Production Analysis PPT @ BEC DOMS

8/3/2019 Production Analysis PPT @ BEC DOMS

1/26

Production Analysis and

Compensation Policy


2/26

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


3/26

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


4/26

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.


5/26


6/26

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.


7/26

Total, Marginal, and Average Product

Total Product

Total product is total output.


8/26


9/26

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.


10/26


11/26

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


12/26


13/26


14/26

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.


15/26


16/26

Marginal Rate of Technical

Substitution MRTSXY=-MPX/MPY

Rational Limits ofInput Substitution

MPX


17/26


18/26

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


19/26

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.


20/26


21/26

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


22/26

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


23/26


24/26

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.


25/26

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.


26/26

Production Analysis PPT @ BEC DOMS

Documents