Cost Theory
Presented by: Stephen Mark M. Cundangan
“There ain’t no such
things as free lunch”
- Frank Herbert
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1 Cost Concepts
Types of cost relevant to the topic
Explicit Cost – can be considered as expenses or out-of-pocket costs (rent,
raw materials, fuel, wages, etc.) which are normally recorded in a firm’s
accounts.
Implicit Cost/Opportunity cost – the cost of forgoing the next most profitable
use of the resource, or benefit that could be obtained from the next-best use.
Historical Cost – it represent actual cast outlay, this means measuring costs in
historical terms.
Current cost – the amount that would be paid for an item under present market
condition.
Replacement cost –Item costed that may no longer be available due to
change, so appropriate cost must be applied.
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Types of Cost that are relevant with the topic
Sunk Cost – costs that has already been incurred and cannot be recovered.
Incremental Cost – refers to changes in costs caused by a particular decision;
relevant costs for decision-making.
Private Cost (internal cost) – costs that accrue directly to the individuals
performing a particular activity.
Social Cost (external cost) – costs that are passed on to other parties, and are
often difficult to value.
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Cost Concepts & Its
2 Relevance In Managerial
Decision-Making Analysis
Relevance of cost
concepts
1. There are no right or wrong in using cost concepts but the right
usage of the costs discussed could help a person make best
decision.
2. Managers must be careful in using cost information prepared by
the accountants, since it may be prepared and categorized for
different purpose
3. Determination of costs is not always purely objective; sometimes
considerable degree of judgement is often required.
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3 Short Run vs
Long Run 🏃
Short-run Behavior
This concept states that within a certain
period in the future, at least one input is
FIXED while others are variable.
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Four main types of unit cost in the short run
1. Marginal Cost (MC):
MC = change in total costs/change in output or
MC = C/ Q
2. Average variable cost (AVC):
AVC=VC/Q
3. Average fixed cost (AFC):
AFC = FC/Q
4. Average total cost (ATC):
ATC = TC/Q
or
ATC = (FC+VC)/Q = FC/Q + VC/Q = AFC+AVC
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Derivation of cost functions from
production functions example
Output, Q Capital, K Labor, L Fixed Cost Variable Total Cost
Quarter AFC=FC/Q AVC=VC/Q ATC=TC/Q MC=▲C/▲Q
(units) (machines) (workers) (FC) Cost (VC) (TC)
0 3 0 1,500 0 1,500 - - - -
Q1
13 3 1 1,500 400 1,900 115 31 146 31
27 3 2 1,500 800 2,300 56 30 85 29
Q2
39 3 3 1,500 1,200 2,700 38 31 69 33
50 3 4 1,500 1,600 3,100 30 32 62 36
Q3
59 3 5 1,500 2,000 3,500 25 34 59 44
64 3 6 1,500 2,400 3,900 23 38 61 80
Q4
66 3 7 1,500 2,800 4,300 23 42 65 200
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Relationship of Costs in Graph
TC and TVC are parallel to each other
The distance of FC (5,000) is the distance
5,000
between TC and TVC, since:
4,500
TC = TVC + FC
4,000
3,500
3,000
Cost
2,500
2,000
1,500
1,000
500
0
0 20 40 60 80
Production
Fixed Cost Variable Cost Total Cost
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Relationship of Costs in Graph MC curve is U-shaped. MC falls to begin
with as output rises, because of increasing
returns, and then, after reaching output Q1,
it begins to rise because of diminishing
250 returns.
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MC curve intersects both AVC & ATC a
150 their minimum points.
Cost
a. AVC curve is also U-shaped, & inversely
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proportional to average product when AP is
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rising.
b. AFC – as output rises the FC become
0 spread over the output causing the AFC to
0 10 20 30 40 50 60 70
fall continuously.
Production
c. ATC is also U-shaped because it is the
Ave. Fixed Cost Ave. Variable Cost sum of AVC and AFC.
Ave. Total Cost Marginal Cost
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Economic Efficiency
The output involve economic efficiency, and therefore be said
that Q3 is the most efficient level of output in the short run for a
firm of given plant size.
However, this does not imply that this output is an optimal
output since only cost are being considered, not revenue,
therefore it tells nothing about profit.
This type of efficiency in the short run can be viewed as a
compromise between spreading fixed cost and getting
diminishing returns.
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Points to Notice
In a certain number of workers, the Ave. Production of Labor
and the Marginal Production of Labor diminishes. This event is
called The Law of Diminishing Marginal Production.
The Law of Diminishing Marginal Production
It states that the advantages gained from slight improvement
on the input side of production equation will only advance at a
certain point and will decrease after that certain point.
Ex. The productivity of the last 3 workers are lesser than the first
3 workers. Not because they are lazy but due to the fixed inputs
that are present.
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The Law of Diminishing Marginal Production
Only occur in short run since in Long run, those fixed inputs
can be increased by the company.
Ex. Additional machines can be added to increase
production.
That the reasons for diminishing marginal production in short-
run are no longer present in the Long run.
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Long-run
Behavior
🌏
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Derivation of cost functions from
production functions example
Much more complicated than short-run since all factors of production and
costs are variable.
With the Cobb-Douglas production function it can be shown that the long-run
cost function is a power function.
The proof of this derivation is beyond the scope of this text, and involves
Lagrangian multiplier analysis. However, this function represent output
elasticities.
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Economies of scale
Are aspects of increasing scale that lead to falling long-run unit
costs. This can be classified in various ways:
Internal/External
1. Internal economies arise from the growth of the firm itself;
controllable and can be influence by management
decision-making.
2. External economies arise from the growth of the industry.
3. Economies of concentration arise when firms in the same
industry are located close to each other.
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Economies of scale
Physical/Monetary
Physical economies cause increasing returns to scale, while
monetary economies reduce input of prices.
Level: product, plant and firm.
In general some of the cost advantages arise from producing
more of one product, some from producing with a larger plant
size, and some from producing with a larger firm.
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Four main categories if internal economies of scale
1. Technical economies – arise mainly from increased specialization and
indivisibilities.
Ex. Specialized equipment or production process that can increase the
effectivity and efficiency of labor and capital productivity.
2. Managerial economies – managers who are skillful and productive at
performing managerial functions.
3. Marketing economies – these relate mainly to obtaining bulk discounts.
Ex. If a frim buy twice as much advertising space or time, the total cost
will usually less than double, thus the unit cost will fall.
4. Financial economies – Obvious factor here is that large firms can often borrow
at a lower interest rate
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Diseconomies of scale
Are aspects of increasing scale that lead to rising long-run unit
cost.
Like the economies of scale, they can be internal or external,
physical or monetary, and can arise at the level of product,
plant or firm.
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Four main sources of diseconomies of scale
1. Technical diseconomies – Increased specialization can also result to
problems.
Ex. Workers who suffers from low motivation can reduces productivity
and increase the chance of industrial unrest. Or days lost due to strikes.
2. Managerial diseconomies – Difficulties in management experienced by large
firms.
Ex. Lack of co-ordination and cooperation among departments that
create inefficiencies among them.
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Four main sources of diseconomies of scale
3. Marketing diseconomies – In some occasion high demands may drive up the
price of such inputs.
Ex. firm may have to offer higher wages just to attract a desired quantity
of workers to meet the production of high demands.
4. Transportation diseconomies – Larger firms, particularly if they only use one
plant, may face additional transportation cost as they try to increase the size
of their market; the average transportation distance of goods to customers
will increase.
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Economies of scope
This means that the production of one good reduces the cost of
producing another related good.
Ex. Different car models being produced at the same plant.
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4 Relationship Between
Production and Cost
Relationships between short-and long-run cost curves
In the long-run the firm is able to use the least-cost combination of inputs
to produce any given output, meaning that it can select the scale
appropriate to its level of operation.
This also means that the long-run curve (LAC) is an envelope of its short-
run average cost (SAC).
a. Optimal scale
This is reach when marginal cost are equal to marginal benefits.
b. Minimum efficient scale
Defined as the smallest scale at which long-run average cost is
minimized.
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c. Multiplant production
Horizontally integrated – when a
company wishes to grow through this
strategy, it aims is to acquire a similar
company that operates at the same
level in an industry.
Vertically integrated – involves the
acquisition of business operations within
the same production vertical.
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Strategy implications
Managers must make decisions regarding optimal plant size and scale
of operation in a dynamic environment.
Managers must be prepared for the eventuality that there may be a
mismatch between the quantity that the firm produces and the
quantity that it sells.
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5 Purpose & Principles
of Cost-Volume-Profit
Analysis
Purpose & assumption
Cost-volume-profit (CVP) analysis examines relationship between
cost, revenues and profit on the one hand and volume of output on
the other.
This is applied mainly to short-run situations.
And it is sometimes referred to as break-even analysis.
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The two points where cost and
revenue meet in the graph are
the two break-even points.
Between these two points will
be a profit-maximizing output.
Although such situations can be
analyzed using CVP methods, it is
more common to make the following
assumptions:
1. Marginal Cost is constant at all levels of output. This implies that the total
cost functions is linear.
2. Firms are price-takers, meaning that they are operating under conditions of
perfect competition.
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Break-even output
This can be derived mathematically, using linear cost and revenue
functions. The revenue function, R=PQ, is set equal to the cost
function, C=a+bQ, and we then solve for Q:
PQ = a+bQ
Q(P-b) = a
This gives the following expression for the break-even output:
BEO = a/(P-b)
Where a =fixed cost, b=average variable cost, P=price. The
denominator in this expression, (P-b), is often referred to as the
profit contribution
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Profit contribution
This is define as the money that each unit sold contributes to fixed cost
and profit. For example, a firm may have fixed cost of $10,000 per month
and variable cost of $12 per unit; the market price may be $20.
Profit contribution (IIc) = 20-12 =$8
To interpret this it is necessary to find the break-even output:
BEO = 10,000/8 =1,250 units per month
If the firm produces 1,251 units, II=$8; if it produces 1,252 units, II=$16. Thus
the firm is contributing $8 to profit for every unit it produces above the
break-even output. And the firm is contributing $8 to fixed cost for every
unit it produces below break-even output.
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Operating leverage
The degree of operating leverage (DOL) refers to the percentage change
in profit resulting from a 1 per cent change in units sold. Expressed
mathematically as:
Thus it can be interpreted as an elasticity of profits with respect to output:
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Operating leverage
With linear cost and revenue functions the profit function must also be
linear, therefore the DOL will vary with output. It will always be largest
close to the break-even output.
Ex. If the firm is producing 1,500 units per month, the DOL is
calculated as follows:
C = 10,000+12Q
R = 20Q
II = 8Q – 10,000 = $2,000 at output of 1,500 units
DOL = 8 x 1,500/2,000 = 6
The interpretation of this result is that a 1 per cent increase in output will
increase profit by 6 per cent.
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Limitations of CVP analysis
The main one limitation is the set of restrictive assumptions on which it is
often based. Profit does not usually increase linearly with out; many firms
will have to reduce price in order to increase sales because they are not
price-takers.
Furthermore, as output increase they are likely to face diminishing returns
as they approach capacity in the short term; inefficiencies and the
payment of overtime wages may increase unit variable costs.
In the long run a number of factors may invalidate the simplified analysis
above. Therefore, CVP analysis must be used with care, as with other
decision tools.
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Problem-solving
6 Approach for Applying
Cost-Volume-Profit
analysis
This approach is designed as an aid to solving CVP problems. Assuming
linear cost and revenue functions, all CVP analysis is based on the
following five equations:
1. Cost C = a + bQ
2. Revenue R = PQ
3. Profit II = R – C
4. Break-even BEO = a/(P – b)
5. Profit contribution IIc = P- b
The equations often have to be used in a sequence. The key is to use
the equations in the correct sequence, starting off with the values that
are known and working towards the required unknown.
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The existence of an equation with two or more unknowns does not
necessarily create an impasse; it may be necessary to treat the problem
as a system of equations that need to be solved simultaneously.
The mathematical rule is that we always need the same number of
equations as unknowns in order to solve for the unknowns.
This however does not guarantee a
solution in general terms; it is a necessary
condition, but not a sufficient one.
In linear CVP problems the rule is a useful one.
Other useful aid to solving these more complex problems is to tabulate
the data in T-table with two columns, one relating to each entity, before
processing it.
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The existence of an equation with two or more unknowns does not
necessarily create an impasse; it may be necessary to treat the problem
as a system of equations that need to be solved simultaneously.
The mathematical rule is that we always need the same number of
equations as unknowns in order to solve for the unknowns.
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Problem examples
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Problem examples
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Problem examples
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Case Study Article: Are Negative Interest Rates on the Way in the U.S.?
https://knowledge.wharton.upenn.edu/article/negative-interest-rates-
way/
Questions:
1. What are the implications of Negative Interest Rates to an economy?
2. Is it good to invest/have a business in an economy that has Negative
Interest Rates? Why?
Business Articles:
https://www.businesstimes.com.sg/government-economy/philippines-
inflation-slows-for-first-time-in-four-months-in-feb
https://www.nytimes.com/2020/10/21/business/economy/fed-
lifeline-funds.html
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End of Presentation
Thank You 47
