MANAGERIAL ECONOMICS 11th Edition

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MANAGERIAL ECONOMICS 11th Edition

• By
• Mark Hirschey

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Production Analysis and Compensation Policy

• Chapter 8

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Chapter 8OVERVIEW

• 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
• Productivity Measurement

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Production Functions

• Production efficiency is what and how to
  produce.
• Production function A schedule (or table or
  mathematical equation) showing the maximum amount
  of output that can be produced from any specified
  set of inputs given the existing technology. The
  production function is a catalog of output
  possibilities.

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• Production functions are determined by
  technology, equipment and input prices.
• Discrete production function involve distinct
  patterns for input combinations.
• Continuous production functions employ inputs in
  small increments.

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Returns to Scale and Returns to a Factor

• Two important relations between inputs and
  outputs
• Returns to scale measure output effect of
  increasing all inputs.
• Returns to a factor measure output effect of
  increasing one input.

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Total, Marginal, and Average Product

• Total Product
• Total product is total output.
• Marginal Product
• Marginal product is the change in output caused
  by increasing input use.
• If MPX?Q/?Xgt 0, total product is rising.
• If MPX?Q/?Xlt 0, total product is falling (rare).
• Average product
• APXQ/X.

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Law of Diminishing Returns to a Factor

• Diminishing Returns to a Factor Concept As the
  number of units of the variable input increases,
  other inputs held constant, a point will be
  reached beyond which the marginal product
  decreases.
• MPX tends to diminish as X use grows.
• If MPX grew with use of X, there would be no
  limit to input usage.
• MPXlt 0 implies irrational input use (rare).

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Input Combination Choice

• Production Isoquants
• Isoquant is a curve that represents the different
  input combinations used to efficiently produced a
  specified output.
• Efficiency (technical efficiency) in this case is
  achieved when the maximum possible amount of
  output is produced at the lowest possible cost.

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Input Y
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Input X
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• Input Factor Substitution (page 246)
• Isoquant shape shows input substitutability.
• Perfect Substitutes Straight lines.
• Perfect Complements Right angles.
• Imperfect Substitutability C-shaped.

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Marginal Rate of Technical Substitution

• MRTS Amount of one input that must be
  substituted for another to maintain constant
  output.
• MRTSXY-MPX/MPY (Slope Isoquant)
• Slope Rational Limits of Input Substitution
• MPXlt0 or MPYlt0 are never observed.

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Marginal Revenue Product and Optimal Employment

• In order to understand HOW factors of
  productions should be combined for maximum
  efficiency, we need to shift from the analysis of
  the physical productivity of inputs to their
  economic productivity, or net revenue-generating
  capability.
• Marginal Revenue Product
• Amount of revenue generated by employing the last
  input unit.
• MRPx MPx x MRQ ?TR/?X.

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Returns to Scale

• Evaluating Returns to Scale
• Returns to scale show the output effect of
  increasing all inputs.
• Constant returns to scale When a given
  percentage increase in all inputs leads to an
  identical percentage increase in output
• Increasing returns to scale When the
  proportional increase in output is larger than an
  underlying proportional increase in input
• Decreasing returns to scale When output
  increases at a rate less than the proportionate
  increase in inputs

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• Output Elasticity and Returns to Scale
• Output elasticity Percentage change in output
  associated with a 1 change in all inputs.
• Output elasticity is eQ ?Q/Q ?Xi/Xi where Xi
  is all inputs (labor, capital, etc.)
• eQ gt 1 implies increasing returns.
• eQ 1 implies constant returns.
• eQ lt 1 implies decreasing returns.

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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 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.

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Self Test Problem 1
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Self Test Problem 2
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