MicroEconomics theory and application 12th by browning an zupan chapter 07

 Define total, average, and marginal product, and explain the law of diminishing marginal returns in the short-run setting when at least some inputs are fixed.. Relating Output to Input

MICROECONOMICS: Theory & Applications

By Edgar K Browning & Mark A Zupan

John Wiley & Sons, Inc.

12 th Edition, Copyright 2015

Chapter 7: Production

Prepared by Dr Della Lee Sue, Marist College

Learning Objectives

 Establish the relationship between inputs and output

 Define total, average, and marginal product, and explain the law of diminishing marginal returns in the short-run setting when at least some inputs are fixed

 Investigate the ability of a firm to vary its output in the long run when all inputs are variable

 Explore returns to scale: how a firm’s output response is affected by a

proportionate change in all inputs

 Describe how production relationships can be estimated and some different potential functional forms for those relationships

7.1 RELATING OUTPUT TO INPUTS

Establish the relationship between inputs and output.

Relating Output to Inputs

 Factors of production – inputs or ingredients mixed together by a firm through

its technology to produce output

 Production function – a relationship between inputs and output that identifies

the maximum output that can be produced per time period by each specific

combination of inputs

Q = f(L,K)

 Technologically efficient – a condition in which the firm produces the

maximum output from any given combination of labor and capital inputs

7.2 PRODUCTION WHEN ONLY ONE INPUT IS VARIABLE:

THE SHORT RUN

Distinguish between variable and fixed inputs.

Production When Only One Input is

Variable: The Short Run

 Fixed inputs - resources a firm cannot feasibly vary over the time period

involved

 Total product - the total output of the firm

 Average product - the total output (or total product) divided by the amount of

the input used to produce that output

 Marginal product - the change in total output that results from a one-unit

change in the amount of an input, holding the quantities of other inputs constant

Table 7.1

The Relationship Between Average and Marginal Product Curves

 When the marginal product is greater than average product, average product must be increasing

 When the marginal product is less than average product, average product must

be decreasing

 When the marginal and average products are equal, average product is at a maximum

Figure 7.1 - Total, Average, and Marginal

Product Curves

The Geometry of Product Curves

 Average product of labor (at a point)

 slope of a straight line from the origin to that point on the total product curve

 Marginal product of labor (at a point):

 change in total product with a small change in the use of

an input

 slope of the total product curve at that point

 steeper total product curve => output rises faster as more input is used => larger marginal product

Figure 7.2 – Deriving Average and

Marginal Product

The Law of Diminishing Marginal Returns

 A relationship between output and input that holds that as the amount of some input is increased in equal increments, while technology and other inputs are held constant, the resulting increments in output will decrease in magnitude

 Two keys points:

 At least one input is fixed.

 Technology must remain unchanged.

7.3 PRODUCTION WHEN ALL INPUTS ARE VARIABLE:

THE LONG RUN

Define total, average, and marginal product, and explain the law of

diminishing marginal returns in the short-run setting when at least some inputs are fixed.

Production When All Inputs Are Variable:

The Long Run

inputs is impractical

 Long run – a period of time in which the firm can vary all its inputs

 Variable inputs – all inputs in the long run

Production Isoquants

 Isoquant – a curve that shows all the combinations of inputs that, when used in

a technologically efficient way, will produce a certain level of output

Figure 7.3 - Production Isoquants

Marginal Rate of Technical Substitution

MRTS and the Marginal Products of

Inputs

MRTSLK = (-) ΔK/ΔL = MPL/MPK

MRTS and the Marginal Products of Inputs (Derivation)

Figure 7.4 - Isoquants Relating Gasoline and Commuting Time

7.4 RETURNS TO SCALE

Investigate the ability of a firm to vary its output in the long run when all inputs are variable.

Returns to Scale

 Constant returns to scale – a situation in which a proportional increase in all

inputs increases output in the same proportion

 Increasing returns to scale – a situation in which output increases in greater

proportion than input use

 Decreasing returns to scale – a situation in which output increases less than

proportionally to input use

Factors Giving Rise to Increasing Returns

 Division and specialization of labor

 Arithmetic relationship - “Volume” capacity increases faster than “area”

dimensions

 Large-scale technologies

Factors Giving Rise to Decreasing Returns

Inefficiency of managing large operations:

 Coordination and control become difficult

 Loss or distortion of information

 Complexity of communication channels

 More time is required to make and implement decisions

Figure 7.5 - Returns to Scale

7.5 FUNCTIONAL FORMS AND

EMPIRICAL ESTIMATION OF

PRODUCTION FUNCTIONS

Explore returns to scale: how a firm’s output response is affected by a proportionate change in all inputs.

Functional Forms and Empirical

Estimation of Production Functions

 Functional Forms

 Linear

 Q = a + bL + cK

 Multiplicative

 Cobb-Douglas production function: Q = aLbKc

 Empirical Estimation Techniques

 Survey

 Experimentation

 Regression analysis

Linear Forms of Production Functions

Multiplicative Forms of Production

Functions: Cobb-Douglas as an

Example

Exponents and Cobb-Douglas

Production Functions

• b + c > 1 increasing returns to scale

• b + c = 1 constant returns to scale

• b + c < 1 decreasing returns to scale

7.6 THE MATHEMATICS BEHIND

PRODUCTION THEORY*

Describe how production relationships can be estimated and some

different potential functional forms for those relationships.

The Marginal-Average Product

Relationship

The Marginal-Average Product

Relationship

Summary:

• Whenever MPL>APL, APL is increasing.

• Whenever MPL<APL, APL is decreasing.

• Whenever MPL=APL, APL is at a maximum.

(continued)

MRTS and the Ratio of Inputs’ Marginal Products

MRTS and the Ratio of Inputs’

Marginal Products

Summary

 Marginal product measures the additional output

produced when only one input is varied and other inputs are held constant.

 The slope of an isoquant (dK/dL), equals (minus) the ratio of the marginal products of the inputs.

 MRTS equals the ratio of marginal products.

(continued)

Some Additional Properties of Constant Returns to Scale Production Functions

 “Linear Homogeneous Function” – a production function that exhibits constant returns to scale

 Cobb-Douglas production function (example):

where 0<α<1

Some Additional Properties of Constant Returns to

Properties:

 Marginal products depend on relative input utilization

 MRTS depends on relative input utilization