Cost Output Relationship; Estimation of Cost and Output

COST-OUTPUT
RELATIONSHIP AND ESTIMATION OF RELATIONSHIP BETWEEN
Submitted By:
Dheeraj Rawal
MBA (1st Year)
Submitted To:
Ms. Sakshi Sharma
Associate Professor

OVERVIEW
• INTRODUCTION
• COST OUTPUT RELATIONSHIP
• ESTIMATION OF COST OUTPUT RELATIONSHIP
• SHORT TERM COST ESTIMATION
• LONG TERM COST ESTIMATION
• PURPOSE OF SHORT AND LONG TERM COST ESTIMATION
• METHODS OF ESTIMATION COST FUNCTION
• PROBLEM IN THE ESTIMATION OF COST

COST-OUTPUT
RELATIONSHIP
Cost can be defined as monetary expenses
that are incurred by an organization for a
specified thing or activity.
Quantity of goods or services produced in a
given time period, by a firm, industry, or
country
The theory of costs deal with the behaviour of costs in relation to change in output.

JOEL
DEAN(ECONOMIST)
In 1936, Joel Dean pioneered the study of cost output behaviour in industry and
depicted that the total cost increase with the output.
Since then a large number of studies have been done in this field.
These studies can be classified into two broad groups
1 Short Run Cost Estimation
2 Long Run Cost Estimation

Estimation of
Cost Output
Relationship
1. Short Run
Cost
Estimation
2. Long Run
Cost
Estimation
 Total Fixed Cost (TFC)
 Total Variable Cost (TVC)
 Total Cost (TC)
 Average Fixed Cost (AFC)
 Average Variable Cost (AVC)
 Average Cost (AC)
 Marginal Cost (MC)
 Long Run Total Cost
 Long Run Average Cost – A
Traditional Approach
 Modern Approach to Long Run
Cost Behaviour: The L Shaped
Scale Curve
 Long Run Marginal Cost

1. SHORT RUN COST ESTIMATION
Expansion in Short Run
 Conceptually, in short run, the quantity of at
least one input is fixed and the other quantities
inputs can be varied.
 In other words, The Short Run is a period which
doesn’t permit alterations in the fixed
equipment and in the size of the organization
 Factors Remains Same : Such as Land,
Machinery.
 Factors Vary with Time : Such as Labor, Capital.
In the short run, the expansion Is done by hiring more labor and increasing capital.
The existing size of the plant or building cannot be increased in case of the short run.

Total Fixed Costs (TFC)
 It refers to the costs that remain fixed in the short
period. These costs do not change with the change
in the level of output.
 Example: Rents, Interest and Salaries.
 Fixed costs have implication even when the
production of an organization is zero.
 Also known as supplementary costs, indirect costs,
overhead costs, historical costs, and unavoidable
costs.
 TFC remains constant with respect to change in the
level of output. Therefore the slope of TFC curve is
a horizontal straight line.
Total Fixed Cost (TFC) is the sum of the short run explicit fixed costs (imply cash payments made
to outsiders for acquiring resources) and implicit costs (refers to cost of self owned resources
that neither take the form of cash outlays nor they appear in the accounting system) incurred by
the entrepreneur.

Total Variable Costs (TVC)
 It refers to the costs that change with the
change in the level of production.
 Example: Raw Material, Hiring Labor,
Electricity.
 If the output is zero, then the variable cost
is also zero.
 These costs are also called prime cost,
direct costs, and avoidable costs.
Total Variable Cost (TVC) is the sum of amounts spent for each of the variable inputs
used.

Total Cost (TC)
 TC changes with the change in level of output as
there is a change in TVC.
 It should be noted that both TVC and TC increase
initially at decreasing rate and then they increase
at increasing rate.
 Here, decreasing rate implies that the rate at
which cost increases with respect to output is less.
 Increasing rate implies the rate at which cost
increases with respect to output is more.
Total Cost (TC) involves the sum of the total fixed costs and total variable costs.
Total Cost = TFC + TVC

Average Fixed Cost (AFC)
 It refers to the per unit fixed costs of
production.
 In other words, AFC implies fixed cost of
production divided by the quantity of output
produced.
 As discussed, TFC is constant as production
increase, thus AFC falls.
 As shown AFC curve as a declining curve,
which never touched the horizontal axis
because fixed cost cannot be zero.
 This curve is known as rectangular hyperbola,
which represents total fixed costs remain sane
at all levels.
Average Fixed Cost = Total Fixed Cost/Output

Average Variable Cost (AVC)
 It refers to the per unit variable costs of
production.
 It implies organization's variable costs divided
by the quantity of output produced.
 Initially, AVC decreases as output increases.
After a certain point of time, AVC increases
with respect to increase in output.
 Thus, it is a U shaped curve.
Average Variable Cost = Total Variable Cost/Output

Average Cost (AC)
 It refers to the total costs of
production per unit of output.
 AC is also equal to the sum total of
AFC and AVC.
 AC curve is also U shaped curve as
average cost initially decreases as
output increases. After a certain point
of time, AC increases as output
increase.
Average Cost = Total Cost/Output

Marginal Cost (MC)
 It refers to the addition to the total
cost for producing an additional
unit of the product.
 MC curve is also a U shaped curve
as marginal cost initially decreases
as output increases and
afterwards, rises as output
increases. This is because TC
increases at decreasing rate and
then increases at increasing rate.
Marginal Cost(MC) = ΔTotal Cost/Output

 Average Costs curve are the sum of AFC and
AVC.
 As output increases, TFC remains fixed, thus
AFC declines.
 Thus, as AC equals to AFC+AVC, AC also
declines as output increases.
 AVC increases steeply after reaching minimum
and this increase in AVC is more than fall in
AFC.
 After that, AC starts rising as output increases.
 Thus, AC curve is U shaped curve.

 At initial stage of production, AC falls when output
increases. AFC falls steeply in the beginning as fixed factors
are used in a better way. The variable factor are used to
assist fixed factors.
 Therefore, AVC falls, which results in the fall of AC.
However, AC will increase after a certain stage as more
variable factors will be used. TVC increases sharply as
output increases; thus AVC also increases. In other words,
variable factors cannot be used in place of fixed factors.
Thus, AVC and AC output increases.
 The relation between AC and MC is discussed as follows:
 When MC falls, AC also falls. The rate of fall in MC is more than the AC as it is distributed over entire output. Thus, AC
decreases at the lower rate than MC.
 When MC increases, AC also increases, but at the lower rate.
 MC intersects AC at its minimum as when AC falls, MC begins to rise. Thus AC=MC at the point of intersection.

1. LONG RUN COST ESTIMATION
 In the long run, all the factors of production
used by an organization vary.
 The exiting size of the plant or building can be
increase in case of long run. There is no fixed
inputs of cost in the long run.
 Long run is a period which all the costs
change as all the factors of production are
variable. There is no distinction between the
Long run Total Cost (LTC) and long run
variable cost as there is no fixed cost.
It should be noted that the ability of an organization of changing inputs enables it to
product at lower cost in the long run.

Long Run Total Cost (LTC)
 It refers to minimum cost at which
given level of output can be
produced.
 LTC represents the least cost of
different quantities of output.
 LTC is always less than or equal to
short run total cost, but it is never
more than short run cost.
As shown in figure, short run total costs curve; STC1, STC2 and STC3 are shown
depicting different plant sizes. The LTC curve is made by joining the minimum points of
short run total cost curves. Therefore LTC envelopes the STC curve.

Long Run Average Cost – A Traditional Approach
 Long Run Average Cost is equal to long run
total costs divided by the level of output. The
derivation of long run average costs is done
from the short run average cost curves.
 In the short run, plant is fixed and each short
run curve corresponds to a particular plant. The
long run average costs curve is also called U
shaped curve or planning curve or envelope
curve as it helps in making organizational plans
for expanding production and achieving
minimum costs.
Suppose there are three sizes of the plant and no other size of plant can be built. In short run, the
plant sizes are fixed thus organization increase or decrease the variable factor. However in the
long run the organization can select amongst the plants which help in achieving minimum possible
cost at a given level of output.

Modern Approach to Long Run Cost Behaviour: The L shaped Scale Curve
 We know that long run average costs
curves are U-shaped curve. However,
according to empirical studies LAC
curves are L shaped rather than U
shaped. The reasons for the L shaped
curve are as follows:
• Increase in technical progress: Brings a
decline in the unit cost. In the first stage, the cost is
higher. The technical progress will lower the costs
of production. With further technical progress, the
unit cost drops at lower pace. Thus, LAC curve will
become L Shaped.
• Produce at Lower Cost: Implies that as output increases, the efficiency of the organization
improves and thus, it lowers the costs.

Long Run Marginal Cost (LMC)
 It is defined as added cost of
producing an additional unit of a
commodity when all inputs are
variable.
 This cost is derived from short run
marginal cost.
If perpendiculars are drawn point A, B & C respectively, then they would intersect SMC curve at P,Q
and R respectively. By joining P, Q and R, the LMC curve would be drawn. It should be noted that
LMC equals to SMC, when LMC is a tangent to the LAC. OB is the output at which:
SAC2 = SMC2 = LAC = LMC
We can also draw the relation between LMC and LAC as follows:
When LMC < LAC, LAC falls
When LMC = LAC, LAC is constant.
When LMC > LAC, LAC arises.

PURPOSE OF SHORT RUN AND LONG RUN COST
ESTIMATION
Short run function tells the behaviour of marginal cost, which helps
us in determining output and price.
Long run cost function helps us in determining the most efficient size
of plant.
Short run function assume that it is the variable inputs influence cost.
Long run cost function allows for changes in all inputs, even capital can also
change along with other factors.

METHODS OF
ESTIMATING
COST
FUNCTIONS
Accounting
Method
High-Low
Method
Scattergraph
Method
Regression
Method

ACCOUNTING METHOD
Total variable costs
= Variable cost per unit
Number of units produced and sold
 The account analysis approach requires that each
individual cost is examined, and based on judgment
is categorized as a fixed or variable cost. Then all
variable costs or fixed cost are totaled.
 Variable cost per unit or is calculated by dividing the
total of all variable costs by the number of units
produced and sold.
 Fixed cost per unit or is calculated by dividing the
total of all fixed costs by the number of units
produced and sold.
Total fixed costs
= Fixed cost per unit
Number of units produced and sold

HIGH LOW METHOD
• The high-low method uses the highest and lowest
activity levels of a data set to estimate the portion of a
mixed cost that is variable and the portion that is fixed.
• This method uses only the high and low activity levels
to calculate the variable and fixed costs, it may be
misleading if the activity levels are not representative
of the normal activity.
• The high-low method is most accurate when the costs
incurred at the high and low levels of activity are
representation of the majority of the other data points.
Y2 - Y1
X2 - X1
Month Units Costs
January 20 10000
February 25 12000
March 22 11500
April 30 14500
May 28 14000
Example
Where,
X2 is the high activity level
X1 is the low activity level
Y2 is the total cost at the high activity level
Y1 is the total cost at the low activity level

SCATTERGRAPH METHOD
• Creating a scatter graph is another method
of estimating fixed and variable costs. It
provides a visual picture of the total costs
at different activity levels. However, it is
often hard to visualize the cost equation line
through the data points, especially if the
data is varied.
Rise
Run
'Rise' is the difference in total costs and
'run' is the difference in number of homes
cleaned.

REGRESSION METHOD
 It involves estimating the cost function using past data or the dependent and the independent
variables. The cost function is based on the regression of the relevant variables. The cost
function will depend on the relationship between the dependent variable and the independent
variable. The dependent variable will constitute the relevant cost which may be service,
variable cost, overhead cost etc. The independent variable will be the cost drivers where the
cost drivers will be labour hours, units of labour or raw materials, units of output etc.
 In regression analysis, a regression model of the form y= a + bx for a simple regression is
obtained.
 For a multiple regression, a regression model of the form Y = a + b1x1 +b2x2 + bnxn is obtained.
where, A is a fixed cost, X1,X2,XN are cost drivers; b1,b2 bn are changes in cost with the change in
value of cost driver.

PROBLEMS IN THE ESTIMATION OF COST
FUNCTION
Time period
Cost adjustments
Technical
Economic versus accounting cost data
Changes in accounting practices

Thank you……
Presented By:
Dheeraj Rawal
Master of Business Administration

Cost Output Relationship; Estimation of Cost and Output

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