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MANAGERIALMANAGERIAL

ECONOMICS 11ECONOMICS 11thth EditionEdition

ByBy

Mark HirscheyMark Hirschey

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Production Analysis andProduction Analysis and

Compensation PolicyCompensation PolicyChapter 8Chapter 8

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Chapter8Chapter8

OVERVIEWOVERVIEW Production Functions

Total, Marginal, and Average Product

Law of Diminishing Returns to a Factor

InputCombination 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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Chapter8 KEY CONCEPTSChapter8 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 function productivity growth labor productivity multifactor productivity

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Production Functions

Properties ofProduction 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 effectof increasing 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 outputcaused 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 Xuse grows.

If MPX grew with use ofX, 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 implyimperfect substitutability.

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Marginal Rate ofTechnical

Substitution MRTSXY=-MPX/MPY

Rational Limits of Input Substitution

MPX

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Marginal Revenue Product and

Optimal Employment Marginal Revenue Product

MRPL is the revenue gain after all variablecosts except labor costs.

MRPL= MPL x MRQ=TR/L.

Optimal Level of a Single Input

Set MRPL=PL to get optimal employment.

Illustration of Optimal Employment

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Optimal Combination of Multiple

Inputs Budget Lines

Least-cost production occurs when MPX/PX= MPY/PYand PX/PY= MPX/MPY

Expansion Path Shows efficient input combinations as output grows.

Illustration of Optimal InputProportions

Input proportions are optimal when no additionaloutput could be produce for the same cost.

Optimal input proportions is a necessary but notsufficient condition for profit maximization.

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Optimal Levels of Multiple Inputs

Optimal Employment and ProfitMaximization

Profits are maximized when MR

PX=

PX for allinputs.

Profit maximization requires optimal inputproportions plus an optimal level of output.

Illustration of Optimal Levels of MultipleInputs

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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 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 theBureau of Labor Statistics (since 1800s).

Productivity growth is the rate of change in outputper unit of input.

Labor productivity is the change in output per workerhour.

Uses and Limitations ofProductivity DataData Quality changes make productivity measurementQuality changes make productivity measurement

difficult.difficult.

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