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Chapter 4Cost Theory and Analysis

Costs depend on Firm’s production function and Market’s inputs’ supply function.Given the relationship between combinations of inputs and the level of Q, and the input prices the costs associated with different levels of Q can be determined.Costs of production vary due to the variations in level of Q and changes in factor prices.

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SignificanceCost of Production is the basis of Product Pricing Decisions.Resource Allocation decisions are based on the basis of analysis of cost.Decisions to add a new product is based on the basis of comparing additional revenues to the additional costs.Decisions on capital investment are made by comparing the rate of return on investment with the opportunity cost of the funds.

For non-profit sector (government agencies), decisions are based on the principle : value of benefits exceeds the cost of the project.

Cost FunctionFirm’s cost function examines the relationbetween a firm’s costs of production and its volume of output. To determine the cost of producing certain level of output – 1. quantities of various inputs 2. prices of inputs are necessary.

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Cost function can be derived from production function by adding information about factor prices.C = f (Q, P1, I1, P2, I2, ……..Pn, In)C = Cost of ProductionQ = Level of OutputP1, P2 …= Prices of various factorsI1, I2… = Quantities of factor inputs 1, 2, etc.

If L and K are the amounts of the factors of production and Q is the level of output, thenL = f1 (Q) and K = f2 (Q).Total cost for producing the output level Q is C = (L X PL ) + (K X PK ) orC = PL X f1 (Q) + PK X f2 (Q) orC = f (Q).Since PL and PK are constant, C is only a function of Q.

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Total Cost (TC) is an increasing function of output.An increase in input price, would lead to an increase in the cost of production.The relationship between TC and Q though is unique in direction, is varying in terms of magnitude.

Types of CostEconomic Cost: Payments made by a firm to all the factors (hired + self owned) used in the production.

Explicit Cost: Payments made to the factors hired outside the control of the firm.Known as out-of-pocket costs.Implicit Cost: Payments made to the self-owned resources used in production.Also known as opportunity cost, book cost or non-cash costs.Opportunity Cost: Value of resource in its next best use, i.e., if it were not being used for the present purpose.Value of the next best alternative that must be sacrificed or foregone.

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Direct Cost: Costs which can be directly attributed to production of a given product.raw material, labor and machine time involved in the production of each unit.Indirect Cost: Costs that can not easily and accurately be separated and attributed to individual units of production, except on arbitrary basis.Stationery and other administrative expenses, depreciation of plant and buildings.Direct (Separable) and Indirect (Common Costs).

In a multi-product firm, raw material cost is separable product-wise but managementcost is not separable.Sunk Costs: Expenditures that have been made in the past or that must be paid in future as a part of a contractual agreement.Such costs are invariance with the decision, hence are irrelevant for decision making.Consultant fee, Cost of inventory, future rental payments that must be paid in future as a part of a contractual agreement.

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Marginal Cost: Change in TC associated with a one-unit change in Q.Incremental Cost: Total additional costs of implementing a managerial decision which vary with the decision.Referred to as relevant costs, incurred as a result of the decision under consideration.Cost associated with adding a new product line, acquiring a major competitor etc.

Historical Cost: Actual cost incurred at the time the asset was acquired.Price at which that asset was acquired originally in the past.Replacement Cost: Price that would be required to be paid if a new asset is to replace the old one.Two costs (HC & RC) differ due to price variations over time.

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For managerial decisions HC may not be appropriate.Private Costs: Costs incurred by an individual firm engaged in relevant activity. Includes both explicit and implicit costs that a firm incurs in production.Social Costs: Costs incurred by the society as a whole.External costs passed on to persons (society at large) not involved in the activity in any direct way.

True picture of real or social costs of Q would be obtained, if external costs will be included in the production costs.Ignoring external costs may lead to an inefficient allocation of resources in society.Fixed Costs: Costs in total which do not vary with changes in output. TFC ≠ f (Q).Must be incurred even if output level is zero.Independent of the level of Q of the firm.Variable Costs: Costs which vary with the level of output. TVC = f (Q).

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LR Costs: Refer to costs across all possible production capacities.Costs when all factors of production are subject to change. In LR all costs are variable costs.SR Costs: Stand for costs within a given production capacity.Costs when at least one of the factors of production is fixed.Total Costs: Sum total of explicit and implicit costs. In the SR, STC = TFC + TVC.

Average Cost: Stands for per unit cost. Calculated as TC / Q. In SR, SAC = AFC + AVC.TC is useful for break-even & profit analysis.AC is relevant for estimating profit margin per unit of sales.MC is significant in deciding the optimum level of output.

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Class Assignment 1.A furniture shop makes 100 chairs per month and sells them at $ 15 per piece. The expenses on rent of the shop, cost of material are worth $ 500, the wage bills stand at $ 240 and electricity bill is $ 50 per month. The shop has invested $ 5000 of which $2500 is the own fund and the remaining $2500 is a loan from a bank at the interest rate of 18% per annum. Assuming imputed costs of owners’ time, own shop and own savings of $ 2500 for the month are $300, $100 and $ 25 respectively.Q. Calculate the explicit and implicit costs and find out the Business profit and Economic profit.

SR Cost-Output RelationshipAssuming two inputs L and K, Total Cost,TC = (L X PL) + (K X PK)If L is the variable input & K is the fixed input, then TVC = L X PL and TFC = K X PK

AVC = TVC / QATC = TC / Q, TFC / Q + TVC / Q, AFC + AVCMC = ∆ TC / ∆QIf factor prices PK = 50$, PL = 30$ and K = 2, the various calculations of TFC, TVC, TC, AFC, AVC, AC and MC are as follows:

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30.04.22.91.3310210100110.4737

7.53.92.51.4280180100412.0726

3.33.72.21.5250150100913.6685

2.73.22.01.72201201001114.8594

1.84.01.92.1190901001716.0483

1.95.11.93.2160601001615.5312

2.08.72.06.7130301001515.0151

----1000100--00

MCACAVCAFCTCTVCTFCMPAPQL

SR Production Function & Cost Output Relationship

AFC falls continuously as output expands because TFC is invariance to Q.AP and AVC as well as MP and MC are inversely related.AVC first falls as Q expands, after a certain point the relationship is reversed.The shape of AVC is due to the Law of Diminishing Returns.AC first falls as Q increases but again after a certain point the trend is reversed. Since ATC = AFC + AVC, the shape of ATC follows from those of AFC and AVC.

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Trend of MC is derived from MP. Influenced by the Law of Variable Returns.TFC curve is horizontal.TVC curve starts from origin. TC curve starts from a point above the origin and then follows the shape of the TVC curve.TC and TVC curves are parallel.MC curve passes through the minimumpoints of both the AVC and ATC curves.

Fixed cost

Total cost

Cost

Output

TFC

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Variable cost

Cost

Output

STFC

STFC

0 Q

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STVCSTVC

STC

STVC

STFC

Q0

STFC, STVC, STC

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0

P E

F

Output

AFC

AFC

R

Q SSS

S

AVC

Q

AVC

O

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MC

AVC

AP

MP

Maximum MPAnd Minimum MC

Maximum APAnd Minimum AVC

output

Cost

AP & MP

Labor

Relationships between Product Curves and Cost Curves

Relationships between Product Curves and Cost Curves

Over the range of rising MP, MC is falling.When MP is at maximum, MC is at minimum.Over the range of rising AP, AVC is falling.When AP is at maximum, AVC is minimum.Over the range of Diminishing Marginal Product, MC is rising.Over the range of Diminishing Average Product, AVC is rising.

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AC

AVC

MC

AC & MC increase as the physicallimit to plant capacity is

approached

Point of Diminishing Returns

Output

Cost

SR Average and Marginal Cost Curves

A

SR Average Cost Curves are U- shaped.MC curve intersects both the AVC and ACcurves at their minimum points.The point of Diminishing Returns corresponds to point A at which MC begins to increase.Class Assignment 2. If the total cost function of a firm TC = 120 + 50Q – 10Q2 + Q3 , find out the various cost as given below by putting the value of Q from 0 to 10.

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910

876543210

MCACAVCAFCTCTVCTFCQ

Cost –output Relationships

LR Cost-Output RelationshipIn LR being factors are not fixed, all LR costs are variable.In LR, the firm is concerned with optimum firm size whereas SR is concerned with optimum Q within a given plant size.In LR firms change the scale of their operations by varying all inputs.Given factor prices and specific production function, the least-costs associated with various levels of Q, yields LR TC schedule.

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2.001.08350325

1.001.00300300

0.401.00250250

0.671.60200125

3.003.0015050

---0

LMCLACLTCOutput (Q)

LR Cost-Output Relationship

AB

LTC

Q

LTC

LAC

LMC

Q

LMCLAC

Economies of scale

Diseconomies of scale

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The LTC curve is first concave & then convex as looked from the output axis.At the point of inflexion on LTC curve (A),LMC takes the minimum value.At point of kink on LTC curve (B), LACassumes the minimum value.LAC is the least when LMC = LAC.LAC curve is falling when LMC < LAC.LAC curve is rising when LMC > LAC.

In the presence of Returns to scale & fixed input prices:1. When Returns to scale are increasing, LTC increases as Q increases but at a less than proportionate rate.2. When Returns to scale are constant, LTC & Q move in the same direction and same proportion.

3. When returns to scale are decreasing, LTCincreases at a faster rate than does Q.

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LAC Curve: The Envelope CurveLAC curve envelopes all SAC curves, for the LR cost can not exceed the SR cost.LAC curve is known as Planning curve as it is a guide to the producer to plan for the future expansion of Q.LAC is the locus of the tangency points of the SAC curves. LAC curve is U-shaped as SAC curves are but it is more flatter than the SAC curves.

Q

LAC

E

N

SAC 1 SAC 2 SAC 3

0

LAC

A B

N1 N2 N3

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The points of tangency between SAC curves and LAC represent the least cost way of producing particular Q.As SAC1 is tangent to LAC curve at point A, it indicates the least cost output point. Point B depicts the lowest AC along SAC1.Decision to produce output level at N2 is possible by choosing at point B on the first plant to minimize AC.The firm could reduce AC further with a larger plant associated with another SAC.

Optimum output in the LR is at ON level.A firm’s LAC is the lowest cost per unit at which the firm can produce a given level of output by varying all the factors.

Economies and Diseconomies of ScaleEconomies of scale mean the reductions in per unit cost of production (LAC) when a firm expands its output.Diseconomies of scale refer the increase in AC as output goes up.

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Economies of scale are two types: 1. Real Economies (Internal Economies) 2. Pecuniary Economies (Ext. Economies)Internal economies accrue to a firm by expanding the scale of production to the optimum point.Helps in better use of underutilized inputs.Associated with a reduction in inputs used-raw materials, labor, capital etc. Internal economies are broadly divided into:

1. Production Economies2. Selling and Marketing Economies3. Managerial Economies4. Transport and Storage Economies

Production Economies: a. Labor economies:Labor economies are achieved as the scale of output increases. Division of Labor & Specialization.Time saving and Automation

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b. Technical economies:Are associated with the ‘fixed capital’.Arise from the use of better plant, machinery, equipment & techniques of production.Specialization and indivisibilities of capital.Economies of superior techniques.Economies of the use of by-products.

c. Inventory economies:To meet the random changes in the input & output sides of the operation of the firm.Inventories in raw materialsInventories in ready products

Selling and Marketing Economies:Associated mostly with the distribution of the product of a firm.Advertising economiesLarge-scale promotionExclusive dealers with obligation for maintaining service departmentsModel-change economies Managerial Economies:Concerned with both the production and distribution activities of the firm.

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Specialization of ManagementDecentralization of Decision MakingMechanization of managerial functionTransport and Storage Economies:Concerned partly with production side and partly on the selling side of the firm.Causes of Internal economies:Indivisibilities: Larger scale of production makes better use of certain factors of production which can not be used in parts.

Specialization: Large scale of production makes it possible to introduce better division of labor leads to more units of output at a lesser average cost.Pecuniary Economies (External Economies):These economies are common to all the firms in an industryLower prices of its raw materials, bought at special discounts from its suppliers.Lower costs of external finance.Lower advertising prices to larger firms for large scale advertisement.

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Transport rates are often lower if the amounts of goods transported are large.Causes of External economies:Localization of Industries: Concentration of firms at a particular place results in endowing in certain advantages to the firms. Specialization: Growth of an area induces the emergence of firms supplying specialized services at a lower cost. Diseconomies of scale: Beyond a certain point, firm compels to produce more output at an increasing cost per unit.

Internal Diseconomies are:Limits of the EntrepreneurManagerial hierarchyReduction in efficiencyExternal Diseconomies are:High demand for specialized laborRise in rental cost due to over-concentration Trade unions

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o Q

AC

Increasing

returns to scale Constant returnsto scale

Decreasing returns to scale

Q1 Q 2

Economies of scale

Constant cost

Diseconomies of scale

LAC

Economies of ScopeRefers to reduction in production costs by producing a set of different goods together rather than separately.Efficiencies arise when a firm produces more than one product.Exist when the TC of producing given quantities of two goods in the same firm is less than producing those quantities in two single-product firms.

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Measured in terms of saving in cost (SC) of production.Saving in cost is measured as

C(Q1) + C(Q2) – C(Q1,Q2) SC = ------------------------------------

C(Q1,Q2) C(Q1), C(Q2) represents the cost of producing output Q1,Q2 respectively and C(Q1,Q2) the joint cost of producing both outputs.With economies of scope, the joint cost is less than the sum of individual costs, SC > 0

With diseconomies of scope, SC is negative.Larger the value of SC, the greater the economies of scope.Class Assignment:3A firm will produce X at $ 50,000 per 1000 units and Y at $ 30,000 per 1000 units if it produces only one of these products. However 1000 units of each type of X and Y can be produced for a total of $ 70,000 if both are produced together. Find out the saving in cost.