The Theory of Cost

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TOPIC: THEORY OF COST SUBMITTED TO MOHAMMED BELAL UDDIN LECTURER DEPARTMENT OF ACCOUNTING

COMILLA UNIVERSITY

SUBMITTED BY : GROUP NO: NAME OF THE GROUP MEMBERS

1. NAZMUN NAHAR 2. MD ALAMIN CHOWDHURY 3. TANIA AFRIN 4. EMDADUL BARI 5. MARJANA AKTER 6.DILARA BEGUM

ROLL 20 06 10 15 25 41

SUBMISSION DATE: APRIL 29, 2008

Comilla University


Salmanpur, Kotbari Comilla-3500. April 29,2008 Mohammed Belal Uddin Lecturer Department of Accounting (BBA Faculty) Comilla University. Dear Sir, We are submitted the report on “The Theory of Costs” of the subject of “Micro Economics”. Our effort to present the necessary topics about “The Theory of Costs”. We have tried to focus all the relevant secession according to the requirement. We have asked to submit the report and we have tried our level best to make the report factual, informative and logical supported by the economist and other respective. We feel encouraging and optimistic if you take if as a simple person for any mistakes on the report.

Sincerely Yours Nazmun Nahar Leader of ....................... group Department of Accounting Comilla University.


Contents Part-A (1)The (1)The traditional theory of costs (2) Modern Modern theory of costs

Part-B 1.

Definition. i. Total Co Cost. ii. ii. Fine Fined d Cos Cost. t. iii. Variable Variable Cost. Cost. iv. Averag Averagee Cost. Cost. v. v. Marg Margin inal al Cost Cost.. vi. The theory theory of opportun opportunity ity Cost. Cost.

2.

Relatio tionship between AK and AVC.

Part-C 1. 2. 3. 4. 5. 6. 7. curve.

Short-run. Long-run. Disti istin nguis guish h betw betweeen sho shorrt-r t-run & lo long-r ng-ru un. Char Charac acte teri rist stic icss of long long aver averag agee cost cost curv curve. e. Deriv eriva atio tion of of LP LPAC cu curve from from SAR SARC cur curv ve. i. The average fined co cost. ii. The average variable cost. iii. The average total cost. Long Long-ru -run n cos costs ts In moder modern n Mic Micro roec econ onom omic ic theor theory: y: The The ‘L-s ‘L-sha hape ped’ d’ scal scalee

Part-D 1. 2.

Recommendation. Bibliography.


EXECUTIVE SUMMARY

Cost functions are derived functions they are derived from the production function, which describes the available efficient methods of production at any one time. Econom Economic ic theor theory y distin distingui guishe shess betwee between n shortshort-ru run n and long-r long-run un costs. costs. Short-run costs are the costs over a period during which some factors of production are fined the long run costs are the costs over a period long enough to permit the change of all factors of production. In the long-run all factors become variable. The internal economics of scale relate only to the long-run and are built into the shape of the long-run cost curve the external economics affect the position of the cost curves. Both the short-run and the long-run cost curves wil willl shif shiftt if exte extern rnal al econ econom omic icss affe affect ct the the pric prices es of the the fact factor orss or the the production function. The traditional theory of costs is U-shaped some recent developments in the theory of costs which reject the strict U-shape of the short-run cost curves on the grounds that its assumptions are not realistic and question the ‘envelop’ long-run cost curve on the grounds that diseconomies are not a necessary consequence of large-scale operations.


Part-A

1.

The traditional theory of costs: Traditional theory distinguishes between the short ran and the longrun.

The

factor’s

is

fixed:

usually

capital

equipment

and

entrepreneurship entrepreneurship are considered considered as fixed in the short run. run. The long run is period over which all factors become variable. 2.

Modern theory of costs: The The U-sh U-shap aped ed cost cost curv curves es of the the trad tradit itio iona nall theo theory ry have have be been en questioned by various writers both on theoretical a priori and on empirical grounds. As early as 1939 George Stigler suggested that the short-run average variable cost has a flat stretch over a range of output output which which reflec reflects ts the facts facts in their their produc productiv tivee capac capacity ity.. The reasons in detail by various economists. The shape of the long-run cost curve has attracted greater attention in economic literature, due probably to the serious policy implications of the economics of large scale production. Like, the traditional theory, modern microeconomics distinguishes between short-run and long-run costs.


PART-B Total Total cost: cost: Total Total cost cost repres represent entss the lowest lowest total total expens expensee needed needed to produce each level of output. Total cost

=

Fixed cost + Variable cost

Te

=

Fe + Vc.

Fixed cost

:

Fixed co cost is is th that co cost wh which do does no not va vary wi with th the le level

1.

Salaries of administrative staff.

2.

Depreciation on machinery.

3.

Expe Expens nsee for for buil buildi ding ng depr deprec ecia iati tion on and and rep repai air. r.

of output. e.g.

Y

cost Total fixed cost

O

X

output Variable cost: Variable cost is the cost which varies with the level of output. e.g. e.g.:: I) Row Row mate materi rial als. s. ii) Direct labor. iii) Running expense of fixed capital. Y total variable cost

O


Y

TC E p

c

TFC S

O

X

At Point C, FC = Oc, Vc = O ∴ TC = FD + FD = FD + DC = FE. Marginal cost: Marginal cost is the additional cost resulting in increasing output by one unit produced. Again, the changes in total cost due to the change in output. MC =

dc dq

Average cost : Average cost is the per unit cost of output.

AC

TC

= =

AFC = AVC = ATC/TC=

Tc

=

Q

TFC + TVC TFC output TVC output

TFC

+

TVC

output

Total

cos

output

t


Unit 1

FC 10

Output 50

AFC 1 5

2

10

100

1 10

3

10

150

1 15

4

10

200

1 20

Y Y

TVC

c b

cost

a AFC O Here,

X O AVC at a

=

AVC at b

=

AVC at d

=

ac oc bD oD dE

oE

output

X


The Relationship between ATC and AVC Y AVC

ATC

A

AFC O

X X1

X2

The AVE is a part of ATC Given: ATC = AFC + AVC Both AVC and ATC are U-shaped reflecting the law of variable proportions. Howe Howeve ver, r, the the mini minimu mum m poin pointt of the the ATC ATC occu occurs rs to the the righ rightt of the the maximum point of the AVC. This his is due due to the the fact act that that ATC incl inclu udes des AFC and the the latt latteer fal falls continuously with increases in output. After the AVC has reached its lowest point and starts rising, its rise is over certain range offset by the fall in the AFC, so that the ATC continuous to fail (over that range). Despite the increase in AVC. However, the rise in AVC eventually becomes greater the AVC approaches the ATC asymptotically as x increases. The minimum AVC is reached at x1 while the ATC is at its minimum at x2. Between x1 and x2 the fall in APC more than offsets the rise in AVC so that the ATC continuous to fall. Beyond x2 the increase in AVC is not offset by the fall in AFC.


The theory of opportunity cost

Opportunity cost: cost: According to this doctrine (opportunity cost) the cost of producing one commodity is used in their best alternative uses.

e.g.

----- Tk.10,000.00 ------

Investment in bond = Tk. 100 interest Deposit in Bank = Tk.90.00 interest.

Opportunity gain: When the benefit acquired from the current employment of resources is greater than benefit receipts from its best alternative use that there is an opportunity gain.

Opportunity loss: When the benefit acquired from the current employment of resources is than than be bene nefi fitt rece receip ipts ts from from its its be best st alte altern rnat ativ ivee use use that that ther theree is an opportunity loss.


Distinguish between long-run and short-run are given below:

Short-run I)

ii)

iii) iv) v)

It is is a pr production si situation whe when n at least ast one of the the inputs used in production is fixed. i.e. the producer can’t increase the amount of such inputs to increase production even when market market conditions conditions required required that additional output to be produced. In short-run plant size is usua usuall lly y cons consid ider ered ed as the the fixed input. Law of variable proportion is applicable in short-run. The expansion of output with one factor at least constant.

Long-run I)

It is a production situation when all the factors of production are variable.

ii) ii)

i.e i.e. the the pro produc ducer can inc increase ease any of the inputs to increase production is required.

iii) iii)

Sinc Sincee all fac factor tors are are varia ariab ble in long long-r -run un,, ther theree is fixe fixed d cost. Law of return to scale is applicable in long-run. Chang hangee in in ou output tput as all all fac facto torrs changes by the same proportion.

iv) v) v)


Characteristics Characteristics of long-run average cost curve: 1.

U-shaped: U-shaped : Long Long-r -run un aver averag agee cost cost curv curvee is usu usually ally U-sh U-shap aped ed.. Because at the beginning of production we get economics scale and afte afterr a cert certai ain n poin pointt we get get dise diseco cono nomi mies es scal scalee whic which h make makess ushaped.

2.

Envelop curve: curve: Long-run average cost curve is an envelop curve because it consists of all the short-run curve.

3.

Long Long-r -run un ave avera rage ge cos costt curv curvee is tang tangen entt to the the law law poi point nt of of shor short-r t-run un curve. Only at the law point of long-run average cost curve is E.

4.

Optimum scale of plant plant:: The law point of long-run average cost curve shows optimum scale of plant. Because this point shows the lowest average possible. Before and after this point average cost is minimum.

5.

All points of long-run average cost curve shows least cost of producing a given level of output. So, that, ATC rises. Y SAC2 SAC1 COST

X O OUTPUT

SAC3


Derivation of LRAC curve from SRAC curve: In the long-run all factors are assumed to become variable. We said that the long-run cost curve is a planning curve, in the sense that it is a guide to the entrepreneur entrepreneur in this decision to plant the future expansion of his output. The long-run average cost curve is derived from short-run cost curves. Each point of the LAC corresponds to a point on a short-run cost curve, which is tangent to the LAC at that point. The derivation of LRAC curve from SRAC curve are discussed below in detail: Assure: as a first approximation, that the available technology to the firm at a particular point of time includes three methods of production, each with a different plant size: A small plant, medium plant and large plant. The small plant operates with costs denoted by a curve SAC1, the medium size plant operates with the costs on SAC2 and the large plant size gives rise to the cost shown on SAC3. It the firm plans to produce output x1, it will choose the small plant, if it plan planss to prod produc ucee x2, x2, it will will choo choose se the the me mediu dium m plan plant. t. If it wish wishes es to produces x3 it will choose the large-size plant. It the firm starts with the small plant and its demand gradually increases, it will produce at lower costs (up to level x1). Beyond that point costs start increasing. If its demand reaches the level x1. the firm can either continue to produce with the small plant or it can install the medium size plant.


The decision at this point depends not on costs but the expectations about its future demand it the firm expects that the demand will expand further than x1” it will install the medium plant, because with this plant outputs larger than x2’ are produced produced with a lower cost. Similar Similar considerations hold for the decision of the firm when it reaches the level x2’. If it expects its demand to stay constant at this levels the firm will not install the larger plant, given that it insulates a larger inquestment which s profitable only it demand expands beyond x2’. For example, the level of output x3 is produced at a cost c3. With the larger plant, while it costs c2’ if produced with the medium size plant.

Average fixed cost: This is the cost of indirect factors such as: 1. 2. 3. 4. 5. 6.

Sala Salary ry & oth other er expe expens nses es of admi admini nist stra rati tive ve staf staff. f. Sal Salary ary of wond wondeers who are fix fixed to paid. aid. The were & tear of machinery. The expens penses es of ma mainten ntenan ance ce of buildi ilding ngs. s. The expens penses es of ma mainten ntenan ance ce of land on Whic hich the the pla plant is ins install talleed and and oper opera ates tes.

The business man will choose the size of plant which will allow him to produce level of output more flexibility & efficiently. The plant will have a capaci capacity ty larger larger than than the “expe “expecte cted d avera average” ge” level level,, this is calle called d reser reserve ve capacity. The does it for various reasons. Such as:

© © © © © ©

To meet seasonal & cy........ fluctuation. To comply with the increase demand so that It will not so rival. To comply with future growth. To adjust with the technology. To be more flexible in production.


In summary the businessman will not necessarily choose the plant which will give him today the lowest cost, but rather than equipment which will allow him the greatest possible flexibility. C

A

B

COST

OX

X XA

XB

OUTPUT Under these conditions the AFC curve is shown in the graph. The firm has some “Largest “Largest capacity” units units of machinery which sets an absolute limit to the short run expansion of output. The firm has also small unit machinery which sets a limit to expansion to boundary A. If we shift in short-run to expansion of output we have to pay more cost either by paying over time to direct labor for for working longer longer hours on by buying some some additional small plant. So AFC curve shifts upwards and starts falling again.


Average variable cost cost::

© © ©

Direct labor which karris with output. Raw materials. Running expenses of machinery. machinery.

C MC savc COST MC

O

SAVC=MC

OUTPUT

X

In modern theory the SAVC has a source-type shape. It is broadly U shaped but has a flat stretch over a range of output. It is occurred due to reserve capacity. Over this stretch the SAVC is equal to the MC. These both are constant per constant per unit of output. To the left of the stretch, MC lies below the SAVC and opposite to the right of that. The falling close to the better utilization of the fixed factor & increasing skill and productivity of the variable factor. The increasing part of SAVC reflects reduction in labour productivity due to the longer house of work, increasing overtime, the


wastes of material and more frequent breakdown of machinery. Reserve capacity makes it possible to have constant SAVC with a certain range of output.

Average total cost cost:: The average total cost is obtained by adding the average fixed cost and average variable costs at each level of output. The ATC is shown in the figure. The ATC curve falls continuously up to the level output x4 at which the reserve capacity is exhausted. Beyond that level ATC will start rising. The MC will interest the average total cost curve at its minimum point which occurs to the right of the level of output x4 at which the flat stretch of the AVC ends.


Long run costs in modern microeconomic theory: The L-Shaped scale curve These are distinguished into production costs and marginal costs. all costs are variable in long run and they give rise to a long-run cost curve which is roughly L-shaped. The fall continuously with increases in output. At very large scale of output marginal cost may rise. but the fall in production costs more than offsets the increase in the marginal costs, so that the total LAC falls with increases in scale. Production Costs: Production costs fall steeply to begin with and then gradually as the scale as the production production increas increases. es. The L-shape L-shape of the production production cost cost curve is explai explained ned by the techni technical cal econom economics ics of large large scale scale produc productio tion. n. Initia Initially lly these economics are substantial but after a certain level of output is reached all or most of these economics are attained and the firm is said to have reached the minimum optimal scale, given the technology of the industry. If new techniques are invented for larger scales of output, they must be cheaper to operate. but even with the existing known known techniques some economics economics can always be achieved at larger outputs : (a) economies from further decentralization decentralization and improvement in skills. skills. (b) lower repairs costs may be attained attained if the firm reaches a certain size. (c) the firm, especially if it is is multi-product, may well undertake undertake itself the produ producti ction on of some some of the materials materials or equipm equipment ent which it needs needs instead of buying them from other firms. Marginal Cost: Production cost fall smoothly at very large scales, while managerial costs rise only slowly at very large scales. Modern theorists seem to accept that the fall in technical technical costs more than offsets offsets costs more than offsets the probable probable rise of managerial costs, so that the LRAC curve fall smoothly or remains constant at very large scales of output. we may draw the Lac implied implied by the modern theory theory of costs as follows. follows. For each short run period we obtain the SRAC which includes production costs, administration costs, other fixed costs and an allowance for normal profit. Assume that we have a technology with four plant business, with costs falling as size increases. we said that in business practice it is customary to consider that a plant is used normally when it operates at a level between two thirds and three quarters of capacity.


C

C

LAC

LAC=LMC LMC

O

minimum optimum level LAC X O

X

Following this procedure, and assuming that the typical load factor of each plant plant is two thirds thirds of its full capac capacity ity,, we may draw draw the LAC curve curve by joining the points on the SATC curves corresponding to the two thirds of the full capacity capacity of each plant size. If we assume that there is a large number number of available plant sizes the LAC curve will be continuous. The characteristic of of this LAC curve is that (a) it does not turn up at very large scales of output; (B)it is not the envelope of the SATC curves, but rather intersects them(at the level of output defined by the typical load factor of each plant). If, as some writers believe, the LAC falls continuously (though smoothly at very large scales of output), the LMC will lie below the LAC at all scales. If there is a minimum optimal scale of plant at which all possible scale economics are reaped(as Bain and other writers have suggested), beyond that scale the LAC rema remain inss cons consta tant nt.. In this this case case the the LMC LMC lies lies belo below w the the LAC LAC unti untill the the minimum optimal scale is reached and coincides with the LAC beyond the level of output.

The Theory of Cost

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