 12

31

A Firm’s Isoquants

0 5Units of labor per month

10

Uni

ts o

f ca

pita

l per

mon

th

5

10

Q1 (290)

Q2 (415)

Q3 (475)

a

b

cd

e

hf

g

Isoquant Q1 shows all technologically efficient combinations of labor and capital that can be used to produce 290 units of output. Isoquant Q2 reflects 415 units, and Q3 reflects 475 units. Each isoquant has a negative slope and is convex to the origin



• Slope of an isoquant–Measures the ability of additional units of

one resource • To substitute in production for another

resource –Negative



• Marginal rate of technical substitution–MRTS –Rate at which labor substitutes for capital

without affecting output–Absolute value of the slope of the

isoquant–MRTS = MPL/MPC



• Isocost lines–All combinations of capital and labor a

firm can hire for a given total cost–Are parallel – reflect the same relative

resource prices • Slope of isocost line

–Negative –Price of labor divided by price of capital

34

r

w

wTC

rTC

/

/


Exhibit 13

35

A Firm’s Isocost Lines

5 10 150

Units of labor per month

5

10U

nits

of

capi

tal p

er m

onth

TC = $15,000

TC = $19,000

TC = $22,500

Slope = -w/r = -$1,500/$2,500 = -0.6

Each isocost line shows combinations of labor and capital that can be purchased for a given amount of total cost. The slope of each equals the negative of the monthly wage rate divided by the rental cost of capital per month. Higher costs are represented by isocost lines farther from the origin.



• Minimum cost to produce a given output–Tangency between isocost line and

isoquant–Same slope = MRTS = ratio of input

prices = w/r• The firm adjusts resource use so that

– Rate at which one input substitutes for another in production = rate at which one resource exchanges for another in resource markets


Exhibit 14

37

A Firm’s Optimal Combination of Inputs

Q1 (290)

Q2 (415)

Q3 (475)

f

5 100


5

10U

nits

of

capi

tal p

er m

onth

TC = $19,000

a

e

At point e, isoquant Q2 is tangent to the isocost line. The optimal combination of inputs is 6 units of labor and 4 units of capital. The most that can be produced for $19,000 is 415 units. Another way of looking at this is that point e identifies the least costly way of producing 415 units.



• Expansion path–Connect the tangency points between

isoquants and isocost lines• Least-cost input combinations for producing

several output rates–Slopes upward–Lowest long-run total cost for each rate

of output


Exhibit 15

39

A Firm’s Expansion Path

Expansion path

Q2

L L’0


C

Uni

ts o

f ca

pita

l per

mon

th

Q4

Q3

Q1

d

h

TC3

TC2

TC1

TC4

ab

c

Points of tangency between isoquants and isocost lines identify the least costly resource combination of producing each particular quantity of output. Connecting these tangency points traces out the firm’s expansion path, which usually slopes up to the right, indicating that more of both goods is needed to increase output.


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