Chapter 6
Firms and
Production
Topics
•  The Ownership and Management of Firms.
•  Production.
•  Short-Run Production: One Variable and One Fixed
Input.
•  Long-Run Production: Two Variable Inputs.
•  Returns to Scale.
•  Productivity and Technical Change.
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The Ownership and Management of
Firms
•  Firm - an organization that converts
inputs such as labor, materials, energy,
and capital into outputs, the goods and
services that it sells.
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Private, Public, and Nonprofit Firms
•  (For-profit) Private sector – firms owned
by individuals or other nongovernmental
entities and whose owners try to earn a
profit.
•  Public sector – firms and organizations
that are owned by governments or
government agencies.
•  Nonprofit or not-for-profit sector –
organizations neither government-owned
nor intended to earn a profit.
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Ownership of For-Profit Firms
•  Sole proprietorships are firms owned and run by
a single individual.
•  General partnerships (partnerships) are
businesses jointly owned and controlled by two
or more people.
•  Corporations are owned by shareholders in
proportion to the numbers of shares of stock
they hold.
w  Owners have limited liability - Personal assets of
corporate owners cannot be taken to pay a
corporation’s debts even if it goes into bankruptcy.
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What Owners Want?
•  Main assumption: firm’s owners try to
maximize profit!
•  Profit (p) - the difference between
revenues, R, and costs, C:
p=R–C
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What Owners Want? (cont.)
•  To maximize profit a firm must produce as
efficiently as possible.
•  A firm engages in efficient production
(achieves technological efficiency) if it
cannot produce its current level of output
with fewer inputs, given existing
knowledge about technology and the
organization of production.
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Production
•  A firm uses a technology or production process
to transform inputs or factors of production into
outputs.
•  Capital (K) - long-lived inputs.
w  land, buildings (factories, stores), and equipment
(machines, trucks).
•  Labor (L) - human services.
w  managers, skilled workers (architects, economists,
engineers, plumbers), and less-skilled workers
(custodians, construction laborers, assembly-line
workers).
•  Materials (M) - raw goods (oil, water, wheat)
and processed products (aluminum, plastic,
paper, steel).
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Production Function
•  Production function - the relationship
between the quantities of inputs used and
the maximum quantity of output that can
be produced, given current knowledge
about technology and organization.
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Production Function (cont.)
Inputs
(L, K)
Production
Function
q = f(L, K)
Output
q
•  Formally,
q = f(L, K)
w  where q units of output are produced using L units
of labor services and K units of capital (the
number of conveyor belts).
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Time and the Variability of Inputs
•  Short run - a period of time so brief that at least
one factor of production cannot be varied
practically.
w  Fixed input - a factor of production that cannot be
varied practically in the short run.
w  Variable input - a factor of production whose
quantity can be changed readily by the firm during
the relevant time period.
•  Long run - a lengthy enough period of time that
all inputs can be varied.
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Short-Run Production
•  In the short run, the firm’s production
function is
q = f(L, K)
w where q is output, L is workers, and K is the
fixed number of units of capital.
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Table 6.1 Total Product, Marginal Product, and
Average Product of Labor with Fixed Capital
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Total Product of Labor
•  Total product of labor- the amount of
output (or total product) that can be
produced by a given amount of labor.
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Marginal Product of Labor
•  Marginal product of labor (MPL ) - the
change in total output, Dq, resulting from using
an extra unit of labor, DL, holding other factors
constant:
Δq
MPL =
ΔL
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Average Product of Labor
•  Average product of labor (APL ) - the ratio of
output, q, to the number of workers, L, used to
produce that output:
q
APL =
L
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Output, q, Units per day
C
110
90
56
(b)
B
0
A
4
Diminishing Marginal
Returns sets in!
(a)
APL, MPL
Figure 6.1
Production
Relationships
with Variable
Labor
6!
11!
L, Workers per day
a!
20!
15
b!
Average product, APL
Marginal product, MPL
0
4
c!
6!
11!
L, Workers per day
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Law of Diminishing Marginal Returns
If a firm keeps increasing an input, holding
all other inputs and technology constant,
the corresponding increases in output will
become smaller eventually.
w That is, if only one input is increased, the
marginal product of that input will diminish
eventually.
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Long-Run Production
•  In the long run both labor and capital are
variable inputs.
•  It is possible to substitute one input for the
other while holding output constant.
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Isoquants
•  Isoquant - a curve that shows the
efficient combinations of labor and capital
that can produce a single (iso) level of
output (quantity).
•  Equation for an isoquant:
q = f (L, K).
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Table 6.2 Output Produced with
Two Variable Inputs
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6
3
2
a
K, Units of capital per d ay
Figure 6.2 Family of Isoquants
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1
0
b
e
c
f
q = 35
d
1
2
3
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6
q
= 14
L
,
Wo
r
kers
per d
ay
q = 24
Properties of Isoquants
1.  The farther an isoquant is from the origin,
the greater the level of output.
2.  Isoquants do not cross.
3.  Isoquants slope downward
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Figure 6.3(a) and (b)
Substitutability of Inputs
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Figure 6.3(c) Substitutability of
Inputs
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Application: A Semiconductor Integrated
Circuit Isoquant
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Substituting Inputs
•  Marginal rate of technical substitution
(MRTS) - the number of extra units of one
input needed to replace one unit of another
input that enables a firm to keep the amount
of output it produces constant.
change in capital ΔK
MRTS =
=
change in labor
ΔL
Slope of Isoquant!
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Figure 6.4 How the Marginal Rate of Technical
Substitution Varies Along an Isoquant
K, Units of capital per d ay
M RTS in a P r inting and Pu blishing U.S. Fir m
16
a
DK = –6
10
DL = 1
–3
5
4
b
7
0
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c
1
–2 1
–1
1
2
3
4
d
5
1
e
q = 10
6
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7
9
10
L
,
Wo
r
k
ers per d
ay
8
Substitutability of Inputs and Marginal
Products
•  Along an isoquant Dq = 0, or:
Extra units
of labor
Extra units
of capital
(MPL x ΔL) + (MPK x ΔK) = 0.
Increase in
q per extra
unit of labor
w or
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Increase in
q per extra
unit of
capital
MPL
DL
= - - MPK
DK
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= MRTS Solved Problem 6.1
•  Does the marginal rate of technical
substitution vary along the isoquant for
the firm that produced potato salad using
Idaho and Maine potatoes? What is the
MRTS at each point along the isoquant?
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Returns to Scale
•  How much does output change if a firm
increases all its inputs proportionately?
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Constant Returns to Scale (CRS)
•  Property of a production function whereby
when all inputs are increased by a certain
percentage, output increases by that
same percentage.
f(2L, 2K) = 2f(L, K).
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Increasing Returns to Scale (IRS)
•  Property of a production function whereby
output rises more than in proportion to an
equal increase in all inputs
f(2L, 2K) > 2f(L, K).
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Decreasing Returns to Scale (DRS)
•  Property of a production function whereby
output increases less than in proportion to
an equal percentage increase in all inputs
f(2L, 2K) < 2f(L, K).
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The Cobb-Douglas Production Function
•  It is one the most widely estimated
production functions.
q = ALaKb
g=a+b determines the returns to scale.
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Solved Problem 6.2
•  Under what conditions does a CobbDouglas production function (Equation
6.4, q = ALaKb) exhibit decreasing,
constant, or increasing returns to scale?
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Application: Returns to Scale in U.S.
Manufacturing
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Application: Returns to Scale in U.S.
Manufacturing
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Application: Returns to Scale in U.S.
Manufacturing
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Figure 6.5 Varying Scale Economies
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Productivity and Technical Change
•  Productivity may differ across firms –
produce different amounts of output with a
given amount of inputs.
•  After a technical or managerial innovation,
a firm can produce more today from a
given amount of inputs than it could in the
past.
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Innovations
•  Technical progress - an advance in
knowledge that allows more output to be
produced with the same level of inputs.
•  Better management or organization of the
production process similarly allows the
firm to produce more output from given
levels of inputs.
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Innovations (cont.)
•  Neutral technical change – a firm can
produce more output using the same ratio
of inputs.
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Table 6.3 Annual Percentage Rates of Neutral
Productivity Growth for Computer and Related
Capital Goods
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