Chapter Seven - An-Najah Videos

Chapter Seven

Costs

© 2009 Pearson Addison-Wesley. All rights reserved. 7-2

Topics

Measuring Costs.

Short-Run Costs.

Long-Run Costs.

Lower Costs in the Long Run.

Cost of Producing Multiple Goods.


Economic Cost

Economic cost or opportunity cost -the value of the best alternative use of a resource.

Explicit costs - firm’s direct, out-of-pocket payments for inputs to its production process during a given time period. ,

Workers’ wages, managers’ salaries, etc. and payments for materials.

Implicit costs – cost of use inputs that may not have an explicit price.

value of the working time of the firm’s owner


Economic Vs Accounting Cost

According to Bookkeepers:

The purpose of cost estimation:

a. To minimize firm’s tax for this year

b. To reflect good impression for stock holders about the firm’s performance

SO: Accounting Profits = TR – TC

Where TC = Explicit costs, such as:

- Wages - Salaries - Rent

- Row material payment

- Amortization OR (Depreciation)


Economic Vs Accounting Cost

According to Economists:

To run a firm profitably, a manager acts like an economist and consider all relevant costs:

SO: Econ. Profits = TR – TC

Where TC = Explicit cost + Implicit cost

- Explicit costs do not contain depreciation, economists amortizes capital using the rule of the best rental rate for capital, which is an implicit cost

- Implicit cost: Such as:

a. Opportunity cost for capital, or the best alternative use (Rental rate)

b. Opportunity cost for the production factors owned to owner, or the best alternative use.


Short-Run Cost Measures

Fixed cost (F) - a production expense that does not vary with output.

Variable cost (VC) - a production expense that changes with the quantity of output produced.

Cost (total cost, C) - the sum of a firm’s variable cost and fixed cost:

C = VC + F


Marginal Cost.

marginal cost (MC) - the amount by which

a firm’s cost changes if the firm produces

one more unit of output.

And since only variable costs change with

output:

q

CMC

q

VCMC


Average Costs.

average fixed cost (AFC) - the fixed cost divided by the units of output produced:

AFC = F/q.

average variable cost (AVC) - the variable cost divided by the units of output produced:

AVC = VC/q.

average cost (AC) - the total cost divided by the units of output produced:

AC = C/qAC = AFC + AVC.


Table 7.1 Variation of Short-Run

Cost with Output


Figure 7.1 Short-

Run Cost Curves

120

216

400

48

0 6 10

10

42 8

Quantity, q, Units per day


6

b

a

B

A

42 8

C

F

1

1

27

20

VC

MC

AC

AVC

AFC

Cost, $

Cost per

unit,

$

(a)

(b)

60

2827

20

8

0


Relationship between average and

marginal cost curves

10


6

b

a

42 8

MC

AC

AVC

Co

st

per

un

it,

$ 60

2827

20

8

0

When MC is

lower than

AVC, AVC is

decreasing…

and when MC is

larger than AVC,

AVC is increases

…so MC = AVC, at

the lowest point of

the AVC curve!

When MC is

lower than

AC, AC is

decreasing…

and when MC is

larger than AC,

AC is increases

…so MC = AC, at

the lowest point of

the AC curve!


Figure 7.2 Variable Cost and Total

Product of Labor


Shape of the Marginal Cost Curve

MC = VC/q.

But in the short run,

VC = w.L (can you tell why?)

Therefore,

MC = w.(L/q)

The additional output created by every additional unit of labor is:

q/ L = MPL

Therefore,

MC = w/ MPL


Shape of the Average Cost Curves

AVC = VC/q.

But in the short-run, with only labor as an

input:

AVC = VC/q = wL/q

And since q/L = APL, then

AVC = VC/q = w/APLL


Application Short-Run Cost Curves for a

Furniture Manufacturer


Table 7.2 Effect of a Specific Tax of

$10 per Unit on Short-Run Costs


Figure 7.3 Effect of a Specific Tax on

Cost CurvesC

osts

per

un

it,

$

155 8 100

q, Units per day

80

37

27

$10

$10

ACa = ACb + 10

ACb

MCb

MCa = MCb + 10

A $10.00 tax shifts

both the AVC and

MC by exactly

$10…


Solved Problem 7.1

What is the effect of a lump-sum

franchise tax on the quantity at which a

firm’s after tax average cost curve

reaches its minimum? (Assume that the

firm’s before-tax average cost curve is

U-shaped.)


Solved Problem 7.1


Long-Run Costs

Fixed costs are avoidable in the long

run.

in the long F = 0.

As a result, the long-run total cost equals:

C = VC


Input Choice

isocost line - all the combinations of

inputs that require the same (iso-) total

expenditure (cost).

The firm’s total cost equation is:

C = wL + rK.

Labor

Costs

Capital

Costs


Input Choice (Cont).

The firm’s total cost equation is:

C = wL + rK.

We get the Isocost equation by setting fixing the

costs at a particular level:

C = wL + rK.

And then solving for K (variable along y-axis):

K = r- Lw

rC


Table 7.3 Bundles of Labor and

Capital That Cost the Firm $100


Figure 7.4 A Family of Isocost LinesK

, U

nits o

f ca

pita

l p

er

year

a

d

e

$100 isocost

L, Units of labor per year

$100

$1010 =

$100

$5= 20

Isocost Equation

K = r- Lw

rC

Initial ValuesC = $100w = $5r = $10

15

2.5

10

5

7.5

5

c

b

L = 5

K = 2.5

For each extra unit

of capital it uses,

the firm must use

two fewer units of

labor to hold its

cost constant.

Slope = -1/2 = w/r



, U

nits o

f ca

pita

l p

er

year

a

e

$150 isocost$100 isocost


$150

$1015 =

$100

$1010 =

$100

$5= 20

$150

$5= 30

Isocost Equation

K = r- Lw

rC


An increase in C….



, U

nits o

f ca

pita

l p

er

year

a

e

$150 isocost$100 isocost$50 isocost


$150

$1015 =

$100

$1010 =

$50

$105 =

$50

$5= 10

$100

$5= 20

$150

$5= 30

Isocost Equation

K = r- Lw

rC


A decrease in C….


Combining Cost and Production

Information.

The firm can choose any of three equivalent approaches to minimize its cost:

Lowest-isocost rule - pick the bundle of inputs where the lowest isocost line touches the isoquant.

Tangency rule - pick the bundle of inputs where the isoquant is tangent to the isocost line.

Last-dollar rule - pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.


Figure 7.5 Cost MinimizationK

, U

nits o

f capital per

hour

x

500 L, Units of labor per hour

100

q = 100 isoquant

$3,000isocost

$2,000

isocost

$1,000isocost

Isocost Equation

K = r- Lw

rC

Initial Valuesq = 100

C = $2,000w = $24r = $8

Isoquant SlopeMPL

MPK

= MRTS-

Which of these

three Isocost would

allow the firm to

produce the 100

units of output at

the lowest possible

cost?



, U

nits o

f capital per

hour

y

x

z

11650240

L, Units of labor per hour

100

303

28

q = 100 isoquant

$3,000isocost

$2,000

isocost

$1,000isocost

Isocost Equation

K = r- Lw

rC


C = $2,000w = $24r = $8

Isoquant Slope

MPL

MPK

= MRTS-


Cost Minimization

At the point of tangency, the slope of the

isoquant equals the slope of the isocost.

Therefore,

r

MP

w

MP

r

w

MP

MP

MP

MPMRTS

r

wMRTS

KL

K

L

K

L

last-dollar rule: cost is

minimized if inputs

are chosen so

that the last dollar

spent on labor adds

as much extra output

as the last dollar

spent on capital.

© 2009 Pearson Addison-Wesley. All rights reserved.


, U

nits o

f capital per

hour

y

x

z

11650240


100

303

28

q = 100 isoquant

$3,000isocost

$2,000

isocost

$1,000isocost


C = $2,000w = $24r = $8

w rMPL MPK=

MPL = 0.6q/L

MPK = 0.4q/K

=24 81.2 0.4

= = 0.05

Spending one more dollar

on labor at x gets the firm

as much extra output as

spending the same

amount on capital.

© 2009 Pearson Addison-Wesley. All rights reserved.


, U

nits o

f capital per

hour

y

x

z

11650240


100

303

28

q = 100 isoquant

$3,000isocost

$2,000

isocost

$1,000isocost


C = $2,000w = $24r = $8

w

r

MPL

MPK

MPL = 0.6q/L

MPK = 0.4q/K

= 24

8

2.5

0.13=

= 0.1

if the firm shifts one dollar from

capital to labor, output falls by

0.017 because there is less capital

but also increases by 0.1 because

there is more labor for a net gain of

0.083 more output at the same

cost….

= 0.02So …the firm should shift

even more resources from

capital to labor—which

increases the marginal product

of capital and decreases the

marginal product of labor.


Figure 7.6 Change in Factor PriceK

, U

nits o

f ca

pita

l p

er

ho

ur

x

77500 L, Workers per hour

100

52

q = 100 isoquant

Original

isocost,

$2,000

New isocost,

$1,032

w rMPL MPK=

Minimizing Cost Rule

A decrease in w…. Initial Valuesq = 100

C = $2,000w = $24r = $8w2 = $8C2 = $1,032

v


How Long-Run Cost Varies with Output

expansion path - the cost-minimizing

combination of labor and capital for each

output level


Figure 7.7(a) Expansion Path

K, U

nits o

f ca

pita

l p

er

ho

ur

x

y

z

10075500 L, Workers per hour

150

200

100

Expansion path

$3,000isocost

$2,000isocost

$4,000isocost

q = 100 Isoquant

q = 200 Isoquant

q = 300 Isoquant


Figure 7.7(b) Expansion Path and

Long-Run Cost Curve (cont’d)


Solved Problem 7.4

What is the long-run cost function for a

fixed-proportions production function

(Chapter 6) when it takes one unit of

labor and one unit of capital to produce

one unit of output? Describe the long-

run cost curve.


Figure 7.8 Long-

Run Cost Curves


Economies of Scale

economies of scale - property of a cost

function whereby the average cost of

production falls as output expands.

diseconomies of scale - property of a

cost function whereby the average cost

of production rises when output

increases.


Table 7.4 Returns to Scale and

Long-Run Costs


Table 7.5 Shape of Average Cost

Curves in Canadian Manufacturing


Long-Run Average Cost

In its long-run planning, a firm chooses a

plant size and makes other investments

so as to minimize its long-run cost on

the basis of how many units it produces.

Once it chooses its plant size and

equipment, these inputs are fixed in the

short run.

Thus, the firm’s long-run decision determines its

short-run cost.


Figure 7.9 Long-Run Average Cost as the

Envelope of Short-Run Average Cost CurvesA

vera

ge c

ost, $

a

bd

e

SRAC1 SRAC2SRAC3

SRAC3LRAC

c

q2

q1

q, Output per day

10

0

12


Application Long-Run Cost Curves in Furniture

Manufacturing and Oil Pipelines


Application Long-Run Cost Curves in Furniture

Manufacturing and Oil Pipelines


Application Choosing an Ink-Jet or a

Laser Printer


Figure 7.10 Long-Run and

Short-Run Expansion Paths


How Learning by Doing Lowers Costs

learning by doing - the productive skills

and knowledge that workers and

managers gain from experience


Figure 7.11 Learning by Doing


Cost of Producing Multiple Goods

economies of scope - situation in

which it is less expensive to produce

goods jointly than separately.

production possibility frontier - the

maximum amount of outputs that can be

produced from a fixed amount of input


Figure 7.12 Joint Production

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