Theory of Cost.pptx managerial economics basics and matrix

Chapter 3: Theory of Cost
Managerial Economics

Concept of Cost
Cost is defined as those expenses faced by a business in the
process of supplying goods and services to consumers.

Types of Costs
Explicit cost (EC) is the direct monetary expenditure or out-of-
pocket expenses paid for the ﬁrm’s resources, such as material,
wages, interest on loans, rent etc.
Implicit cost (IC) is the indirect nonmonetary cost that can only be
estimated by the opportunity cost which is the loss of earnings due
to lost opportunities.
Therefore: Economic profit =TR- EC – IC; Accounting profit = TR-EC
A sunk cost is a cost that an entity has incurred, and which it can no
longer recover. It is type of fixed cost that can’t be recouped or which
is lost forever once paid. Thus, it should not be considered when
making the decision to continue investing in an ongoing project.

Fixed costs are those, which are fixed in volume for a certain given
output. It does not vary with the variation in the output.
• Cost of managerial and administrative staff,
• Depreciation of machinery
• Maintenance of land etc. can be example of fixed costs.
Variable costs are those, which vary with the variation in the total
output. Variable costs include cost of raw materials, direct labor
charges, etc.
Total Cost (TC) represents the value of the total resources
requirements for the production of goods and services.

Average Costs (AC) = TC/Q, Q is the total output.
Marginal Costs (MC) is the addition to the total cost on account of
producing and additional unit of the product or, marginal cost is the
cost of marginal unit produced.
MC= ∆TC/ ∆Q= ∆TVC/ ∆Q ; TC = TVC + TFC = EMC+TFC, TVC=EMC
Short Run Costs: Some inputs are fixed in short run.
Fixed costs are costs associated with such fixed inputs must be paid
regardless of the level of output produced.
Long run cost: the long run simply refers to a period of time during
which all inputs can be varied.

Total Cost Curve in the Short Run

Total cost curve
The total-fixed-cost curve is horizontal at $6,000, indicating that TFC
is constant for all levels of output.
TVC starts at the origin, because the firm incurs no variable costs if
production is zero;
TVC rises as output increases, because to produce more the firm
must use more resources, thereby increasing cost.
Total cost curve lies above the TVC curve by an amount exactly equal
to $6,000 (TFC) at each output level.
Consequently, TC and TVC are parallel and have identical shapes.

Average and Marginal cost schedules

Short Run Average and Marginal Cost Curves
SMC first declines, reaches a minimum at Q 1, and rises thereafter.
AVC first declines, reaches a minimum at Q2 (SMC = AVC), and rises
thereafter. ATC first declines, reaches a minimum at Q3 (SMC = ATC) ,
and rises thereafter.
AFC declines continuously.

Short Run Average and Marginal Cost Curves
SMC lies below both AVC and ATC over the range for which these
curves decline; SMC lies above them when they are rising.
If SMC is below AVC, each additional unit of output adds less to cost
than the AVC of that unit. Thus AVC must decline over this range.
When SMC is above AVC, each additional unit of output adds more to
cost than AVC. In this case, AVC must rise.
So when SMC is less than AVC, AVC is falling; when SMC is greater
than AVC, AVC is rising.

• It refers to mathematical relation between cost of a product and
the various determinants of cost.
C=f(q) Where:
• C= cost of production
• Q= quantity of output
• f= functional r/ship
The basic principle of the cost behavior is that the total cost
increases with the increase in output.
Cost Function

SHORT-RUN COSTS AND PRODUCTION
• If 4 units of labor are employed, the firm can produce (a maximum of) 100 units; if 6
units of labor are employed, the firm’s maximum output is 200 units; and so on.
(Remember, the production function assumes technical efficiency.)
• If the price of a unit of labor services (w)= $1,000 Wage rate Hence TVC= w X L
• If 3 units of capital in the short run ( K=3) and that capital costs $2,000 per unit to
employ. Thus the TFC =r X K=$2,000X3=$6,000
Where r is the price of a unit of capital services.
Therefore TC = wL + rK

Average, Marginal Cost and Production
Q= 25 X 4, AVC=TVC/Q=(1000 X 4)/(25 X 4)=(w X L)/(AP X L)= 40=w/AP
MP is the additional labor employed to increase production in 100-unit
intervals.

Graph of AVC,
SMC, AP, and MP
Assume the wage rate is $21.
From 0 to 500 units of Labor,
MP > AP and AP is rising. But,
SMC & AVC falling b/c of
inverse r/ship
SMC=w/MP, AVC=w/AP
AP = Q/L,Q=6.5X500=3,250
MP reaches maximum and
MC reaches minimum at
3,250 units of output.
MC=w/MP=21/9,
AVC=3.23=w/AP=21/65.

Production and Cost curves
• When MP (AP) is increasing, MC (AVC) is decreasing.
• When MP (AP) is decreasing, MC (AVC) is increasing.
• When MP = AP at maximum AP, MC = AVC at minimum AVC
In short run, the effect of the law of diminishing marginal product
on the marginal cost of production. MP generally rises at first, then
diminishes b/c capital is fixed.
As MP begins to fall, MC begins to rise. In previous Figure, MP
begins to fall beyond 500 units of labor (beyond point A in Panel A).
MC begins to rise beyond 3,250 units of output (beyond point a in
Panel B). In the range between 500 and 800 units of labor.

MP is falling, but while MP still lies above AP, AP continues to rise
up to point C, where MP = AP. At point C, AP reaches its maximum
value at 800 units of labor. When 800 units of labor are employed,
5,600 units of output are produced (5,600 = AP X L = 7 X 800). Thus,
at 5,600 units of output, MC =AVC= $3, SMC = w/MP = $21/7 = $3,
AVC = w/AP = $21/7 = $3
So, at 5,600 units of output, AVC reaches its minimum and is equal
to MC.

• If labor usage increases beyond 800 units. MP is below AP, and AP
continues to decrease but never becomes negative. MP will
eventually become negative.
• Manager who wishes to minimize costs would never hire an amount
of labor that would have a negative marginal product. If MP is
negative, the manager could increase output by decreasing labor
usage, and this would also decrease the firm’s expenditure on labor.
• At 1,100 units of labor, AP is 6, and output is 6,600 units (= AP X L = 6
X 1,100).
• MC= $5.25 and AVC = $3.50 when 6,600 units are produced.
SMC = w/MP and AVC = w/AP

Long-run average and Cost curve
• A curve that defines the minimum average cost of producing
alternative levels of output, allowing for optimal selection of both
fixed and variable factors of production.

Economies of Scale
Economies of scale: Exist when long-run average costs decline as output is increased.
Diseconomies of scale: Exist when long-run average costs rise as output is increased.
Constant returns to scale: Exist when long-run average costs remain constant as
output is increased.

The relationship between increased per-worker productivity and
reduced per worker cost at fixed labor prices associated with an
increase in output and experience is called the learning curve effect.
The learning curve effect measures an increase in per-worker
productivity associated with an improvement in labor skills from on
the job experience.
It can be achieved by employee training and off-site continuing
education programs, the adoption of new production, organizational
and managerial techniques, the replacement of higher cost with
lower cost materials, new product design, and so on.
LEARNING CURVE EFFECT

Empirical Production Function is the mathematical form of the
production function to be estimated.
Cubic empirical specification for a short-run production function is
derived from a long-run cubic production function
Cubic form of the long-run production function is expressed as:
Holding capital constant at K units (K =K ), the short-run cubic
production function is
Empirical estimates of production and costs
3 3 2 2
Q aK L bK L
 
3 3 2 2
Q aK L bK L
  3 2
AL BL
 
3 2
A aK B bK
 
Where and
2
AP Q L AL BL
   2
3 2
MP Q L AL BL
 
  

Short-run Cubic Production Function
The level of labor usage beyond which marginal product begins to
fall, and diminishing returns set in, is Lm = − B /3A Differentiation
of MP. When MP= AP and average product is at its maximum
La = − B /2A  Differentiation of AP or Equating as AP=MP

Estimation of production functions
Linear Production Function: Q=F(K,L)=aK + bL
Q=F(K,L)=4K + L  Capital is always 4 times as productive as labor.
F(5,2)= 4(5) + 1(2)=22
MPk=a, MPL=b  Possible to verify by derivative
The marginal product of an input is simply the coefficient of the
input in the linear production function.
Thus, the marginal product of an input is independent of the
quantity of the input used.
Linear production functions do not obey the law of diminishing
marginal product.

Estimation of production functions
•Examples of production functions
•power function: exponential for one input
Q = aLb
if b > 1, MP increasing  = 3x2
if b = 1, MP constant = 3x
if b < 1, MP decreasing = 3x1/2

Estimation of production functions: Example

Problems
1. For each of the following situations, determine whether the manager is concerned with
a short-run or a long-run production decision. Explain briefly in each case.
a. A petroleum drilling supervisor on an offshore drilling platform decides
to add an extra six-hour shift each day to keep the drill rig running 24 hours
per day.
b. The vice president of offshore petroleum drilling operations in the Gulf of Mexico
chooses to deploy three more offshore drilling platforms in the Gulf.
c. A manufacturing engineer plans the production schedule for the month.
d. After studying a demographic report on future increases in birthrates, a hospital
administrator decides to add a new pediatric wing to the hospital.

Problems
During a year of operation, a firm collects $175,000 in revenue and
spends $80,000 on raw materials, labor expense, utilities, and rent. The
owners of the firm have provided $500,000 of their own money to the
firm instead of investing the money and earning a 14 percent annual
rate of return.
a. The explicit costs of the firm are $___ . The implicit costs are $___ .
Total economic cost is $___.
b. The firm earns economic profit of $___.
c. The firm’s accounting profit is $___.
d. If the owners could earn 20 percent annually on the money they
have invested in the firm, the economic profit of the firm would be___.

Theory of Cost.pptx managerial economics basics and matrix

10. Assume average variable cost is constant over a range of output. What is
marginal cost over this range? What is happening to average total cost over this
range?
11. Suppose that a firm is currently employing 20 workers, the only variable input,
at a wage rate of $60. The average product of labor is 30, the last worker added 12
units to total output, and total fixed cost is $3,600.
a. What is marginal cost?
b. What is average variable cost?
c. How much output is being produced?
d. What is average total cost?
e. Is average variable cost increasing, constant, or decreasing? What about average
total cost?

Solution for Q-11:
Given: L= 20 workers, Wage rate= 60, Average product of Labor=30. Last
worker added 12 units to total output, TFC= $3,600.
a. MC= ∆TC/∆Q=60/12=5
b. AVC= TVC/Q=WL/Q= 60X20/APLXL= 1200/600=2
c. Q=APL X L= 30 X 20=600
d. ATC=AVC + AFC= 2 + 3600/600 =8
e. ATC (8)>MC (5) >AVC (2). Thus, AVC is increasing but ATC is decreasing.

12. The cost function for Managerial Enterprises is given by C(Q) = 20 + 3Q2.
Determine the marginal cost, average fixed cost, average variable cost, and
average total cost when Q = 10.
Answer:
Using the formula for marginal cost (here a = c = 0), we know that MC = 6Q. Thus,
the marginal cost when Q = 10 is $60.
To find the various average costs, we must first calculate total costs. The total cost
of producing 10 units of output is C(10) = 20 +3(10)2 = $320
Fixed costs are those costs that do not vary with output; thus fixed costs are $20.
Variable costs are the costs that vary with output, namely VC(Q) = 3Q2. Thus,
VC(10) = 3(10)2 = $300. It follows that the average fixed cost of producing 10 units
is $2, the average variable cost is $30, and the average total cost is $32.

Problem : A firm’s total cost function is
Required: Suppose that the firm produces 10 units of output.
Calculate TFC, TVC, ATC, AFC, AVC, and MC.
The Cost Function (Example)

LONG-RUN COSTS AND OUTPUT DECISIONS
 In the Long-run production – all inputs are variable
 If all inputs of a firm change - the scale of the firm changes
 Firms increase size of the firm or scale of production by changing the fixed inputs of
short run production – in order to increase output
 Long-run cost behavior of a firm is derived from – short run costs of separate
production plants
 In order to discuss about long run We look at firms in three short-run circumstances:
i. firms earning economic profits,
ii. firms suffering economic losses but continuing to operate to reduce or minimize those
losses, and firms that decide to shut down and bear losses just equal to fixed costs.

Short-run Conditions and Long-run Directions
ABC Car Wash Weekly Costs
TOTAL FIXED COSTS (TFC)
TOTAL VARIABLE COSTS
(TVC) (800 WASHES)
TOTAL COSTS
(TC = TFC + TVC) $ 3,600
1. Normal return to
investors
$ 1,000 1.
2.
Labor
Materials
$ 1,000
600
Total revenue (TR)
at P = $5 (800 x $5) $ 4,000
2. Other fixed costs
(maintenance contract,
insurance, etc.) 1,000
$ 1,600 Profit (TR - TC) $ 400
$ 2,000
LONG-RUN COSTS AND OUTPUT DECISIONS

Producing at a Loss to offset Fixed Costs: The ABC Car wash
A firm will operate if total revenue covers total variable cost
CASE 1: SHUT DOWN CASE 2: OPERATE AT PRICE = $3
Total Revenue (q = 0) $ 0 Total Revenue ($3 x 800) $ 2,400
Fixed costs
Variable costs
Total costs
+
$
$
2,000
0
2,000
Fixed costs
Variable costs
Total costs
+
$
$
2,000
1,600
3,600
Profit/loss (TR - TC) - $ 2,000 Operating profit/loss (TR - TVC) $ 800
Total profit/loss (TR - TC) - $ 1,200
 If revenues exceed variable costs, operating profit is positive and can be used to
offset fixed costs and reduce losses, and it will pay the firm to keep operating.
 If revenues are smaller than variable costs, the firm suffers operating losses that
push total losses above fixed costs. In this case, the firm can minimize its losses by
shutting down.

Shutting Down to Minimize Loss
A Firm Will Shut Down If Total Revenue Is Less Than Total Variable Cost
CASE 1: SHUT DOWN CASE 2: OPERATE AT PRICE = $1.50
Total Revenue (q = 0) $ 0 Total revenue ($1.50 x 800) $ 1,200
Fixed costs
Variable costs
Total costs
+
$
$
2,000
0
2,000
Fixed costs
Variable costs
Total costs
+
$
$
2,000
1,600
3,600
Profit/loss (TR - TC): - $ 2,000 Operating profit/loss (TR - TVC) - $ 400
Total profit/loss (TR - TC) - $ 2,400
 Any time that price (average revenue) is below the minimum point on the average variable cost curve, total revenue
will be less than total variable cost, and operating profit will be negative—that is, there will be a loss on operation.
 In other words, when price is below all points on the average variable cost curve, the firm will suffer operating losses at
any possible output level the firm could choose.
 When this is the case, the firm will stop producing and bear losses equal to fixed costs. This is why the bottom of the
average variable cost curve is called the shut-down point.
 At all prices above it, the marginal cost curve shows the profit-maximizing level of output. At all prices below it,
optimal short-run output is zero.

 The short-run supply curve of a competitive firm is that portion of its marginal
cost curve that lies above its average variable cost curve
 As long as price (which is equal to average revenue per unit) is sufficient to cover
average variable costs, the firm stands to gain by operating instead of shutting
down.
 Shut-down point The lowest point on
the average variable cost curve.
 When price falls below the minimum
point on AVC, total revenue is
insufficient to cover variable costs and
the firm will shut down and bear losses
equal to fixed costs.

 The Industry Supply Curve in the Short Run Is the Horizontal Sum of the
Marginal Cost Curves (above AVC) of All the Firms in an Industry
short-run industry supply curve The sum of the marginal cost curves (above
AVC) of all the firms in an industry.

LONG-RUN DIRECTIONS
Profits, Losses, and Perfectly Competitive Firm Decisions in the Long and Short Run
SHORT-RUN
CONDITION
SHORT-RUN
DECISION
LONG-RUN
DECISION
Profits TR > TC P = MC: operate Expand: new firms enter
Losses 1. With operating profit P = MC: operate Contract: firms exit
(TR  TVC) (losses < fixed costs)
2. With operating losses Shut down: Contract: firms exit
(TR < TVC) losses = fixed costs

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