Read and respond

ECO 518

Unit 3 Lecture This lecture will function as a guide to assist you in studying. It contains questions that you

should be able to answer after you read the chapters. As you read the text book think about the

questions posed below. The answers comprise the main topics and concepts that you should

know and understand after you have finished your readings. There are no quiz or test activities

associated with this lecture content.

Unit Learning Outcomes

Unit 3

ULO 1. Define the production function and explain the difference between a short-run and a

long-run production function

ULO 2. Decipher the law of diminishing returns and how it relates to the three stages of

Production explaining why a rational firm always tries to operate in stage II.

ULO 3. Compare and contrast the various types of inputs that go into a production function for a

manufacturing company and for a service company ULO 4. Explain the linkages between the production function and the cost function.

ULO 5. Delineate average cost, average variable cost, and average fixed cost.

CHAPTER SIX

The Theory and Estimation of

Production

Appendices are available under the chapter tab at the publisher’s website especially for

students.

http://wps.prenhall.com/bp_keat_managerial_7/236/60596/15512752.cw/index.html

KEY LEARNING POINTS The topics in this chapter represent the foundation for the economic analysis of supply. A firm’s

production function (input and resulting output) is discussed in addition to explaining the various

forms of production functions, law of diminishing returns and the three states of production. As

the authors explains, no matter how much revenue is generated by the marketing plan, if the

cost of production cannot be contained, the company will not be able to earn an acceptable

level of profit. In economics, the analysis of cost begins with the study of the production

function (P. 187).

The Production Function Defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology Q=f(X1, X2, ..., Xk) Q = level of output X1, X2, ..., Xk = inputs used in production Key Assumptions:

• Given ‘state of the art’ production technology

• whatever input or input combinations are included in a particular function, the output

resulting from their utilization is at the maximum level

For simplicity we will often consider a production function of two inputs: Q=f(X, Y) Q = output X = labor Y = capital Short-run production function shows the maximum quantity of output that can be produced

by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged.

Long-run production function shows the maximum quantity of output that can be produced by

a set of inputs, assuming the firm is free to vary the amount of all the inputs being used.

Ask yourself: What does the term Production Function refers to?

Short-run analysis of Total, Average, and Marginal Product Alternative terms in reference to inputs

• ‘inputs’

• ‘factors’

• ‘factors of production’

• ‘resources’

Alternative terms in reference to outputs

• ‘output’

• ‘quantity’ (Q)

• ‘total product’ (TP)

• ‘product’

Marginal product (MP) = change in output (Total Product) resulting from a unit change in a variable input Average product (AP) = Total Product per unit of input used

Figure 6.1 Short-Run Production with Y=2

• if MP > AP then AP is rising

• if MP < AP then AP is falling

• MP=AP when AP is maximized

X

Q MP

X 

 

X

Q AP

X 

• Law of diminishing returns: as additional units of a variable input are combined with a

fixed input, after some point the additional output (i.e., marginal product) starts to

diminish

• nothing says when diminishing returns will start to take effect

• all inputs added to the production process have the same productivity

Ask Yourself: What is the law of diminishing return? Why this law is considered a short-run

phenomenon?

The Three Stages of Production in the short run:

• Stage I: from zero units of the variable input to where AP is maximized (where MP=AP)

• Stage II: from the maximum AP to where MP=0

• Stage III: from where MP=0 on

In the short run, rational firms should be operating only in Stage II

• Q: Why not Stage III?  firm uses more variable inputs to produce less output

• Q: Why not Stage I?  underutilizing fixed capacity, so can increase output per unit by

increasing the amount of the variable input

What level of input usage within Stage II is best for the firm? The answer depends upon:

• how many units of output the firm can

• sell the price of the product

• the monetary costs of employing the variable input

Total revenue product (TRP) = market value of the firm’s output, computed by multiplying the

total product by the market price

TRP = Q · P

Marginal revenue product (MRP) = change in the firm’s TRP resulting from a unit change in

the number of inputs used

MRP = MP · P =

Total labor cost (TLC) = total cost of using the variable input labor, computed by multiplying

the wage rate by the number of variable inputs employed

TLC = w · X

Marginal labor cost (MLC) = change in total labor cost resulting from a unit change in the

number of variable inputs used

MLC = w

Summary of relationship between demand for output and demand for a single input:

X

TRP





A profit-maximizing firm operating in perfectly competitive output and input markets will be using

the optimal amount of an input at the point at which the monetary value of the input’s marginal

product is equal to the additional cost of using that input

MRP = MLC

Multiple variable inputs

Consider the relationship between the ratio of the marginal product of one input and its cost to

the ratio of the marginal product of the other input(s) and their cost.

Ask Yourself: What is the difference between a short-run and long-run production function?

Long-run Production Function In the long run, a firm has enough time to change the amount of all its inputs. The long run production process is described by the concept of returns to scale Returns to scale = the resulting increase in total output as all inputs increase If all inputs into the production process are doubled, three things can happen:

• output can more than double o ‘increasing returns to scale’ (IRTS)

• output can exactly double o ‘constant returns to scale’ (CRTS)

• output can less than double o ‘decreasing returns to scale’ (DRTS)

One way to measure returns to scale is to use a coefficient of output elasticity:

if EQ > 1 then IRTS if EQ = 1 then CRTS if EQ < 1 then DRTS

Returns to scale can also be described using the following equation:

hQ = f(kX, kY) if h > k then IRTS if h = k then CRTS if h < k then DRTS

Estimation of Production Function Examples of production functions:

• short run: one fixed factor, one variable factor

o Q = f(L)K • cubic: increasing marginal returns followed by decreasing marginal returns

o Q = a + bL + cL2 – dL3

• quadratic: diminishing marginal returns but no Stage I

k

k

w

MP

w

MP

w

MP 

2

2

1

1

inputsallinchangePercentage

QinchangePercentage 

Q E

o Q = a + bL - cL2

• Power function: exponential for one input Q = aLb

if b > 1, MP increasing if b = 1, MP constant if b < 1, MP decreasing

Advantage: can be transformed into a linear (regression) equation when expressed in log terms

• Cobb-Douglas function: exponential for two inputs Q = aLbKc

if b + c > 1, IRTS if b + c = 1, CRTS if b + c < 1, DRTS

Cobb-Douglas production function Advantages:

• can investigate MP of one factor holding others fixed

• elasticities of factors are equal to their exponents

• can be estimated by linear regression

• can accommodate any number of independent variables

• does not require constant technology Shortcomings:

• cannot show MP going through all three stages in one specification

• cannot show a firm or industry passing through increasing, constant, and decreasing

returns to scale

• specification of data to be used in empirical estimates

• Statistical estimation of production functions

• inputs should be measured as ‘flow’ rather than ‘stock’ variables, which is not always

possible

• usually, the most important input is labor

• most difficult input variable is capital

• must choose between time series and cross-sectional analysis

• Aggregate production functions: whole industries or an economy

• gathering data for aggregate functions can be difficult:

• for an economy … GDP could be used

• for an industry … data from Census of Manufactures or production index from Federal

Reserve Board

• for labor … data from Bureau of Labor Statistics

Ask Yourself: What are some of the problems of measuring productivity in actual work

situation?

Importance of Production Function in Managerial Decision Making Capacity planning: planning the amount of fixed inputs that will be used along with the variable

inputs.

Good capacity planning requires:

• accurate forecasts of demand

• effective communication between the production and marketing functions

Example: cell phones

• Asian consumers want new phone every 6 months

• demand for 3G products

• Nokia, Samsung, Sony, Ericsson must be speedy and flexible

Example: Zara

• Spanish fashion retailer

• factories located close to stores

• quick response time of 2-4 weeks

Application: call centers

• service activity

• production function is

• Q = f(X,Y)

• where Q = number of calls

• X = variable inputs

• Y = fixed input

Application: China’s workers

• is China running out of workers?

• industrial boom

• e.g. bicycle factory in Guangdong Provence

CHAPTER SEVEN

The Theory and Estimation of Cost

KEY LEARNING POINTS Chapter 7 states accounting data have generally been used to investigate short-run and long-

run cost functions. Economic and Accounting definitions of costs can differ substantially and

presents the researcher with a host of problems. Depending on how the data are collected,

adjustments for price, changes, geographic differentials, and other variations must be made.

This chapter discusses the use of cost, production and cost, short run and long run cost,

economics of scope and scale, supply chain management and ways companies have cut costs

to remain competitive.

The Importance of cost in Managerial Decisions Ways to contain or cut costs popular during the past decade

• most common: reduce number of people on the payroll

• outsourcing components of the business

• merge, consolidate, then reduce headcount

Definition and use of Cost in Economic Analysis • Relevant cost: a cost that is affected by a management decision

• Historical cost: cost incurred at the time of procurement

• Opportunity cost: amount or subjective value that is forgone in choosing one activity over the next best alternative

• Incremental cost: varies with the range of options available in the decision

• Sunk cost: does not vary in accordance with decision alternatives

Ask yourself: Can you name one relevant cost?

Relationship between Production and Cost Cost function is simply the production function expressed in monetary rather than physical units.

We assume the firm is a ‘price taker’ in the input market

• Total variable cost (TVC) = the cost associated with the variable input, found by

multiplying the number of units by the unit price

• Marginal cost (MC) = the rate of change in total variable cost

The law of diminishing returns (Chapter 6) implies that MC will eventually increase

Plotting TP and TVC illustrates that they are mirror images of each other. When TP increases

at an increasing rate, TVC increases at a decreasing rate

MP

W

Q

TVC MC 



 

Short-run Cost Function For simplicity use the following assumptions:

• the firm employs two inputs, labor and capital

• the firm operates in a short-run production period where labor is variable, capital is fixed

• the firm produces a single product

• the firm employs a fixed level of technology

• the firm operates at every level of output in the most efficient way

• the firm operates in perfectly competitive input markets and must pay for its inputs at a

given market rate (it is a ‘price taker’)

• the short-run production function is affected by the law of diminishing returns

• Short-run cost function

Standard variables in the short-run cost function:

• Quantity (Q) is the amount of output that a firm can produce in the short run

• Total fixed cost (TFC) is the total cost of using the fixed input, capital (K)

Standard variables in the short-run cost function:

• Total variable cost (TVC) is the total cost of using the variable input, labor (L)

• Total cost (TC) is the total cost of using all the firm’s inputs,

• TC = TFC + TVC Standard variables in the short-run cost function:

• Average fixed cost (AFC) is the average per-unit cost of using the fixed input K

AFC = TFC/Q

• Average variable cost (AVC) is the average per-unit cost of using the variable input L

AVC = TVC/Q

Standard variables in the short-run cost function:

• Average total cost (AC) is the average per-unit cost of all the firm’s inputs AC = AFC + AVC = TC/Q

• Marginal cost (MC) is the change in a firm’s total cost (or total variable cost) resulting from a unit change in output MC = TC/ Q = TVC/ Q

For a graphical example of the cost variables see page 261.

Important observations:

AFC declines steadily

• when MC = AVC, AVC is at a minimum

• when MC < AVC, AVC is falling

• when MC > AVC, AVC is rising The same three rules apply for average cost (AC) as for AVC

A reduction in the firm’s fixed cost would cause the average cost line to shift downward.

A reduction in the firm’s variable cost would cause all three cost lines (AC, AVC, MC) to shift.

Alternative specifications of the Total Cost function (relating total cost and output)

• cubic relationship as output increases, total cost first increases at a decreasing rate, then increases at an increasing rate.

Alternative specifications of the Total Cost function (relating total cost and output)

• quadratic relationship as output increases, total cost increases at an increasing rate

• linear relationship as output increases, total cost increases at a constant rate

Ask yourself: Changes in the Short-run total costs result from changes in which cost?

Long-run Cost Function In the long run, all inputs to a firm’s production function may be changed

• because there are no fixed inputs, there are no fixed costs

• the firm’s long run marginal cost pertains to returns to scale

• at first increasing returns to scale, then as firms mature they achieve constant returns,

then ultimately decreasing returns to scale

When a firm experiences increasing returns to scale:

• a proportional increase in all inputs increases output by a greater proportion

• as output increases by some percentage, total cost of production increases by some lesser percentage

Economies of scale: situation where a firm’s long-run average cost (LRAC) declines as output

increases. Diseconomies of scale: situation where a firm’s LRAC increases as output

increases. In general, the LRAC curve is u-shaped.

Reasons for long-run economies:

• specialization of labor and capital

• prices of inputs may fall with volume discounts in firm’s purchasing

• use of capital equipment with better price-performance ratios

• larger firms may be able to raise funds in capital markets at a lower cost

• larger firms may be able to spread out promotional costs

• Long-run cost function

Reasons for diseconomies of scale

• scale of production becomes so large that it affects the total market demand for inputs,

so input prices rise

• transportation costs tend to rise as production grows, due to handling expenses,

insurance, security, and inventory costs

• Long-run cost function

Review Figure 7.9 Capacity level and Short-Run Average Cost.

• In long run, the firm can choose any level of capacity

• Once it commits to a level of capacity, at least one of the inputs must be fixed. This then

becomes a short-run problem

• The LRAC curve is an envelope of SRAC curves, and outlines the lowest per-unit costs

the firm will incur over a range of output

Learning Curve Learning curve: line showing the relationship between labor cost and additional units of output. Downward slope indicates additional cost per unit declines as the level of output increases because workers improve with practice Learning curve:

• measured in terms of percentage decrease in additional labor cost as output doubles Yx = Kx

n

Yx = units of factor or cost to produce the xth unit K = factor units or cost to produce the Kth (usually first) unit x = product unit (the xth unit) n = log S/log 2 S = slope parameter

Economies of Scope Economies of scope: reduction of a firm’s unit cost by producing two or more goods or

services jointly rather than separately. This is closely related to economies of scale.

Supply Chain Management Supply chain management (SCM): efforts by a firm to improve efficiencies through each link of

a firm’s supply chain from supplier to customer

• transaction costs are incurred by using resources outside the firm

• coordination costs arise because of uncertainty and complexity of tasks

• information costs arise to properly coordinate activities between the firm and its suppliers

Ways to develop better supplier relationships

• strategic alliance: firm and outside supplier join together in some sharing of resources

• competitive tension: firm uses two or more suppliers, thereby helping the firm keep its

purchase prices under control

Ways Companies cut Costs to Remain Competitive • the strategic use of cost

• reduction in cost of materials

• using information technology to reduce costs

• reduction of process costs

• relocation to lower-wage countries or regions

• mergers, consolidation, and subsequent downsizing

• layoffs and plant closings

Global Application: Manufacturing Chemicals in China Review Manufacturing Chemicals in China, and consider the following:

• labor content relatively low

• high use of equipment and raw materials

• noncost reasons for outsourcing