Dr. Karim Kobeissi

C h a p t e r 6 : C o s t A n a l y s i s

C o s t - D e fi n i ti o n

Sum of the inputs may multiplied

by their respective prices and

added together give the money

value of the inputs, that is the

cost of production.

What Makes Cost Analysis Difficult?

Cost analysis is made difficult by the effects of

unforeseen inflation, unpredictable changes in

technology, and the dynamic nature of input

and output market.

Why Cost Analysis is Important?

You may have heard the phrase "if they had just done a simple

cost-benefit analysis" used in critiquing a decision. There are

different types of costs with different impacts on a decision.

Understanding the different types of costs and their impacts

will help us make better decisions, and hopefully help us avoid

being asked why we didn't use a cost-benefit analysis.

The Different Types of Cost Historical Vs Current Costs

– Historical Cost is the actual cash outlay (acquisition cost adjusted

for depreciation and, in some cases, damages).

– Current Cost is the present cost of previously acquired items.

For example, Computers cost much less today than they did just a

few years age. Therefore, current cost for such items is

determined by what is referred to as a replacement cost which is

defined as the cost of duplicating these items by using the current

technology.

The Different Types of Cost ( c o n )Explicit Vs Implicit Costs

– Explicit Costs are defined as the out of pocket money.

– Implicit Costs are noncash expenses. An example of an implicit cost

is the opportunity cost of a sole proprietor working in his/her own

business. For example, Gina works as a sole proprietor and her

business reported a net income (revenues - expenses ) of $30,000

for the year. Since a sole proprietor does not receive a salary, there

is no explicit cost reported for Gina's work in her business. However,

if Gina is foregoing a salary of $40,000 from another company, that

is an implicit cost for her business. After considering this implicit

cost, Gina is losing $10,000 by working in her proprietorship.

The Different Types of Cost ( c o n )Sunk Vs Incremental Costs– Sunk costs , also known as fixed costs, are irreversible

expenses incurred previously. They are irrelevant to present decisions. For example, if you decide to have your employees work three shifts instead of two, your rent should stay the same.

– Incremental cost, also known as variable cost, is the change in cost tied to a managerial present decision. For example, If you pay your employees hourly and you need them to work more hours, your labor costs will increase incrementally.

N.B. Incremental cost can involve multiple units of output.• Marginal cost involves a single unit of output.

S u n k C o s t s• In the 1970's Lockhead spent $ 1 billiondeveloping a new airplane (Tristar). Aftersinking the money, it was clear that the venture

was not going to be a success.• Lockhead went to its creditors, and askedfor more money, saying, “We have to keepgoing, or else the $ 1 billion will be totallywasted.”

S u n k C o s t s

Some of the creditors said, “Why put in

more money, since there is no way we can

recoup our investment?”

Who was right?

S u n k C o s t s

Answer: Both arguments are wrong. The billion

dollar initial investment is a sunk cost that is

irrelevant to the decision.

We should compare the extra

revenue of continuing with the

extra cost.

“Don’t cry over spilt milk”

S u n k C o s t s

In the long run, Some fixed costs remain sunk

while others might not be.

For example, In the long run, you can sell your

factory and exit the industry if the profits

remain negative.

The Different Types of Cost ( c o n ) Short-run Vs Long-run Costs

– In the short run, at least one input (e.g. factory size) is fixed. The

short run cost is the cost of production at various production (output) levels

for a specific plant size and a given operating environment The short run

cost function for a particular factory is the relationship between output and

cost; i.e., the cost that is incurred (Yi) in producing various levels of output

(Xi). There for total short-run cost (TC) can be classified into fixed cost – FC –

(stays constant no matter what level of output; e.g., rent) and variable cost –

VC - (vary with the level of output ; e.g., power bills): TC = FC + VC .

Short Run Cost Table

The Short-run Cost Curves Show Minimum Cost in a Given Production Environment

The Different Types of Cost ( c o n )

- In the long run, costs are all variable. This means that even capital (e.g., plant)

can be altered. Output level can be changed by changing both capital and

labor. We say that changing the amount of capital that a producer uses is

changing its "scale“.

By changing scale in the long run, a firm can choose which short run

average total cost curve it wants to have Choose the IDEAL factory

for producing that level of output (Quantity Demanded =QD) for an

extended period of time at a minimum long run average total cost

(LRATC).

Long Run Average Total Cost (LRATC)The Long Run Average Total Cost (LRATC) curve of a

firm shows the minimum average total cost at which a firm can produce any given level of output in the long run (when all inputs are variables).

In the long run, a firm will use the level of capital (or other inputs that are fixed in the short run) that can produce a given level of output at the lowest possible average cost. Consequently, the LRATC curve is the envelope of the short run average total cost (SRATC) curves, where each SRATC curve is defined by a specific quantity of capital (or other fixed input).

If we drew all of the short run average total cost curves (SRATC) that a producer could select between (each corresponding to a specific plant), and then draw another curve containing all of these, the new curve is called the long run average total cost curve (LRATC) that shows the minimum cost in an ideal environment.

Plant Optimal Size with minimum LRATC

0QD Qi

Average Cost Per Unit

The Different Types of Cost ( c o n )

The long run cost function shows the cost

of production at various plant sizes and

operating conditions. It reflects the

economies and diseconomies of scale

which are a helpful guide for decisions-

making process (e.g., choosing the

optimal plant).

E c o n o m i e s o f S c a l e

ECONOMIES OF SCALE (increasing

returns to scale) - Exist when

long-run average total cost

(LRATC) decrease as production

increase.

This cost decrease is mainly

due to labor specialization,

commercial, financial managerial

advantages, and applying better

technology.

Constant Returns to Scale (CRTS)

CONSTANT RETURNS TO SCALE

- Exist when long run average

total cost (LRATC) do not

change as production

increases.

It is shown by the flat

portion of the LRATC curve.

Minimum Efficient Scale (MES)

• Minimum Efficient Scale (MES) –

The point at which the increase

in the scale of production yields

no significant unit cost benefits.

MES is the lowest point where

the plant (or firm) can produce

such that its long run average

cost is minimum.

D i s e c o n o m i e s o f S c a l e

DISECONOMIES OF SCALE - Exist

when long-run average total cost

(LRATC) increase as production

increase.

This cost decrease is mainly

due to administrative

disadvantage of large scale

when the firm size expand

beyond the optimal size.

S h a p e o f t h e L R A T C C u r v e

The shape of the LRATC curve is important not only because of its implications for plant scale decision but also because of its effects on the potential level of competition especially when it declines in some industries. Competition in the industry is most vigorous when MES is small in absolute terms.

(U) Shape LRATC – Industry With Strong Competition: (L) Shaped LRATC - Industry With Weak Competition:Industries with low fixed costs. Industries with high fixed costs.

Cost Volume Profit Analysis

A- Profit Maximization Analysis

B- Breakeven Analysis

A- Profit Maximization Analysis

Assume that (X) company has the following: Operations centralized at single plant initially Estimated demand is given by P = 940 - 0.02Q Estimated marginal revenu (derived equation) MR = 940 – 0.04Q Cost structure is given by TC = 250,000 + 40Q + 0.01Q2

1) Compute Maximum Profit Activity Level (Q*) 2) Compute (P*) 3) Compute Maximum Profit4) Compute the quantity for which the short run average cost is minimum (QCM)

1- The profit maximizing activity level (Q*) with centralized production occurs when MR - MC = 0 MR = MC Or MC = derivative (TC) = 0.02 Q + 40 940 – 0.04Q = 0.02 Q + 40 0.06 Q = 900 Q* = 15000 Units.

2- Q* = 15000 P* = 940 - 0.02Q = 640 $3- Maximum Profit = TR - TC = [(P* . Q*) - TC] = (15000 X 640) - [250000 +(40 X15000)

+[0.01 X (15000)2 ]] = 6500000 $4- Minimum cost occurs when AC = MC (TC / Q) = MC 250,000/Q + 40 + 0.01Q = 0.02 Q + 40 (QCM) = 5000 Units.

B- Breakeven Analysis

The break-even point is the point at which total revenue (P. X) and total cost (F + V.X) are equal. It represents the number of units produced and sold (X) needed to make the total cost equal to the total revenue:

P.X = F + V.X X = F / (P-V)

Where: V= Variable cost per unit F= Fixed costsP = Price of unit sold

x