Production

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Production

• ECO61 Microeconomic Analysis
• Udayan Roy
• Fall 2008

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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.

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What Owners Want?

• Main assumption firms owners try to maximize
  profit
• Profit (p) is the difference between revenues, R,
  and costs, C
• p R C

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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)

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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

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Production Function

• Production
• Function
• q f(L, K)

Output q
Inputs (L, K)

• 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).

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The production function may simply be a table of
numbers
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The production function may be an algebraic
formula
Just plug in numbers for L and K to get Q.
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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

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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

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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

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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

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Family of Isoquants
y
a
a
6
, Units of capital per d
The production function above yields the
isoquants on the left.
K
b
3
f
c
e
2
d
1
6
3
2
1
0
L
,
W
o
r
k
ers per d
a
y
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Figure 7.8 Isoquant Example
Productive Inputs Principle Increasing the
amounts of all inputs increases the amount of
output. So, an isoquant must be negatively sloped
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Properties of Isoquants

• Isoquants are thin
• Do not slope upward
• Two isoquants do not cross
• Higher-output isoquants lie farther from the
  origin

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Figure 7.10 Properties of Isoquants
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Figure 7.10 Properties of Isoquants
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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

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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
  pre-change inputs bundle.
• Therefore, MRTSLK - slope of the isoquant

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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

Slope of Isoquant!
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How the Marginal Rate of Technical Substitution
Varies Along an Isoquant
M
R
TS
in a P
r
inting and Pu
b
lishing
U
.
S
.
Fi
r
m
y
a
a
16
, Units of capital per d
b
10
K
3
c
1
7
d
2
1
5
e
1
4
1
0
1
2
3
4
5
6
7
8
9
10
L
,
W
o
r
k
ers per d
a
y
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Substitutability of Inputs and Marginal Products.

• Along an isoquant output doesnt change (Dq 0),
  or
• (MPL x ?L) (MPK x ?K) 0.
• or

Extra units of labor
Extra units of capital
Increase in q per extra unit of labor
Increase in q per extra unit of capital
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Figure 7.12 MRTS
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MRTS and Marginal Product

• Recall the relationship between MRS and marginal
  utility
• Parallel relationship exists between MRTS and
  marginal product
• 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

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Figure 7.13 Declining MRTS

• We often assume that MRTSLK decreases as we
  increase L and decrease K
• Why is this a reasonable assumption?

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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

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Substitutability of Inputs
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Substitutability of Inputs
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Returns to Scale
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Figure 7.17 Returns to Scale
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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).

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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) gt 2f(L, K).

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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) lt 2f(L, K).

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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

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The Cobb-Douglas Production Function

• It one is the most popular estimated functions.
• q ALaKb

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Cobb-Douglas Production Function

• A shows firms general productivity level
• a and b affect relative productivities of labor
  and capital
• Substitution between inputs

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Figure 7.16 Cobb-Douglas Production Function
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