Chapter 5 Production analysis
and policy
KEY CONCEPTS
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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
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marginal rate of technical
ridge lines
marginal revenue product
economic efficiency
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 function
productivity growth
labor productivity
multifactor productivity
OVERVIEW
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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
一.Production Functions
1.Properties of Production Functions
2.Discrete production functions and
Continuous production functions
二. Returns to Scale and
Returns to a Factor
Returns to scale:
all inputs↑→ output effect
Returns to a factor:
one input↑→ output effect
三.Total, Marginal, and
Average Product
1.Total Product
– Total product is total output.
2. Marginal product: the change in output
caused by increasing input use.
MPX=∂Q/∂X
***If MPX> 0, TP↑
If MPX< 0, TP↓
3. Average product
APX=Q/X.
四. Law of Diminishing Returns
to a Factor
1. Definition:
MPX tends to diminish as X use grows.
2.Illustration
– If MPX ↑, then ?
– MPX< 0 then ?
五. Input Combination
Choice
• 1. Production Isoquants
**Technical efficiency is least-cost
production.
• 2. Input Factor Substitution
Isoquant shape ←→ input substitutability.
C-shaped isoquants: common
( imperfect substitutability)
3. Marginal Rate of Technical
Substitution
MRTSXY=-MPX/MPY
4.Ridge lines: Rational Limits of Input
Substitution
六. Optimal Combination of
Multiple Inputs
• 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 of Optimal 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
Optimal Levels of Multiple
Inputs
• Optimal Employment and Profit
Maximization
– Profits are maximized when MRPX = PX
for all inputs.
– Profit maximization requires optimal
input proportions plus an optimal level of
output.
• Illustration of Optimal Levels of
Multiple Inputs
七. Returns to Scale
• Evaluating Returns to Scale
– Returns to scale show the output effect of
increasing all inputs.
• Output Elasticity and Returns to Scale
– Output elasticity is εQ = ∂Q/Q ÷ ∂Xi/Xi
where Xi is all inputs (labor, capital, etc.)
• εQ > 1 implies increasing returns.
• εQ = 1 implies constant returns.
• εQ < 1 implies decreasing returns.
• Returns to Scale Estimation
八. Production Function
Estimation
• Cubic Production Functions
– Display variable returns to scale.
– First increasing, then decreasing
returns are common.
• Power Production Functions
– Allow marginal productivity of each
input to vary with employment of all
inputs.
九. 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 unit of input.
– Labor productivity is the change in output per
worker hour.
• Uses and Limitations of Productivity Data
– Quality changes make productivity
measurement difficult.