production and cost function

7/31/2019 Production and Cost Function

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The Firm:

Production FunctionCost Function

BASIC PRODUCTION

CONCEPTS


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The Firm

Firm

An organization that brings together factors of

productionlabor, land, physical capital, human

capital, and entrepreneurial skillto produce aproduct or service that it hopes can be sold at a

profit


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The Firm

Profit and costs

Accounting profits = total revenues - explicit costs

Explicit Costs

Costs that business managers must take account of

because they must be paid


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The Firm

The goal of the firm: profit maximization

Firms are expected to try to make the positive

difference between total revenues and totalcosts as large as they can.


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The Relationship

Between Output and Inputs

Production Function

The relationship between inputs and output

A technological, not an economic, relationship

The relationship between inputs and maximum

physical output


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The Relationship


Production

Any activity that results in the conversion of

resources into products that can be used in

consumption


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PRODUCTIONINPUTS

PRODUCTION

PROCESS

PRODUCTIONOUTPUT

Land

Labor

CapitalRaw Materials

Entrepreneur

Manufacturing

Assembly

ProcessingService

Finished Products

Semi-processed products

Services


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The Relationship


*Q= output/time periodK= capital

L = labor

Q = (K,L)*

or

Output/time period = some function of capital and labor inputs


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Two types of Production Inputs

Fixed Input

Variable Input

Point of comparison Fixed Input Variable Input

Necessity in Production Supplementary; even in

their absence some

amount of production canbe carried out

Without these factors no

production can be carried

out

Examples Plant, machinery, manager,

land, factory premises

Labor, raw materials,

transport, frieght


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THE LAW OF DIMINISHING RETURNS

When one of the factors of production is held

fixed in supply, successive additions of otherfactors will lead to an increase in returns up to

a point, but beyond this point returns will

diminish


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The Law of Diminishing Returns

NUMBER OFWORKERS

TOTAL PHYSICALPRODUCT (TPP)

MARGINALPHYSICAL

PRODUCT (MPP)

AVERAGE PHYSICALPRODUCT (APP)

1 10 10 10

2 30 30-10=20 15

3 90 90-30=60 30

4 120 120-90=30 30

5 130 130-120=10 26

6 120 120-130=-10 20


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The Relationship


Marginal Physical Product

The physical output that is due to the addition ofone more unit of a variable factor of production

The change in total product occurring when avariable input is increased and all other inputs areheld constant

Also called marginal productor marginal return


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Diminishing Returns, the Production Function,

and Marginal Product


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and Marginal Product: A Hypothetical Case

Figure 22-2, Panel (b)


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Figure 22-2, Panel (c)


and Marginal Product


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COST & PROFIT CONCEPT

Types of Cost

Variable Cost : are expenses

incurred in production that

tend to change directly asproduction increases

Fixed Cost : are expenses

that do not change or vary

with production

TC = TFC + TVC

TVC = (VC/u) (u)


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Revenue : sales generated by anenterprise

TR = (Sp/u) (u)

Profits : difference between the totalrevenue and total cost

TP = TR- TC

TR= TC (Break Even)

TR> TC (Profit)

TC>TR (Losses)


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Cost of Production: An Example

Figure 22-2, Panel (a)


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Costs(dollarperday)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16

Output (calculators per day)

10

14

ATC

AVC

AFC



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AFC

AVC

Costs(dollar

perday)


ATC


TP

ATC = AVC + AFC

AFC = ATC - AVC

AVC


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Short-Run Costs to the Firm

Marginal Cost

The change in total costs due to a one-unit

change in production rate

Marginal costs (MC) =change in total cost

change in output


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TotalTotal Variable Total Marginal

Output Costs Costs Cost(Q/day) (TVC) (TC) (MC)

0 0

1 5

2 8

3 10

4 11

5 13

6 16

7 20

8 25

9 31

10 38

11 46

10

15

18

20

21

23

26

30

35

41

48

56

5

32

1

2

3

45

6

7

8

C

osts(dollarper

day)

2

4

6

8

12

2 4 6 8 100 1 3 5 7 9 11

16


10

14

MC



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1110

AFC

AVC

MC

ATC

9876543210

2

4

6

8

Panel (c)

16

14

12

10

Output (recordable DVDs per day)

Costs(d

ollarsperrecordableDVD)


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Short-Run Costs to the Firm

Answer

As long as marginal physical product rises,

marginal cost will fall, and when marginalphysical product starts to fall (after reaching

the point of diminishing marginal returns),

marginal cost will begin to rise.


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The Relationship Between Diminishing Marginal

Returns and Cost Curves

Labor cost assumed constant

MC =DTC

D

Output

Recall: labor is the variable input

MC =

W

MPP


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Figure 22-3, Panels (b) and (c)

The Relationship Between

Physical Output and Costs


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The Relationship Between

Physical Output and Costs

Figure 22-3, Panels (c) and (d)


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Firms short-run cost curves are a reflection of

the law of diminishing marginal returns.

Given any constant price of the variable input,

marginal costs decline as long as the marginal

product of the variable resource is rising.


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At the point at which diminishing marginal

returns begin, marginal costs begin to rise as

the marginal product of the variable input

begins to decline.


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AVC =TVC

output

AVC =W

AP


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TR = TC

TR =100; TC= 100; TR=TC

TR=100; TC =50, P/L= TR-TC= 100-50= 50Profit

TR=100; TC=200, P/L =TR-TC = 100-200= (100) Breakeven?

P200price shirt; P200,000(machine)); (80/hr labor)

TR= TC

(sp/u) (u)= TFC+TVC 200(x) = 200,000 + 80(x)

200x-80x = 200,000

120x = 200,000

X= 200,000/120 1,667 pairs will have to be sold to break even

< = profit; >=loss


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200x= 200,000 + 80 x; 2,000 (P/L) Profit= how

much profit

200(2,000) = 200,000 + 80 (2,000)

400,000 = 200,000 + 160,000

TR= 400,000

TC =360,000

P/L = 400,000-360,000 P= 40,000


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Preferable Plant Size

and the Long-Run Average Cost Curve

Figure 22-4, Panels (a) and (b)

Panel (b)

Output per Time PeriodQ2Q1

C3

C1

C4C2

Panel (a)

Output per Time Period

SAC2

1SAC

SAC3

LAC

1SAC

2SAC

3SAC

4SAC

5SAC

6SAC

SAC7

SAC8

AverageCost(dollarsperunit

ofoutput)

AverageC

ost(dollarsperunitofoutput)


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Long-Run Cost Curves

Long-Run Average Cost Curve

The locus of points representing the minimum

unit cost of producing any given rate of output,

given current technology and resource prices


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Why the Long-Run Average Cost Curve is U-

Shaped

Economies of Scale

Decreases in long-run average costs resulting from

increases in output


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Shaped

Reasons for economies of scale

Specialization

Dimensional factor

Improved productive equipment


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Shaped

Explaining diseconomies of scale

Limits to the efficient functioning of management


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Minimum Efficient Scale

Minimum Efficient Scale (MES)

The lowest rate of output per unit time at which

long-run average costs for a particular firm are at

a minimum


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Small MES relative to industry demand:

High degree of competition

Large MES relative to industry demand:

Small degree of competition


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Figure 22-6

0

Output per Time Period

LAC

B

1,000

A

10

Lon

g-RunAverage

Costs

(dollarsperunit)


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The Firm: Cost and Output

Determination

End

production and cost function

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