Production
ECO61 Microeconomic
Analysis
Udayan Roy
Fall 2008
What is a firm?
A firm is an organization that converts
inputs such as labor, materials, energy,
and capital into outputs, the goods and
services that it sells.
Sole proprietorships are firms owned and
run by a single individual.
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.
What Owners Want?
Main assumption: firms owners try
to maximize profit
Profit () is the difference between
revenues, R, and costs, C:
=RC
What are the categories of
inputs?
Capital (K) - long-lived inputs.
land, buildings (factories, stores), and equipment
(machines, trucks)
Labor (L) - human services
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)
How firms combine the
inputs?
Production function is 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
Production Function
Inputs
(L, K)
Production
Function
q = f(L, K)
Output
q
Formally,
q = f(L, K)
where q units of output are produced using L
units of labor services and K units of capital
(the number of conveyor belts).
The production function may
simply be a table of numbers
The production function may
be an algebraic formula
Q 15 L K
Q 24 L 12 K
Q 18 min{24 L,12 K }
0.6
Just plug in
numbers for L and
K to get Q.
0.4
Marginal Product of Labor
Marginal product of labor (MPL ) - the
change in total output, Q, resulting from
using an extra unit of labor, L, holding
other factors constant:
Q
MPL
L
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
Production with Two Variable
Inputs
When a firm has more than one
variable input it can produce a given
amount of output with many different
combinations of inputs
E.g., by substituting K for L
7-11
Isoquants
An isoquant identifies all input
combinations (bundles) that
efficiently produce a given level of
output
Note the close similarity to indifference
curves
Can think of isoquants as contour lines
for the hill created by the production
function
7-12
K, Units of capital per d ay
Family of
Isoquants
6
The production function
above yields the isoquants
on the left.
b
f
q = 35
d
q = 24
q = 14
L, Workers per day
Properties of Isoquants
Isoquants are thin
Do not slope upward
Two isoquants do not cross
Higher-output isoquants lie farther
from the origin
7-15
Figure 7.10: Properties of
Isoquants
7-16
Figure 7.10: Properties of
Isoquants
7-17
Substitution Between Inputs
Rate that one input can be substituted for
another is an important factor for managers in
choosing best mix of inputs
Shape of isoquant captures information about
input substitution
Points on an isoquant have same output but different
input mix
Rate of substitution for labor with capital is equal to
negative the slope
7-18
Marginal Rate of Technical
Substitution
Marginal Rate of Technical Substitution
for labor with capital (MRTSLK): the
amount of capital needed to replace labor
while keeping output unchanged, per unit of
replaced labor
Let K be the amount of capital that can replace
L units of labor in a way such that total output
Q = F(L,K) is unchanged.
Then, MRTSLK = - K / L, and
K / L is the slope of the isoquant at the prechange inputs bundle.
Therefore, MRTSLK = - slope of the isoquant
Marginal Rate of Technical
Substitution
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
increase in capital K
MRTS
increase in labor
L
Slope of Isoquant!
How the Marginal Rate of Technical
Substitution Varies Along an Isoquant
K, Units of capital per d ay
MRTS in a Printing and Pu blishing U.S. Firm
16
K = 6
10
L = 1
3
c
1
2 1
7
5
4
d
e
q = 10
10
L, Workers per day
Substitutability of Inputs and Marginal
Products.
Along an isoquant output doesnt change (q =
0), or:
Extra units
Extra units
of labor
of capital
(MPL x L) + (MPK x K) = 0.
Increase in q per
extra unit of labor
or
Increase in q per
extra unit of capital
MPK K 0 MPL L
MPL
K
L
MPK
K
MPL
MRTS slope of isoquant
L
MPK
Figure 7.12: MRTS
7-23
MRTS and Marginal Product
Recall the relationship between MRS and
marginal utility
Parallel relationship exists between
MRTS and marginal product
MRTS LK
MPL
MPK
The more productive labor is relative to
capital, the more capital we must add to
make up for any reduction in labor; the
larger the MRTS
7-24
Figure 7.13: Declining
MRTS
We often assume
that MRTSLK
decreases as we
increase L and
decrease K
Why is this a
reasonable
assumption?
7-25
Extreme Production
Technologies
Two inputs are perfect substitutes if
their functions are identical
Firm is able to exchange one for another at a
fixed rate
Each isoquant is a straight line, constant MRTS
Two inputs are perfect complements
when
They must be used in fixed proportions
Isoquants are L-shaped
7-26
Substitutability of Inputs
Substitutability of Inputs
Returns to Scale
Types of Returns to Scale
Proportional change in
ALL inputs yields
What happens when all
inputs are doubled?
Constant
Same proportional change in
output
Output doubles
Increasing
Greater than proportional
change in output
Output more than
doubles
Decreasing
Less than proportional
change in output
Output less than doubles
7-29
Figure 7.17: Returns to
Scale
7-30
Returns to Scale
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).
Returns to Scale (cont).
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).
Returns to Scale (cont).
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).
Productivity Differences and
Technological Change
A firm is more productive or has
higher productivity when it can
produce more output use the same
amount of inputs
Its production function shifts upward at each
combination of inputs
May be either general change in productivity
of specifically linked to use of one input
Productivity improvement that leaves
MRTS unchanged is factor-neutral
7-34
The Cobb-Douglas Production Function
It one is the most popular estimated
functions.
q = ALK
Cobb-Douglas Production
Function
Q F L, K AL K
A shows firms general productivity level
and affect relative productivities of
labor and capital
MPL AL 1 K
MPK AL K 1
Substitution between inputs:
K
MRTS LK
7-36
Figure: 7.16: Cobb-Douglas
Production Function
7-37
