Post on 06-Apr-2018
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Production Analysis and
Compensation Policy
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OVERVIEW
Production Functions
Total, Marginal, and Average Product
Law of Diminishing Returns to a Factor
Input Combination Choice
Marginal Revenue Product and Optimal Employment
Optimal Combination of Multiple Inputs
Optimal Levels of Multiple Inputs
Returns to Scale
Production Function Estimation
Productivity Measurement
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KEY CONCEPTS
production function
discrete production function
continuous production function
returns to scale
returns to a factor
total product
marginal product
average product
law of diminishing returns isoquant
technical efficiency
input substitution
marginal rate of technical
ridge lines
marginal revenue product
economic efficiency
net marginal revenue
isocost curve (or budget line)constant returns to scale
expansion path
increasing returns to scale
decreasing returns to scale
output elasticity
power production functionproductivity growth
labor productivity
multifactor productivity
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Production Functions
Properties of Production Functions
Production functions are determined by
technology, equipment and input prices. Discrete production functions are lumpy.
Continuous production functions employ
inputs in small increments.
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Returns to Scale and Returns to a
Factor Returns to scale measure output effect of
increasing all inputs.
Returns to a factor measure output effect ofincreasing one input.
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Total, Marginal, and Average Product
Total Product
Total product is total output.
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Marginal Product
Marginal product is the change in output caused
by increasing input use.
If MPX=Q/X> 0, total product is rising.
If MPX=Q/X< 0, total product is falling (rare).
Average product
APX=Q/X.
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Law of Diminishing Returns to a
Factor Diminishing Returns to a Factor Concept
MPX tends to diminish as X use grows.
If MPX grew with use of X, there would be nolimit to input usage.
MPX< 0 implies irrational input use (rare).
Illustration of Diminishing Returns to a Factor
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Input Combination Choice
Production Isoquants
Technical efficiency is least-cost production.
Input Factor Substitution Isoquant shape shows input substitutability.
C-shaped isoquants are common and imply
imperfect substitutability.
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Marginal Rate of Technical
Substitution MRTSXY=-MPX/MPY
Rational Limits ofInput Substitution
MPX
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Marginal Revenue Product and
O
ptimalE
mployment Marginal Revenue Product
MRPL is the revenue gain after all variable costs
except labor costs.
MRPL= MPL x MRQ = TR/L.
Optimal Level of a Single Input
Set MRPL=PL to get optimal employment.
Illustration ofOptimal Employment
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Optimal Combination of Multiple
I
nputs Budget Lines
Least-cost production occurs when MPX/PX = MPY/PY and
PX/PY= MPX/MPY
Expansion Path Shows efficient input combinations as output grows.
Illustration ofOptimal Input Proportions
Input proportions are optimal when no additional output
could be produce for the same cost.
Optimal input proportions is a necessary but not sufficient
condition for profit maximization.
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Optimal Levels of Multiple Inputs
Optimal Employment and Profit
Maximization
Profits are maximized when MRPX
= PX
for all
inputs.
Profit maximization requires optimal input
proportionsplus an optimal level of output.
Illustration ofOptimal Levels of MultipleInputs
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Returns to Scale
Evaluating Returns to Scale
Returns to scale show the output effect of increasing allinputs.
Output Elasticity and Returns to Scale Output elasticity is Q = Q/Q Xi/Xi where Xi is all
inputs (labor, capital, etc.)
Q > 1 implies increasing returns.
Q = 1 implies constant returns. Q < 1 implies decreasing returns.
Returns to Scale Estimation
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Production Function Estimation
Cubic Production Functions
Display variable returns to scale.
First increasing, then decreasing returns arecommon.
Power Production Functions
Allow marginal productivity of each input to vary
with employment of all inputs.
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Productivity Measurement
How Is Productivity Measured?
Productivity measurement is the responsibility of the
Bureau of Labor Statistics (since 1800s).
Productivity growth is the rate of change in output per unitof input.
Labor productivity is the change in output per worker
hour.
Uses and Limitations of Productivity Data Quality changes make productivity measurement difficult.
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