Unit 2 c 2

COST

(COST MEANS SACRIFICE)

MEANING - COST

“ Cost is a sacrifice or foregoing that has occurred or has potential to occur in future, measured in monetary terms”

• Cost results in current or future decrease in cash or other assets or a current or future increase in liability

DETERMINANTS OF COST

• Cost is determined by various factors and each of these has significant implications for cost decisions.

• An increase in any of these will affect cost pattern.

• Important determinant – Price(uncontrollable –largely determined by external

environment) – Marginal efficiency and productivity – Technology – Level of out put.

MATHEMATICAL EXPRESSION- COST

C= F( Q , T , P)

• Where

– C= cost

– Q= out put

– T= technology

– P= price

• Cost are differentiated according to their purpose , type of product and time.

TYPES OF COSTS

• There may be different types of costs incurred by a firm under different circumstances.

• Cost of a firm may include money or may not be measurable in money terms.

• Cost is a function of output in economic theory.

• A managerial economist’s concept of cost does not necessarily coincide with that of accountants.

TYPES OF COST

• Actual Costs / Acquisition / outlay : It means the actual expenditure incurred for acquiring or producing a good or service. These are generally recorded in the books of accounts. Eg. Wages paid, cost of materials purchased, interest paid, etc.

• Opportunity Cost / Alternative Cost: Revenue forgone by not making the best alternative use or opportunities.

• Imputed Cost / Implicit cost: They are the costs which are not actually incurred but would have been incurred in the absence of employment of self-owned factors. These are unrecognized by the accounting systems. Eg. Rent of own building, Salary for Entrepreneur, etc.

• Explicit cost / Paid out costs: Those expenses which are actually paid by the firm. Appears in the accounting books.

• Sunk Costs / Non-avoidable / Non escapable: They are not altered by a change in quantity and cannot be recovered. All the past expenses are sunk costs Eg Depreciation, interest, machineries not in use.

• Incremental / Differential cost ( Avoidable, escapable or Differential): It is the additional cost due to a change in level or nature of business activity.

• Out-of-Pocket costs: These are expenses which are current cash payments to the outsiders. (All Explicit costs)

• Book Costs: These are business costs which do not involve any cash payments but for them a provision is made in the books of account. Eg. Depreciation, Implicit cost.

• Accounting cost / Past Cost: How much expenditure has already been incurred on a particular process or on production as such.

• Economic cost / Future cost: Cost relate to future.

• Direct costs / Traceable / Assignable: These costs have direct relationship with a unit of operation.

• Indirect / Non-traceable / Non assignable: These costs cannot be easily & definitely traced to a plant or department.

• Historical Cost / Original cost: It states the

cost of plant, equipment and materials at the price paid originally for them.

• Replacement cost: It states the cost that the firm would have to incur if it wants to replace or acquire the same assets now.

• Controllable costs: Costs which are capable of being controlled or regulated.

• Non-Controllable cost: costs which cannot be subjected to administrative control and supervision. Eg. Depreciation, Obsolescence.

• Private costs: Micro level. Costs incurred by an individual or a firm for its business activity.

• Social costs: Macro level. Total cost s to the society on account of production of a good.

• Shutdown Costs: Those costs incurred when firm temporarily stops it operations.

• Abandonment Costs: Costs incurred when the firm is retiring altogether.

• Short run costs: a period in which the supply of at least one of the inputs cannot be changed by the firm. Inputs are fixed.

• Long run costs: Period in which all inputs can be carried as desired.

• Fixed Cost: Part of total cost of the firm which does not vary with output.

• Variable cost: Part of total cost that are directly dependent on the volume of output or service.

• Total cost: It is money value of the total resources required for production of goods and services by the firm. TC = FC + VC

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

– AC = TC / n

– n = number of unit

• Marginal cost: It is the change in total cost due to unit change in out put

)( 1 nnn TCTCMC

COSTS IN SHORT RUN

• Classification of costs is on the basis of time

– Short run cost

– Long run cost

• The short run is a time period where some factors of production remain fixed and only few are variable.

– Fixed inputs – land ,machine and technology

– Variable inputs – labor and raw material

Contd…

• Therefore in short run we divide costs in two broad categories

– Fixed costs

• Costs on fixed inputs

– Variable costs

• Costs on variable inputs

TOTAL COSTS FUNCTIONS AND CURVES FOR SHORT RUN

• As we discussed short run cost have two components

• Fixed cost – This cost do not vary with output

– Cost incurred in plant, machinery fitting , equipments, land etc.

– Any change in volume of output does not depends upon fixed cost

– The shape of the TFC(TOTAL FIXED COST) curve is straight line from origin parallel to quantity axis.

GRAPH - TFC

TFC

X AXIS – QUANTITY Y AXIS – COST

• Variable cost

– These are costs that vary with output and are incurred in getting more and more inputs.

– Variable costs are equal to zero if there is no out put

– Cost of raw materials , wages are called variable cost.

– TVC is an inverse S shaped upward sloping curve starting from origin.

GRAPH - TVC

X AXIS – QUANTITY Y AXIS – COST

GRAPH INFERENCE

• The shape of curve determined by law of variable proportions.

• According to this law as more and more units of the variable factor are added in production its productivity goes on increasing.

• This lead to fall in per unit cost in the beginning. if the variable input is increased beyond certain level its marginal productivity starts diminishing.

• So TVC increases at increasing rate.

GRAPH – TOTAL COST

TC

TVC

TFC

X AXIS – QUANTITY Y AXIS – COST

TOTAL COST = TFC + TVC

SHORT RUN – AVERAGE AND MARGINAL COST

• AVERAGE COST

– Average cost is cost per unit of out put

– We can derive AFC (average fixed cost) AVC( average variable cost) and AC (average cost) from total fixed , total variable and total costs respectively.

– AFC is fixed cost per unit of output and this is equal to the ratio of TFC and units of output

• AFC = TFC / NUMBER OF UNITS OF OUT PUT

– AVC is variable cost per unit of out put and this is equal to the ratio of TVC and units of output

• AVC = TVC / NUMBER OF UNITS OF OUT PUT

– AC is total cost per unit of out put

• AC = TC /NUMBER UNITS OF OUTPUT

• MARGINAL COST

– MC is the change in total cost due to unit change in out put

– Rate of change in total cost.

)( 1 nnn TCTCMC

MC

AC

AVC

AFC

X AXIS – QUANTITY Y AXIS – COST

AVERAGE AND MARGINAL COST CURVES- SHORT RUN

• The AVC and AC curve are both U shaped. – This explained by law of diminishing returns.

– Cost decline when there are increasing returns(output)

• AC being the sum of AFC and AVC at each level of output lies above both AFC and AVC curve.

• Initially AC falls with increase in out put reaches minimum and then increases.

AVC , AFC AND AC GRAPH - INFERENCE

..contd

• When both AFC and AVC fall AC also falls.

• AVC soon reaches minimum and start rising .

• While AFC continues to fall.

• How ever the rise in AVC compensate falls in AFC and AVC pulls AC up after reaches a minimum.

MARGINAL COST GRAPH - INFERENCE

• The magnitude of marginal cost is interlinked with changes in average cost.

• When average cost decline MC lies below AC.

• When average costs are constant the MC passes through the minimum points of average cost curves.

• When average cost rise MC curve lies above them.

• AC and AVC fall MC lies below them

• AC and AVC rise MC lies above them.

RELATIONSHIP AMONG CURVES – MATHEMATICALN SUMMARIZATION

• TC = TFC + TVC

• AFC = TFC / Q

• AVC = TVC/ Q

• AC = TC /Q

= (TFC + TVC)/Q

= AFC + AVC

• MC = TC q – TC q-1

= change in total cost (d TC)/ total out put (dQ)

COSTS IN LONG RUN • All cost are variable in the long run since factors

of production – Size of plant

– Machinery and technology are all variable.

• The long run cost function is often referred to as the “planning cost function”

• The long run average cost (LAC) curve is known as the “ planning curve”

• All the cost are variable only the average cost curve is relevant to the firm’s decision making process in the long run.

• Long run cost curve is the composite of many short run cost curves……*

LONG RUN AVERAGE COST (LAC)

• When the plant size and other fixed inputs of the firm increase in the long run the short run cost curves shift to the right.

• We consider in the long run the firm operates with three different plant sizes

– Plant size I , II , III

• It can switch over to a different plant size depending on cost consideration.

…CONTD

• SAC 1 relates to average cost of the firm when the plant size I.

• When the plant size increases to II the corresponding SAC 1 curve is SAC 2 and so on.

• So – Plant size I – SAC I

– Plant size II – SAC II

– Plant size III – SAC III

LAC CURVE

MC1 MC2 MC3

SAC1 SAC2 SAC3

plant size I plant size II plant size III

Q0 Q1 Q2

X AAXIS – QUANTITY Y AXIS –AC,MC

GRAPH- INFERENCE

• As out put increases from Qo to Q1 in the short run the firm can continue to produce along SAC1, utilizing its installed capacity of plant size I.

• Further ahead at an out put level of Q1 this capacity is over worked.

• So it would be the cost effective for the firm to shift to higher plant size say plant size II. – Thus switching from SAC1 to SAC2

• This shift would lower the average cost of the firm.

• The same concept is followed for subsequent output.

…contd • The LAC curve has a scalloping pattern as its

is drawn with three plant sizes only.

• We assumed that the firm operates with only 3 alternative plant sizes.

– But in reality ……………. Multiple such alternatives.

– So in reality it may have multiple SAC also….

• The LAC function is an envelope of the short run cost functions and LAC curves envelopes the SAC curve hence LAC curve is also known as “ envelope curve”

..contd

• The LAC curve is also known as “planning curve”

• According to the entire planning horizon in which the managerial economist can select the most appropriate plant size , given the existing (or expected) level of demand for the product.

LAC - ENVELOPECURVE

SMC1 SMC2

SAC1 SMC2 SAC3

SAC2

Q0 Q1 Q* Q3

X AAXIS – QUANTITY Y AXIS –AC,MC

LONG RUN MARGINAL COST

• Long run marginal cost (LMC) curve joints the points on the short run marginal cost (SMC) curves.

LMC - CURVE

SMC1 SMC2

C

SAC1 SMC2 SAC3

SAC2

A LMC

B

Q0 Q1 Q* Q3

X AAXIS – QUANTITY Y AXIS –AC,MC

GRAPH INFERENCE

• At out put level of Qo. The relevant long run marginal cost is Aqo.

• The LMC curve joins the points A,B,C

• According to assuming sufficient demand the optimum plant size is II.

• So the optimum level of out put is Oq*.

– Where long run and short run marginal cost and average costs are equal.

LAC – DIFFERENT SHAPES

X AAXIS – QUANTITY Y AXIS –AC

LONG RUN TOTAL COST - CURVE

COST LRTC

QUANTITY

GRAPH - INFERENCE

• Once we have the long run average cost of producing an output we can readily derive the long run total cost of output.

• Since total cost is the quantity of output times average cost.

COST OF A MULTIPRODUCT FIRM

• So far we have assumed that the firm produces a single good /service.

• How ever in the real business world many firms produce more than one product.

• A cost of multiproduct firm is differ from costs of single product.

• In order to ascertain the costs of multiproduct form we need to first modify some of the cost concepts.

EXAMPLE

• Take multiproduct firm producing 2 goods – Product 1 and product 2

• For simplicity we assume that the firm uses the same capital requirements in producing the above 2 goods.

• So TC of production would be the sum of fixed cost (TFC) and total variable cost (TVC)- C1 and C2 of producing both the product times the quantities of 2 goods be Q1 and Q2 – TC = TFC + C1 Q1 + C2 Q2

…. CONT

– WEIGHTED AVERAGE COST OF MULTIPRODUCT FIRM

– AC w(Q) = F + C1 (X1 Q) + C2 (X2 Q)

----------------------------------

Q

Where

X1 and X2 are proportions in which products 1 and 2 are produced

Q is the total out put.

COSTS OF JOIN PRODUCTS

• There are certain goods which are produced jointly – That is if one good is produced the other will

automatically be produced.

– Example = normally found in agriculture , minerals etc

• Costing of such products is different from traditional costs method.

• Two or more products undergo the same production process up to split off point

…contd

• Split off point

– The beyond which joint products acquire separate identities and one or more of the products may undergo additional processing there from.

– Example

• Cream and milk

• Oil and gas

JOINT PRODUCTS – COST CONCEPTS

• In this there would be common costs which cannot be identified with a single joint product.

• The join products incur common costs until they reach split off point.

• After the split off point the product incurred the separate costs.

• The allocation of common costs are according to

– Physical measure

– Sales value

LINKAGE BETWEEN COST, REVENUE AND OUTPUT

• TOTAL REVENUE (TR) – Total revenue is the total amount of money received

by a firm from goods sold during certain period of time.

– TR = Q X P • Q – QUANTITY P – PRICE

• AVERAGE REVENUE (AR) – Average revenue is the revenue earned per unit of

output sold. – It is equal to the ratio of TR and out put – AR = TR / Q = (Q x P) / Q – AR = P

…CONTD

• MARGINAL REVENUE (MR)

– Marginal revenue is the revenue a firm gains in producing one additional unit of a commodity

– It is calculated by determining the difference between the total revenues earned before and after increase in production

– MRq = TRq - TR q-1

= d TR / d Q

TR AND MR - RELATIONSHIP

MR is slope of TR CURVE

TR

MR

X AAXIS – QUANTITY Y AXIS –PRICE ,

REVENUE

GRAPH - INFERENCE

• The graph shows the relationship between total revenue and marginal revenue.

• TR will be zero when nothing is sold.

• The shape of TR curve is inverted U starts from origin.

• After it reaches maximum dipping to X axis.

• Rise in total revenue curve is the change in total revenue with rise in level of output – So therefore we can say MR is the slope of TR curve

MR AND AR – RELATION SHIP

• AR curve can have the following positions

– Straight line

– Convex to the origin

– Concave to the origin

PANEL A PANEL B PANEL C

AR AR AR

MR MR MR

X AAXIS – QUANTITY Y AXIS –MR

GRAPH INFERENCE • PANEL A

– When AR is a straight line MR will be lie midway to AR

• PANEL B

– When AR is convex to the origin MR will lie less than midway to AR

• PANEL C

– When AR is concave to the origin MR will lie more than midway to AR

PROFIT MAXIMIZATION

• The profit function shows a range of outputs at which the firm makes positive profits

• Two types of profits – Normal profit

• It is amount of return to the firm which must be earned to keep in that business activity

• It is the part of total cost

– Supernormal profit • Any thing above normal profit is super normal profit

• It is accounting profit occurs when TR > TC

..CONTD

• A firm maximizes profit at the point where MR = MC

• Rules of optimization

– The second order condition of profit maximization requires the slope of MR = slope of MC

BREAK EVEN ANALYSIS

“Break even point is the point where total cost just equals the total revenue it is the no profit and no loss point”

• It is also known as cost volume profit analysis

• It is a first step in planning decision

APPROACHES IN BREAK EVEN ANALYSIS

• Graphical method

• Algebraic method

• Contribution margin

• PV ratio

• Margin of safety.

GRAPHICAL METHOD

TR

PROFIT

TC

E

VC

FC

X AAXIS – QUANTITY Y AXIS – COST

REVEUE

DRAWING -BREAK EVEN GRAPH

• The break even chart assumes constant AVC for a given range of output.

• After point E the firm achieve profit.

• The point E is the break even point.

• The gap between the total costs line and revenue line beyond the break even point represents the level of profit.

• If the gap is such that TC line is above the TR line the area represent loss.

• If the TR line is above TC line the area represent profit

ALGEBRAIC METHOD

• Let us understand the break even analysis algebraically

• Let P be the price of a goods

• Q is the quantity produced

• AVC be the average variable cost

• AFC be the average fixed cost

• Let Q* be the break even output, where total revenue equals total cost.

..contd

• TOTAL REVENUE (TR) = P x Q

• TOTAL COST (TC) = TFC + TVC

= TFC + AVC x Q

• P x Q = TFC + AVC x Q

• (P – AVC) x Q = TFC

Q= TFC/ (P- AVC)

CONTRIBUTION MARGIN

• Contribution margin per unit sales is the difference between price and average variable cost

– CONTRIBUTION MARGIN = P – AVC

• It represents that portion of the price of the commodity produced by the firm that can cover the fixed costs and contribute to profits

PV RATIO

• Profit volume (PV) ratio is the ratio of contribution margin and sales

• It is defined as the ratio of marginal change in profit and marginal change in sales

• PV RATIO = CONTRIBUTION / SALES

• BEP = FC / PV RATIO – FC = FIXED COST

MARGIN OF SAFETY

• Margin of safety

= planned sales – break even sales

LIMITATIONS – BREAK EVEN ANALYSIS

• It does not take into account possible changes in costs over the time period under consideration

• It assumes that whatever is produced is sold

• It does not keep any provision for a changes in selling price.

• It does not allow for changes in market conditions

• It is difficult to find out BEP in service sector.

ECONOMIES OF SCALE

• “Economies” refer to lower costs hence economies of scale would mean lowering of costs of production by way of producing in bulk.

• In simple terms economies of scale refers to the efficiencies associated with large scale of operations.

• When production increases the average cost per unit decreases.

• Economies of scale are extremely important in real world production processes.

TYPES OF ECONOMICS OF SCALE

• INTERNAL ECONOMIES OF SCALE

– Cost per unit depends upon the size of the firm

• EXTERNAL ECONOMIES OF SCALE

– Cost per unit depends upon the size of the industry not the firm.

INTERNAL ECONOMIES • The reason behind the internal economies

– Specialization

• Jobs can be broken down into components/process

• Specialization in particular job

– Greater efficiency of machine

– Managerial economies

• Better supervision, administration, planning & organization

– Financial economies

• Large firms going for large volume of production may able to raise capital from the market with much less difficulties than small firm.

– Production in stages

• Houses all the process in production

EXTERNAL ECONOMIES

• The reason behind external economies

• As an industry grows in size would create various economies for existing firms in the industry

– Technological advancement.

– Easier access to cheaper raw materials.

– Financial institutions in proximity.

– Pool of skilled labors.

DISECONOMIES OF SCALE

• It is a reverse of economies of scale.

• It is refers to decreases in productivity when there are equal increases of all inputs. Assuming that no inputs is fixed.

• Diseconomies may rise if the size of operations become un widely by size. – Coordinating among different work groups and units

may become complex

– Management become less effective and thus indirectly improve costs