The Firms and Theory of Production
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The Firm and Its Economic Problem
A firm is an institution that hires factors of production and
organizes them to produce and sell goods and services.
The Firm’s Goal
A firm’s goal is to maximize profit.
If the firm fails to maximize its profit, the firm is either
eliminated or bought out by other firms seeking to
maximize profit.
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The Firm and Its Economic Problem
Accounting Profit
Accountants measure a firm’s profit to ensure that the firm
pays the correct amount of tax and to show it investors
how their funds are being used.
Profit equals total revenue minus total cost.
Accountants use Internal Revenue Service rules based on
standards established by the Financial Accounting
Standards Board to calculate a firm’s depreciation cost.
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The Firm and Its Economic Problem
Economic Profit
Economists measure a firm’s profit to enable them to
predict the firm’s decisions, and the goal of these
decisions in to maximize economic profit.
Economic profit is equal to total revenue minus total cost,
with total cost measured as the opportunity cost of
production.
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The Firm and Its Economic Problem
A Firm’s Opportunity Cost of Production
A firm’s opportunity cost of production is the value of the
best alternative use of the resources that a firm uses in
production.
A firm’s opportunity cost of production is the sum of the
cost of using resources

Bought in the market

Owned by the firm

Supplied by the firm's owner
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Information and Organization
Types of Business Organization
There are three types of business organization:

Proprietorship

Partnership

Corporation
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Information and Organization
Proprietorship
A proprietorship is a firm with a single owner who has
unlimited liability, or legal responsibility for all debts
incurred by the firm—up to an amount equal to the entire
wealth of the owner.
The proprietor also makes management decisions and
receives the firm’s profit.
Profits are taxed the same as the owner’s other income.
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Information and Organization
Partnership
A partnership is a firm with two or more owners who have
unlimited liability.
Partners must agree on a management structure and how
to divide up the profits.
Profits from partnerships are taxed as the personal income
of the owners.
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Information and Organization
Corporation
A corporation is owned by one or more stockholders with
limited liability, which means the owners who have legal
liability only for the initial value of their investment.
The personal wealth of the stockholders is not at risk if the
firm goes bankrupt.
The profit of corporations is taxed twice—once as a
corporate tax on firm profits, and then again as income
taxes paid by stockholders receiving their after-tax profits
distributed as dividends.
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Markets and Firms
Why Firms?
Firms coordinate production when they can do so more
efficiently than a market.
Four key reasons might make firms more efficient. Firms
can achieve

Lower transactions costs

Economies of scale

Economies of scope

Economies of team production
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Markets and Firms
Transactions costs are the costs arising from finding someone with
whom to do business, reaching agreement on the price and other
aspects of the exchange, and ensuring that the terms of the
agreement are fulfilled.
Economies of scale occur when the cost of producing a unit of a
good falls as its output rate increases.
Economies of scope arise when a firm can use specialized inputs to
produce a range of different goods at a lower cost than otherwise.
Economies of team production
Firms can engage in team production, in which the individuals
specialize in mutually supporting tasks.
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Production
The theory of the firm describes how a firm makes
cost-minimizing production decisions and how the
firm’s resulting cost varies with its output.
Production is a process in which firm transform its
inputs (factor of production) to output
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Production function
Q = F( K, L )
Function showing the highest output that a firm can produce for
every specified combination of inputs.
Q= Total Product
K= Capital (Fixed factor of Production)
L=Labor
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(Variable factor of Production)
The Short Run versus the Long Run
short run Period of time in which quantities of one or
more production factors cannot be changed.
long run Amount of time needed to make all
production inputs variable.
fixed input
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Production factor that cannot be varied
PRODUCTION WITH ONE VARIABLE INPUT (LABOR)
Average and Marginal Products
● average product
Output per unit of a particular input.
● marginal product
Additional output produced as an input is
increased by one unit.
Average product of labor = Output/labor input = q/L
Marginal product of labor = Change in output/change in labor input
= Δq/ΔL
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Production Function
With One Variable Input
Total Product
Marginal Product
Average Product
Production or
Output Elasticity
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TP = Q = f(L)
TP
MPL =
L
TP
APL =
L
MPL
EL = AP
L
PRODUCTION WITH ONE VARIABLE INPUT (LABOR)
Production with One Variable Input
Amount
of Labor (L)
Total
Output (q)
0
10
0
—
1
10
10
10
10
2
10
30
15
20
3
10
60
20
30
4
10
80
20
20
5
10
95
19
15
6
10
108
18
13
7
10
112
16
4
8
10
112
14
0
9
10
108
12
4
10
10
100
10
8
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Average
Product (q/L)
Marginal
Product (∆q/∆L)
—
Amount
of Capital (K)
PRODUCTION WITH ONE VARIABLE INPUT (LABOR)
The Slopes of the Product Curve
Production with One Variable Input
The total product curve in (a) shows
the output produced for different
amounts of labor input.
The average and marginal products
in (b) can be obtained (using the
data in Table 6.1) from the total
product curve.
At point A in (a), the marginal
product is 20 because the tangent
to the total product curve has a
slope of 20.
At point B in (a) the average product
of labor is 20, which is the slope of
the line from the origin to B.
The average product of labor at
point C in (a) is given by the slope
of the line 0C.
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The Law of Diminishing Returns
As additional units of a variable input are combined with
a fixed input, after a point the additional output (marginal
product) starts to diminish. This is the principle that after a
point, the marginal product of a variable input declines.
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The law of diminishing return
Increasing Returns
MP
Diminishing Returns Begins
X
MP
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The law of variable proportions states that as the quantity of one factor is
increased, keeping the other factors fixed, the marginal product of that
factor will eventually decline. This means that upto the use of a certain
amount of variable factor, marginal product of the factor may increase and
after a certain stage it starts diminishing. When the variable factor becomes
relatively abundant, the marginal product may become negative.
Assumptions of Law.
→Constant technology--- This law assumes that technology does not
change throughout the operation of the law.
→Fixed amount of some factors.—One factor of production has to be
fixed for this law.
→ Possibility of varying factor proportions—This law assumes that
variable factors can be --changed in the short run.
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If MP > AP then AP is
rising.
If MP < AP then AP is
falling.
MP=AP when AP is
maximized.
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The three stages of production
Stage I: The range of increasing average product of the
variable input.
From zero units of the variable input to where AP is
maximized
Stage II: The range from the point of maximum AP of
the variable to the point at which the MP of is zero.
From the maximum AP to where MP=0
Stage III: The range of negative marginal product of the
variable input.
From where MP=0 and MP is negative.
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In the short run, rational firms should only be operating
in Stage II.
Why not Stage III?
Firm uses more variable inputs to produce less output
Why not Stage I?
Underutilizing fixed capacity
Can increase output per unit by increasing the amount of
the variable input
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The three stages of Production
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What level of input usage within
Stage II is best for the firm?
The answer depends upon how many units of output
the firm can sell, the price of the product, and the
monetary costs of employing the variable input.
© 2010 Pearson Addison-Wesley
Production With Two Variable Inputs
Isoquants show combinations of two inputs that can
produce the same level of output.
Firms will only use combinations of two inputs
that are in the economic region of production, which is
defined by the portion of each isoquant that is
negatively sloped.
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PRODUCTION WITH TWO VARIABLE INPUTS
Isoquants
TABLE 6.4 Production with Two Variable Inputs
LABOR INPUT
Capital
Input
1
2
3
4
5
1
20
40
55
65
75
2
40
60
75
85
90
3
55
75
90
100
105
4
65
85
100
110
115
5
75
90
105
115
120
● isoquant Curve showing
all possible combinations
of inputs that yield the
same output.
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PRODUCTION WITH TWO VARIABLE INPUTS
Isoquants
● isoquant map
Graph combining a number of
isoquants, used to describe a production function.
Figure 6.4
Production with Two Variable Inputs
(continued)
A set of isoquants, or isoquant
map, describes the firm’s
production function.
Output increases as we move
from isoquant q1 (at which 55
units per year are produced at
points such as A and D),
to isoquant q2 (75 units per year at
points such as B) and
to isoquant q3 (90 units per year at
points such as C and E).
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Marginal Rate of Technical Substitution
Marginal Rate of Technical Substitution: The absolute
value of the slope of the iso-quant. It equals the ratio
the marginal products of the two inputs. Slope of isoquant indicates the quantity of one input that can be
traded for another input, while keeping output
constant.
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Properties of Isoquants
Isoquants are negatively sloped
A higher Isoquants represent a larger output
No two isoquants intersect or touch each other
Isoquants are convex to the origin
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PRODUCTION WITH TWO VARIABLE INPUTS
Diminishing Marginal Returns
Production with Two Variable Inputs
(continued)
Diminishing Marginal Returns
Holding the amount of capital
fixed at a particular level—say 3,
we can see that each additional
unit of labor generates less and
less additional output.
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PRODUCTION WITH TWO VARIABLE INPUTS
Substitution Among Inputs
● marginal rate of technical substitution (MRTS) Amount by
which the quantity of one input can be reduced when one extra
unit of another input is used, so that output remains constant.
Marginal rate of technical
substitution
Like indifference curves,
isoquants are downward
sloping and convex. The
slope of the isoquant at any
point measures the
marginal rate of technical
substitution—the ability of
the firm to replace capital
with labor while maintaining
the same level of output.
On isoquant q2, the MRTS
falls from 2 to 1 to 2/3 to
1/3.
(MP ) / (MP )  (K / L)  MRTS
L
K
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MRTS = − Change in capital input/change in labor input
= − ΔK/ΔL (for a fixed level of q)
PRODUCTION WITH TWO VARIABLE INPUTS
Production Functions—Two Special
Cases
Isoquants When Inputs Are
Perfect Substitutes
When the isoquants are
straight lines, the MRTS is
constant. Thus the rate at
which capital and labor can
be substituted for each
other is the same no matter
what level of inputs is being
used.
Points A, B, and C
represent three different
capital-labor combinations
that generate the same
output q3.
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PRODUCTION WITH TWO VARIABLE INPUTS
Production Functions—Two Special Cases
● fixed-proportions production function
Production function
with L-shaped isoquants, so that only one combination of labor
and capital can be used to produce each level of output.
Fixed-Proportions
Production Function
When the isoquants are Lshaped, only one
combination of labor and
capital can be used to
produce a given output (as at
point A on isoquant q1, point
B on isoquant q2, and point C
on isoquant q3). Adding more
labor alone does not increase
output, nor does adding more
capital alone.
The fixed-proportions
production function describes
situations in which methods
of production are limited.
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Optimal Combination of Inputs
Isocost lines represent all combinations of
two inputs that a firm can purchase with
the same total cost.
C  wL  rK
C  Total Cost
w  Wage Rate of Labor ( L)
C w
K  L
r r
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r  Cost of Capital ( K )
Isocost Lines
An isocost line is a line that identifies all the
combinations of capital and labor, two factor inputs,
that can be purchased at a given total cost.
The line intersects each axis at the quantity of that
input that the firm could purchase if only that input
were purchased.
The slope of an isocost line is (minus) the ratio of input
prices, w/r, indicating the relative prices of inputs.
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Least Costly Input Combination
A point of tangency between an isocost line and an
isoquant show the least costly way of producing a
given output level.
Alternatively, a point of tangency shows the maximum
output attainable at a given cost as well as the
minimum cost necessary to produce that output.
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Interpreting the Tangency Points
Golden rule of cost minimization: a rule that says that
to minimize cost, the firm should employ inputs in
such a way that the marginal product per dollar spent
is equal across all inputs
MPL/w = MPK/r
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If the firm is not producing at a
tangency point…
Whenever MPL/w > MPK/r, a firm can increase
output without increasing production cost by
shifting outlays from capital to labor.
Whenever MPL/w < MPK/r, a firm can increase
output without increasing production cost by
shifting outlays from labor to capital.
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The Expansion Path
The expansion path is a curve formed by connecting
the points of tangency between isocost lines and the
highest respective attainable isoquants.
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Isocost Lines and the Expansion Path
[Figure 8.4]
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Optimal Combination of Inputs
Isocost Lines
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AB
C = $100, w = r = $10
A’B’
C = $140, w = r = $10
A’’B’’
C = $80, w = r = $10
AB*
C = $100, w = $5, r = $10
Optimal Combination of Inputs
MRTS = w/r
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RETURNS TO SCALE
● returns to scale Rate at which output increases as
inputs are increased proportionately.
● increasing returns to scale
Situation in which output
more than doubles when all inputs are doubled.
● constant returns to scale
Situation in which output
doubles when all inputs are doubled.
● decreasing returns to scale
Situation in which output
less than doubles when all inputs are doubled.
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Optimal Combination of Inputs
Effect of a Change in Input Prices
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Returns to Scale
Constant
Returns to
Scale
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Increasing
Returns to
Scale
Decreasing
Returns to
Scale
RETURNS TO SCALE
Describing Returns to Scale
Returns to Scale
When a firm’s production process exhibits
constant returns to scale as shown by a
movement along line 0A in part (a), the
isoquants are equally spaced as output
increases proportionally.
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However, when there are increasing
returns to scale as shown in (b), the
isoquants move closer together as
inputs are increased along the line.
Empirical Production Functions
Cobb-Douglas Production Function
Q = AKaLb
Estimated using Natural Logarithms
ln Q = ln A + a ln K + b ln L
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Estimation of Production
Functions
Aggregate Production Functions
Many studies using Cobb-Douglas did not deal with
individual firms, rather with aggregations of industries or
an economy.
Gathering data for aggregate functions can be difficult.
•For an economy: GDP could be used
•For an industry: data from Census of Manufactures or production
index from Federal Reserve Board
•For labor: data from Bureau of Labor Statistics
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Useful properties
Several Useful Properties :
The Marginal Product of capital and the marginal
Product of labor depend on both the quantity of
capital and the quantity of labor used in
production, as is often the case in the real world.
K and L are represents the output elasticity of labor
and capital and the sum of these exponents gives
the returns on scale.
a+b=1
Constant return to scale
a+b>1
Increasing return to scale
a + b <1
Decreasing return to scale
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Importance of Production Functions in Managerial
Decision Making
Production levels do not depend on how much a
company wants to produce, but on how much its
customers want to buy.
Capacity Planning: planning the amount of fixed inputs
that will be used along with the variable inputs. Good
capacity planning requires:
Accurate forecasts of demand
Effective communication between the production and
marketing functions
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Innovations and Global
Competitiveness
Product Innovation
Process Innovation
Product Cycle Model
Just-In-Time Production System
Competitive Benchmarking
Computer-Aided Design (CAD)
Computer-Aided Manufacturing (CAM)
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Theory of Cost and Estimation
.
Slide 55
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The Nature of Costs
Explicit Costs
Accounting Costs
arise from transactions in which the firm purchases
inputs or the services of inputs from other parties
Economic Costs
Implicit Costs
Explicit cost
Alternative or Opportunity Costs
.
Slide 56
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Implicit Costs
costs associated with the use of the firm’s own resources and
reflect the fact that these resources could be employed
elsewhere
Sunk Costs
.
Slide 57
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Short-Run Cost
Total fixed cost (TFC) – the cost incurred by the firm that does not depend
on how much output it produces
Total variable cost (TVC) – the cost incurred by the firm that depends on
how much output it produces
.
Slide 58
© 2010 Pearson Addison-Wesley
Total cost (TC) – the sum of total fixed and total variable cost at each
output level
Marginal cost (MC) – the change in total cost that results from a one-unit
change in output
Average fixed cost (AFC) – total fixed cost divided by the amount of output
Average variable cost (AVC) – total variable cost divided by the amount of
output
Average total cost (ATC) – total cost divided by the output
.
Slide 59
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Short-Run Cost Functions
Total Cost = TC = f(Q)
Total Fixed Cost = TFC
Total Variable Cost = TVC
TC = TFC + TVC
.
Slide 60
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Short-Run Cost Functions
Average Total Cost = ATC = TC/Q
Average Fixed Cost = AFC = TFC/Q
Average Variable Cost = AVC = TVC/Q
ATC = AFC + AVC
Marginal Cost = TC/Q = TVC/Q
.
Slide 61
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Short-Run Cost Functions
Q
0
1
2
3
4
5
.
TFC
$60
60
60
60
60
60
Slide 62
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TVC
$0
20
30
45
80
135
TC
$60
80
90
105
140
195
AFC
$60
30
20
15
12
AVC
$20
15
15
20
27
ATC
$80
45
35
35
39
MC
$20
10
15
35
55
.
Slide 63
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Behind Cost Relationships
• The shape of the TVC
curve is determined by
the shape of the TP
curve, which in turn
reflects diminishing
marginal returns.
.
Slide 64
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Short-Run Cost Curves
.
Slide 65
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Marginal Cost
The marginal product curve of the variable input generally rises
and then falls, attributable to the law of diminishing marginal
returns.
As a result, the MC curve will first fall and then rise
.
Slide 66
© 2010 Pearson Addison-Wesley
Average Cost
The average product curve rises, reaches a
maximum, and then falls, due to the law of
diminishing marginal productivity.
As a result, the AVC curve will fall and then rise.
The AFC curve declines over the entire range of
output as the amount of total fixed cost is spread
over ever-larger rates of output.
The ATC curve is the sum of AFC and AVC. It
measures the average unit cost of all inputs, both
fixed and variable, and must also be U-shaped.
.
Slide 67
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Marginal-Average Relationships
When marginal cost is below average
(total or variable) cost, average cost will
decline.
When marginal cost is above average
cost, average cost rises.
When average cost is at a minimum,
marginal cost is equal to average cost.
.
Slide 68
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Geometry of Cost Curves
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Long-Run Cost Curves
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Economies of Scale and
Diseconomies of Scale
Economies of scale – a situation in which a firm can
increase its output more than proportionally to its total
input cost
Diseconomies of scale – a situation in which a firm’s
output increases less than proportionally to its total
input cost
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Long-Run Cost Curves
Long-Run Total Cost = LTC = f(Q)
Long-Run Average Cost = LAC = LTC/Q
Long-Run Marginal Cost = LMC = LTC/Q
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Derivation of Long-Run Cost Curves
.
Slide 73
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Relationship Between Long-Run and Short-Run Average Cost Curves
.
Slide 74
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Possible Shapes of
the LAC Curve
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Cost-Volume-Profit Analysis
Total Revenue = TR = (P)(Q)
Total Cost = TC = TFC + (AVC)(Q)
Breakeven Volume TR = TC
(P)(Q) = TFC + (AVC)(Q)
QBE = TFC/(P - AVC)
.
Slide 76
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Cost-Volume-Profit Analysis
P = 40
TFC = 200
AVC = 5
QBE = 40
.
Slide 77
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Empirical Estimation
Functional Form for Short-Run Cost Functions
Theoretical Form
Linear Approximation
TVC  aQ  bQ2  cQ3
TVC  a  bQ
TVC
2
AVC 
 a  bQ  cQ
Q
a
AVC   b
Q
MC  a  2bQ  3cQ 2
.
Slide 78
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MC  b
Empirical Estimation
Theoretical Form
.
Slide 79
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Linear Approximation
Estimating Cost Functions
Techniques:
Surveys
Econometric specification
New entrant/survivor technique – method for
determining the minimum efficient scale of
production in an industry based on
investigating the plant sizes either being built
or used by firms in the industry
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Minimizing Costs Internationally
Foreign Sourcing of Inputs
New International Economies of Scale
Immigration of Skilled Labor
Brain Drain
.
Slide 81
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