8-cost of production.ppt

8/10/2019 8-Cost of Production.ppt

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Copyright 2004 South-Western/

2

Production Function

A firm produces a particular good (q) usingcombinations of inputs

The most common used inputs are capital (k)and labor (l)

One could think in introducing different

inputs: skilled labour, unskilled labour, rawmaterials, intermediate products,technology


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Production Function

The firmsproduction function for a

particular good (q) shows the maximum

amount of the good that can be producedusing alternative combinations of inputs (for

example, capital (k) and labor (l))

q=f(k,l)


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Marginal Productivy

(equivalent to marginal utility). The marginalproductivity (also called marginal physical product) isthe additional output that can be produced by

employing one more unit of that input while holdingother inputs constant.

Given by the first derivative of the productionfunction with respect the input under consideration

kk fk

qMP

capitalofproductphysicalmarginal

ll

l

fq

MP

laborofproductphysicalmarginal


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Diminishing Marginal Productivity

The marginal physical product of an input

depends on how much of the other inputs is

being used In general, we assume diminishing marginal

productivity

0112

2

ffkf

kMP

kkk 0222

2

fffMP

lll

ll

Notice that we also assume that the second derivative of the

Utility function with respect a good is negative


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Diminishing Marginal Productivity

Notice, that the Marginal Productivitygenerally depends on all the inputs

For instance, the marginal productivity oflabor also depend on changes in other inputssuch as capital

we need to considerflkwhich is often > 0

An additional unit of labor will increase theproduction of the good more if there is morecapital available


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Average Physical Product

Another concept is average productivity of acertain input

This is the ratio of the production and the amountof input used

For instance, average labour productivity is:

l

l

ll ),(

inputlaboroutput kfqAP

Note that APlalso depends on the amount of

capital employed


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Isoquant

A curve showing all possible (efficient)

combinations of inputs that are capable of

producing a certain quantity of output

Iso quant

same quantity



Labor

Capital

0

K2

100

200

300

K1

L2 L1



Marginal rate of technicalsubstitution

Shows the rate at which one input can be

substituted for another input, if output remains

constant. (Slope of the isoquant.)

Given Q = f(X1, X2)

MRTS =-dX2 / dX1

= -MP1/ MP2



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Marginal Rate of TechnicalSubstitution (RTS)

lper period

kper period

q = 20

- slope = marginal rate of technical

substitution (RTS)

The slope of an isoquant shows the rate at

which l can be substituted for k

lA

kA

kB

lB

A

B

RTS > 0 and is diminishing for

increasing inputs of labor



12

Marginal Rate of TechnicalSubstitution (RTS)

The marginal rate of technical substitution

(RTS) shows the rate at which labor can besubstituted for capital while holding output

constant along an isoquant

0

)for(qqd

dkkRTS

ll



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RTSand Marginal Productivities

Take the total differential of the production

function:

dkMPdMPdkk

f

d

f

dq k

lll l

Along an isoquant dq = 0, so

dkMPdMP k l

l

kqq MP

MP

d

dkkRTS l

ll

0

)for(


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Isocost curves

Various combinations of inputs that a firm can

buy with the same level of expenditure

PLL + PKK = M

where M is a given money outlay.


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Maximization of output for givencost

Labor

Capital

0

100

200

300R



MPL/PL= MPK/PK

Labor

Capital

0

100

200

300R



Optimal Lot Size

To consider the size of inventory

Find the relationship between size of lot and

total annual cost.



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Isoquant Maps

To illustrate the possible substitution of oneinput for another, we use an isoquant map

An isoquant shows those combinations of kand lthat can produce a given level ofoutput (q0) (rings a bell indifferencecurves)

f(k,l) = q0



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Isoquant Map

lper period

kper period

Each isoquant represents a different level of

output

output rises as we move northeast

q = 30

q = 20



WHAT ARE COSTS?

According to the Law of Supply:

Firms are willing to produce and sell a greater

quantity of a good when the price of the good is

high. This results in a supply curve that slopes upward.

We examine firm behaviour in more detail.



WHAT ARE COSTS?

The Firms Objective

The economic goal of the firm is to maximize

profits.



Total Revenue, Total Cost, and Profit

Total Revenue

The amount a firm receives for the sale of its

output.

Total Cost The market value of the inputs a firm uses in

production.

Profit = Total RevenueTotal Cost



Costs as Opportunity Costs

A firms cost of productionincludes all theopportunity costs of making its output of goods

and services.

Explicit and Implicit Costs

A firms cost of production include explicit costs

and implicit costs.

Explicitcosts are input costs that require a direct paymentby the firm.

Implicitcosts are input costs that do not require payment

of money by the firm.



Economic Profit versus Accounting Profit

Economists measure a firms economic profit astotal revenue minus total cost, including both

explicit and implicit costs.

Accountants measure the accounting profit asthe firms total revenue minus only the firms

explicit costs.


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Figure 1 Economic versus Accountants

Copyright 2004 South-Western

Revenue

Total

opportunitycosts

How an Economist

Views a Firm

How an Accountant

Views a Firm

Revenue

Economicprofit

Implicitcosts

Explicitcosts

Explicitcosts

Accounting

profit


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Table 1 A Production Function and Total Cost:

Copyright2004 South-Western


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Figure 2 Hungry Helens Production Function


Quantity of

Output

(cookiesper hour)

150

140

130

120

110

100

90

80

70

60

50

40

30

20

10

Number of Workers Hired0 1 2 3 4 5

Production function


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THE VARIOUS MEASURES OFCOST

Costs of production may be divided intofixedcosts and variable costs.

Fixed costsare those costs that do not vary

with the quantity of output produced.

Variable costsare those costs that do vary with

the quantity of output produced.


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Table 2 The Various Measures of Cost: Thirsty


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Table 2 The Various Measures of Cost: ThirstyThelmas Lemonade Stand



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Fixed and Variable Costs

Average Costs

Average costs can be determined by dividing the

firms costs by the quantity of output it produces.

The average cost is the cost of each typical unit ofproduct.


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Fixed and Variable Costs

Average Costs

Average Fixed Costs (AFC)

Average Variable Costs (AVC)

Average Total Costs (ATC)

ATC=AFC+AVC


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Average Costs

AFC FC

Q

Fixed cost

Quantity

AVC VC

Q

Variable cost

Quantity

ATC TC

Q

Total cost

Quantity

Table 2 The Various Measures of Cost: Thirsty


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Table 2 The Various Measures of Cost: ThirstyThelmas Lemonade Stand



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Marginal Cost

MC

TC

Q

(change in total cost)

(change in quantity)

Marginal Cost


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Marginal Cost

Quantity TotalCost

MarginalCost

Quantity TotalCost

MarginalCost

0 $3.00

1 3.30 $0.30 6 $7.80 $1.30

2 3.80 0.50 7 9.30 1.50

3 4.50 0.70 8 11.00 1.70

4 5.40 0.90 9 12.90 1.905 6.50 1.10 10 15.00 2.10

Figure 5 Thirsty Thelmas Average-Cost and Marginal-Cost


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Figure 5 Thirsty Thelma s Average Cost and Marginal CostCurves


Costs

$3.503.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

Quantity

of Output

0 1 432 765 98 10

MC

ATC

AVC

AFC


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Cost Curves and Their Shapes

Marginal cost rises with the amount of outputproduced.

This reflects the property of diminishing marginal

product.



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g y g gCurves


Costs

$3.503.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

Quantity

of Output

0 1 432 765 98 10

MC


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Cost Curves and Their Shapes

The average total-cost curve is U-shaped.

At very low levels of output average total cost

is high because fixed cost is spread over only a

few units. Average total cost declines as output increases.

Average total cost starts rising because average

variable cost rises substantially.


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g y g gCurves


Costs

$3.503.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

Quantity

of Output

(glasses of lemonade per hour)

0 1 432 765 98 10

ATC

C


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Relationship between Marginal Cost andAverage Total Cost

When MC is below AC, it is pulling the AC costdown.

When MC is above AC, it is pulling up AC.

When MC = AC, AC is constant, At the bottom ofU-shaped AC, MC=AC=minimum AC.

The marginal-cost curve crosses the average-total-

cost curve at the efficient scale.

Efficient scale is the quantity that minimizes average total

cost.



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g y g gCurves


Costs

$3.503.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

Quantity

of Output

(glasses of lemonade per hour)

0 1 432 765 98 10

ATC

MC


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Typical Cost Curves

Figure 6 Big Bobs Cost Curves


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Figure 6 Big Bob s Cost Curves


(b) Marginal- and Average-Cost Curves

Quantity of Output (bagels per hour)

Costs

$3.00

2.50

2.00

1.50

1.00

0.50

0 42 6 8 141210

MC

ATCAVC

AFC


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Typical Cost Curves

Three Important Properties of Cost Curves

Marginal cost eventually rises with the quantity of

output.

The average-total-cost curve is U-shaped. The marginal-cost curve crosses the average-total-

cost curve at the minimum of average total cost.

COSTS IN THE SHORT RUN AND


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COSTS IN THE SHORT RUN ANDIN THE LONG RUN

For many firms, the division of total costsbetween fixed and variable costs depends on the

time horizon being considered.

In the short run, some costs are fixed. In the long run, fixed costs become variable costs.

Because many costs are fixed in the short run but

variable in the long run, a firms long-run cost

curves differ from its short-run cost curves.

Average Total Cost in the Short and Long Run


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Average Total Cost in the Short and Long Run


Quantity of

Cars per Day

0

Average

TotalCost

1,200

$12,000

ATCin shortrun with

small factory

ATCin shortrun with

medium factory

ATCin shortrun with

large factory

ATCin long run


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Economies and Diseconomies of Scale

Economies of scale refer to the propertywhereby long-run average total cost falls as the

quantity of output increases.

Diseconomies of scale refer to the propertywhereby long-run average total cost rises as the

quantity of output increases.

Constant returns to scale refers to the propertywhereby long-run average total cost stays the

same as the quantity of output increases

Figure 7 Average Total Cost in the Short and Long Run


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Figure 7 Average Total Cost in the Short and Long Run


Quantity of

Cars per Day

0

Average

TotalCost

1,200

$12,000

1,000

10,000

Economies

ofscale

ATCin shortrun with

small factory

ATCin shortrun with

medium factory

ATCin shortrun with

large factory ATCin long run

Diseconomiesof

scale

Constant

returns toscale


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Economies of scope

Exist when the cost of producing two (or more)

products jointly is less than the cost of

producing each one alone.

S = C(Q1) + C(Q2) - C(Q1+ Q2)

C(Q1+ Q2)

8-cost of production.ppt

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