Cost Function.ppt

8/14/2019 Cost Function.ppt

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Cost Accounting

ofFactor Inputs


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Introduction

In the supply process, households first offer thefactors of production they control to the factormarket.

The factors are then transformed by firms into

goods that consumers want.

Productionis the name given to thattransformation of factors into goods.


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The Role of the Firm

A key concept in production is the firm.

Thefirmis an economic institution that

transformsfactors of production(inputs) into

consumer goods (output, quantity supplied).


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A firm: Organizes factors of production.

Produces goods and/or services.

Sells goods it produces to individuals.


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When the firm only organizesproduction it is

called a virtual firm.

Virtual firmssubcontractout all work.

While most firms are not virtual, more and

more of the organizational structure of businessis being separated from production.


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The Firm and the Market

Whether an activity is organized through the

market depends on transaction costs.

Transaction costscosts of undertaking

trades through the market.


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The Firm and the Market

The various forms that businesses organize

themselves include

sole proprietorships,

partnerships, corporations,

for-profit firm,

nonprofit firms, and

cooperatives.


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Firms That Maximize Profit

Profitis the difference between total revenue and

total cost.

Profit = total revenue total cost

= TR TC

= P*Q (TC/Q)*Q


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Firms Maximize Profit

For an economist, total costis explicit payments to

factors of productionplusthe opportunity cost of the

factors provided by the owners.

Total Costs = accounting costs + opportunity costs. Accounting costs = expenses that appear on the

books.


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Total revenueis the amount a firm receives

for selling its good or service plus any increase

in the value of the assets owned by firms.


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Economists and accountants measure profit

differently.


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For accountants, total revenue is total sales

times price.

Profit is explicit revenue less explicit cost.


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For economists, revenue includes any increase or

decrease in the value of any assets the firm owns.

They count implicit costs which include the

opportunity costs of owner-provided factorsof production.


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For economists:

Economic profit =

(explicit and implicit revenue)(explicit and implicit cost)


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Output

Diminishingmarginal

returns

Diminishingabsolute

returns

323028

262422201816141210

86420

1 2 3 4 5 6 7 8 9 10

Increasingmarginal

returns

Number of workers

TP

Outputperworker

1 2 3 4 5 6 7 8 9 10Number of workers

7

6

5

4

3

2

1

0

MP

Diminishingmarginal

returns

Diminishingabsolute

returns

(a) Total product (b) Marginal and average product

AP

A Production Function


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For factors hired or employedby a firm:

The costs are (the value of) the highest-

valued alternative use of the money spentin

hir ing them.They are called explicit costsas they

involve a transfer of money.


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For factors ownedby a firm:

The costs of usingthese factors are (the value

of) the highest-valuedalternative uses of the

factors.

They are called implicit costs()

or imputed costs, as they do

not involve a transfer

of money.


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Classif ication of costs of different factor inputs

Sunk cost (historical cost)

The cost of a past act.

As past options are not available at present, sunk costcannot be avoided now. Sunk cost is not a (present or

future) cost.

Bygone is bygone.It should have no effect onanypresent or future decisions.


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Fixed cost

The cost of employing fixed factors.

It does not change with output.

It is a present cost paid for the use of fixed factorsand hence it affects the net receipt.

It has no effect on MC & no effect onthe determination

of the wealth-maximizing output level.


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Variable costThe cost of employing variable factors.

It changes with output.

It is a present cost paid for the use of variable factors

& hence it affects the net receipt.

It affects marginal cost & hence it affects the wealth-maximizing output.


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Q8.6:

A restaurant is making a short run decision for its production

next month. Identify if the following costs are sunk costs (SC),

fixed costs (FC) or variable costs (VC).

(a) Rent of the restaurant under a 2-year contract ( )

(b) Wage payments ( )

(c) Expenditure on meat and vegetables ( )

(d) Water charges ( )

(e) Electricity charges ( )

(f) Acquisition cost of machines ( )

(g) Continuing possession cost of machines ( )

(h) Operating cost of machines ( )


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Cost Function


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Cost function() describes the

relationship between output and cost.

Output

= ???


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Short-run Cost Curves


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Measure of costsOutput changesCost changes

Total cost (TC)

Change in cost can be expressed in three ways:

Marginal cost (MC)

Average cost (AC)


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Total cost

is the whole amount of payments to al l factorsused

in producing a given amount of output (Q), composed of:

Total fixed cost(TFC): is the whole amount ofpayments to f ixed factors.

Totalvariable cost(TVC): is the whole amount ofpayments to variable factors.


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Totalcost

$400

350

300

250

200

150

10050

0

FC

2 4

M

6 8 10 20 30Quantity of earrings

VCTC

L

Total Cost Curves

O

TC = (VC + FC)


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TVC = w xLtotal variable cost:

Formula:

TC = TFC +TVCTotal Cost:

Assume two factors only:

Capital(fixed factor) and labour(variable factor)

Lunits of labour are employed at a wage rate of w.

a constant independent of outputtotal f ixed cost:


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Average cost/average total cost (ATC)

is the cost per unit of output, composed of :

average f ixed cost(AFC):the f ixed costper unit of output.

average variable cost(AVC):

the var iable costper unit of output.


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Formula:

AVCAFCQ

TVCTFC

Q

TCATC

Average Total Cost:

QTFCAFCaverage f ixed cost:

AP

w

L

Q

w

L

QL

Lw

Q

Lw

Q

TVCAVC

average variable cost:


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ATC curve and AVCcurve will come closer and closer as

the amount of output increases (ATC = AFC + AVC and

AFC drops continuously).

AVCcurve is U-

shaped. (AVC =

w/AP and AP is

inverted-U shaped.)

AFCcurve drops

continuously. (AFC

= TFC/Q)

Features:


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The turning point of ATC curve (b)occurs at a larger

output than the turning point of AVC curve (a). Why?

(b)(a)

At (a), the fall in AFC is >the rise in AVC initially

but at (b), the fall in AFC is


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Marginal Cost

is the change in total cost for producing an additional

unit of output, composed of :

The marginal cost curve goes through the minimum

point of the average total cost curve and average variable

cost curve.

Each of these curves is U-shaped.

marginal f ixed cost(MFC): is the change in f ixed costfor producing an additional unit of output

marginal variable cost(MVC): is the change in variable cost

for producing an additional unit of output.


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The law of diminishing marginal productivity sets

in as more and more of a variable input is added

to a fixed input.

Marginal and average productivities fall and marginal costs

rise.

And when average productivity of the variable input falls,

average variable cost rise.

The average total cost curve is the vertical summation of

the average fixed cost curve and the average variable cost

curve, so it is always higher than both of them.

The U Shape of the Average and

Marginal Cost Curves


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Formula:

0

QTFCMFCmarginal f ixed cost:

MVCMFCQ

TVCTFC

Q

TCMC

Marginal cost:

marginal var iable cost:

MP

w

L

Q

w

L

QL

Lw

Q

Lw

Q

TVCMVC


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MCcurve passes through the minimum points of AVCcurve

and ATCcurve.

MC or MVC

curve is

U-shaped

As TFC is a constant, MFC = 0. So MC = MVC.

MC = MVC = w/MP. As MP curve is inverted-U shaped, MC

or MVC curve is U-shaped.


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MC curve(= MVC

curve) =Slope of TC

curve& TVC curve.

Derivation of total cost

curves:

Notice the points

where MC = mini.;

MC = AVCand MC

= ATC.


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Q8.7: The following table is composed of product items and cost

items of a firm. Suppose the unit cost of capital and labour are $10 and

$20 respectively. Fill in the missing columns..

Units

of

capital

Units

of

labour

TP AP MP TFC TVC TC ATC

4

4

4

4

4

4

1

2

3

4

5

6

2

5

10

14

14

12


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Q8.8(a) When output increases, if AP of a variable factor rises,

what will happen to AVC and ATC?

(b) When output increases, if AP of a variable factor falls,

what wi ll happen to AVC and ATC?


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Long-run Cost Curves


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The firm enjoyseconomies of

scaleat the beginning

LRAC & LRMC

As the scale of production

further, the firm suffers

diseconomies of scale

LRAC & LRMC


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The production scale (combination of factors) with

the lowest LRAC.

Optimum scale

LRAC curve with

a horizontal region

U-shaped LRAC curve

Optimum scale


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LRMC = slope of LRTC

Slope

=LRMC

=LRAC

Derivation of total

cost curves:

Notice the points

where LRMC = mini.and LRMC = LRAC.


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The Relationship Between Productivity

and Costs

The shapes of the cost curves are mirror-

image reflections of the shapes of the

corresponding productivity curves.


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and Costs

When one is increasing, the other is decreasing.

When one is at a maximum, the other is at aminimum.

h l h d


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Costsperunit

Productiv

ityofworkersatt

hisoutput

$1816

141210

86

42

0 4 8 12 16 20 24

98

76543

21

0 4 8 12 16 20 24

AVC

MC

Output Output

A

AP ofworkers

MPof workers


and Costs

l i hi i l d


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Relationship Between Marginal and

Average Costs

The marginal cost and average cost curves are

related.

When marginal cost exceeds average cost, average

cost must be rising.

When marginal cost is less than average cost,

average cost must be falling.

R l i hi B M i l d


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Average Costs

This relationship explains why marginal cost

curves always intersect average cost curves at

the minimum of the average cost curve.

R l i hi B M i l d


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Average Costs

The position of the marginal cost relative to

average total cost tells us whether average

total cost is rising or falling.

R l i hi B M i l d


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Average Costs

To summarize:

If MC > ATC, then ATC is rising.

If MC = ATC, then ATC is at its low point.

If MC < ATC, then ATC is falling.

R l ti hi B t M i l d


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Average Costs

Marginal and average total cost reflect a general

relationship that also holds for marginal cost and

average variable cost.

If MC > AVC, then AVC is rising.

If MC = AVC, then AVC is at its low point.If MC < AVC, then AVC is falling.



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Average Costs

Average total cost will fall when marginal cost

is above average variable cost, so long as

average variable cost does not rise by more

than average fixed cost falls.



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Average Costs

$90

80

70

6050

4030

2010

0

Quantity of output

Area B

Area A Area CMC

ATC

AVC

1 2 3 4 5 6 7 8 9

Q1

B

AVC

ATC

MCQ0A


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Economies of scalerefer to the property whereby long-run

average total cost falls as the quantity of output increases.

Diseconomies of scalerefer to the property whereby long-runaverage total cost rises as the quantity of output increases.

Constant returns to scalerefers to the property whereby long-run

average total cost stays the same as the quantity of output

increases.


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The goal of firms is to maximize profit, which

equals total revenue minus total cost.

When analyzing a firms behavior, it is

important to include all the opportunity costs

of production.

Some opportunity costs are explicit while

other opportunity costs are implicit.


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A firms costs reflect its production process.

A typical firms production function gets flatter as

the quantity of input increases, displaying the

property of diminishing marginal product. A firms total costs are divided between fixed and

variable costs. Fixed costs do not change when the

firm alters the quantity of output produced;

variable costs do change as the firm alters

quantity of output produced.


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Average total cost is total cost divided by thequantity of output.

Marginal cost is the amount by which total

cost would rise if output were increased byone unit.

The marginal cost always rises with thequantity of output.

Average cost first falls as output increases andthen rises.


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The average-total-cost curve is U-shaped.

The marginal-cost curve always crosses the

average-total-cost curve at the minimum of

ATC.

A firms costs often depend on the time

horizon being considered.

In particular, many costs are fixed in the short

run but variable in the long run.

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Cost Function.ppt