The Firm and Production

Overheads

Neoclassical firm - Neoclassical firm -

A neoclassical firm is an organization

and earns the difference between

what it receives in revenue,

and what it spends on inputs (costs).

Nature of the firmNature of the firm

that controls the transformation of inputs(resources it owns or purchases)

into outputs(valued products that it sells),

Business firm

A business firm is an organization, owned and operated by private individuals, that specializes in production.

Production systems, goods, services and factors

A production system or technology is a description

of the set of outputs that can be produced

by a given set of factors of production or inputs

using a given method of production

or production process.

Production TechnologiesProduction Technologies

The technology set (technology for The technology set (technology for

short) for a given production process is short) for a given production process is

defined as the set of all input and defined as the set of all input and

output combinationsoutput combinations such that thesuch that the

output vector y can be produced fromoutput vector y can be produced from

the given set of inputs xthe given set of inputs x

A factor of production (input) is a good or

service that is employed in the production

process.

A product is a good or service that is

the output of a particular production

process.

Expendable factors of production are

raw materials, or produced factors that

are completely used up or consumed

during a single production period.

CapitalCapital is a stock that is not used up

during a single production period,

provides services over time, and

retains a unique identity.

Capital servicesCapital services are the flow of

productive services that can be obtained

from a given capital stock during a

production period.

It is usually possible to separate the right to use

services from ownership of the capital good.

They arise from a specific item of capital

rather than from a production process.

RevenueRevenueRevenue is the total income that comes fromthe sale of the output (goods and services)of a given firm or production process.

Revenue R(p , y) py

Revenue R(p , y) Σm

j 1pj yj

Cost

Cost is the value of all factors of production

used by the firm in producing

a given level of output,

If the input bundle used by a firm for a particular process is(x1, x2, . . . xn) , and wi is the price of the ith input, then

cost C(x , w) C Σn

i 1wi xi

whether a single product or multiple products.

Profit

The profit from a given production plan

π Σm

j 1pj yj Σ

n

i 1wixi

π p y w1x1 w2x2

π p y Σn

i 1wixi

is the revenue obtained from the plan

minus the costs of the inputs used to implement it

Objectives of the firm

We usually assume that firma exists to make money

Given this assumption we can set up the firm leveldecision problem as maximizing the returns fromthe technologies controlled by the firmtaking into account

Such firms are called for-profit firms.

• the demand for final consumption goods,• opportunities for buying and selling

factors (or products) from other firms• the actions of other firms in the market

In a perfectly competitive market, this meansthe firm will take prices as giventake prices as given,and choose the levels of inputs and outputsthat maximize profits

Objectives of the firm

Purely competitive marketsPurely competitive markets

When buyer or sellers in a market are

not able affect the pricenot able affect the priceof a product, we say that the market is purely competitive, or just, competitive.

Why firms?

Gains from specialization

One man draws out the wire, another straightens it, a third cuts it, a fourth points it,a fifth grinds it at the top for receiving the head: to make the head requires three distinct operations; to put it on is a [separate] business, to whiten the pins is another; it is even a trade by itself to put them into the paper; and the important business of making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are all performed by distinct hands.

Examples of gains from specialization

Assembly lines

Machines needed more than on person (2-person saw)

Learning by doing and improved skills

Learning by doing and economies of size

Lower transactions costs

Coordination of production

Lower transportation costs

Lower cost of price discovery or negotiation

Lower costs of making and enforcing contracts

Transactions costs are the time and other costsrequired to carry out and enforce the terms of marketexchanges (transactions)

Examples

Avoiding hold-up problems and opportunistic behavior

Reduced risk

Larger firms may be able to reduce incomerisk by diversification

Diversification is the process of reducing riskby spreading sources of income among differentalternatives

Problems with firms

Agency problems with employees

Lack of market discipline

Communication problems

We denote the set of all feasibleinput-output combinations by T

We describe the technological possibilitiesWe describe the technological possibilitiesfor the firm by its for the firm by its technology settechnology set

(technology for short)(technology for short)

For a given level of inputs, x,For a given level of inputs, x,we call this set the we call this set the Production Possibility SetProduction Possibility Set

just as we denote the set of all outputs produciblewith a given level of inputs x, by P(x)

A particular element of the technology setis called a production plan and we write

(x, y) T

Some input and output combinations (x, y)may not be elements of T

Such combinations are said to be infeasible

Production Functions

The production function is a functionthat gives the maximum output attainablefrom a given combination of inputs.

f(x) maxy

[y: (x, y) ε T]

maxy ε P(x)

[y]

The production function really only makes sensewith one output

y1

y2

P(x)

y

x

P(x1)

x1

The Production Possibility Set with One Output

The Production Function

y = f (x1, x2, x3, . . . xn )

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Input -x

Ou

tpu

t -y

y

y (bushels) = f (land, tillage, seed, fertilizer, … )

Examples

y Axα1

1 xα2

2 5x13

1 x14

2

y x 2 130x 3

y α1x α2x2 α3x

3

10x 20x 2 0.60x 3

The short run and the long run

The short run and the long run have to do withwhat is fixed for a given decision problem

The short-run is a time period brief enough that the firm can vary some, but not allvary some, but not all,of its inputs in a costless manner.

The long-run is a time period long enough that the firm can vary all of its inputs in a costless mannervary all of its inputs in a costless manner

If there are costs associated withvarying the level of an inputwe say that the firm experiences adjustment costs

Fixed inputs

A input whose quantity remains constantquantity remains constant,regardless of how much output is producedin the current decision periodcurrent decision period

is called a fixed inputfixed input

Variable inputs

A variable input is an input whose usage changesas the level of output changesin the current decision period

Fixed, variable, and sunk costs

Fixed costs are those costs that the firmis committed to pay for factors of production,regardless of the firm's current decisions

Suppose x2 = 10 and w2 = $50.

If x2 is fixed, then fixed cost = $500

C(y) 100 6y 0.4y 2 .02y 3

Suppose

Example of fixed costs

020406080100120140160

0 2 4 6 8 10 12 14 16 18 20Output - y

Co

st

FC

Sunk costs

The portion of fixed cost that is not recoverableif the firm liquidates, is called sunk cost

Example of a pizza restaurant

Sub-lease of land or a building

Sell off tables and chairs

Specialized pizza oven

Fixed cost = sunk cost + avoidable fixed cost

Variable costs

Variable costs are those costs that are affectedby the firm's actions in the current period

Variable costs occur because of the decisionto purchase additional factorspurchase additional factors or factor servicesfor use in production.

TVC Σn1

i 1wixi

n1 is the number of variable inputs

Variable Cost

0

100

200

300

400

500

0 5 10 15 20 25 30Output - y

Co

st

VC

Example of variable cost

TFC Σn

i n1

wi x̄i

Fixed costs

The bar over x denotes it is fixed

Fixed costs are those costs that the firmis committed to pay for factors of production,regardless of the firm's current decisions

Inputs n1 - n are all fixed

TC TVC TFC

Σn1

i 1wixi Σ

n

i n1

wixi

Σn

i 1wixi

Total costs

The sum of fixed cost and variable costis called fixed cost.

Example

x1 = cooks

x3 = brat buns

x2 = brats

x4 = grills

x5 = brat turners x6= charcoal

Variable Cooks, brats, buns, charcoal

Fixed Grills, brat turners

n = 6 n1 = 4

TVC w1x1 w2x2 w3x3 w4x4

TFC w5x5 w6x6

Variable and fixed cost

Example of total cost

0

100

200

300

400

500

0 5 10 15 20 25 30Output - y

Co

st

VC

TC

FC

Production in the short run

Total (physical) product - TP (TPP)

Total product (y) is the maximum quantityof output that can be producedfrom a given combination of inputs.

It is the value of the production function y = f (x1, x2 , . . . , xn )

Example numerical function

y f(x1 ,x2 ,x3 , ,xn)

f(x1 , x2)

1 200x1 20x2 40x 21 200x1x2 20x 2

2

2x 31 x 3

2

Story

x1 - number of laborers hauling hay

y - bales of hay hauled per hour

x2 - number of tractor-wagon combinations

Data with 1 tractor and wagonTotal

Input 1 Input 2 Product x1 x2 y (TPP)labor wagons bales0.00 0.00 ---1.0 1.0 38.02.0 1.0 144.03.0 1.0 306.04.0 1.0 512.05.0 1.0 750.06.0 1.0 1008.07.0 1.0 1274.08.0 1.0 1536.09.0 1.0 1782.010.0 1.0 2000.011.0 1.0 2178.012.0 1.0 2304.013.0 1.0 2366.014.0 1.0 2352.0

Total Product of Input 1 - x2 = 1

030060090012001500180021002400

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Input - x1

Ou

tpu

t -

y

y

Graph of total product

Marginal (Physical) Product

Marginal (physical) product is the increase inoutput that results from a one unit increase in a particular input

In discrete terms or average termsthe marginal product of the ith input is given as

where y1 and x1 are the level of output and input after the change in the input level and y0 and x0 are the levels before the change in input use.

MPi ΔyΔxi

y 1 y 0

x 1i x

0i

For small changes in xi, the marginal productis given by the derivative

MPi f(x)xi

yxi

Example calculations

Change x1 from 4 to 5

Input 1 Input 2 Productx1 x2 y (TPP)labor wagons bales0.00 0.00 ---1.0 1.0 38.02.0 1.0 144.03.0 1.0 306.04.0 1.0 512.05.0 1.0 750.06.0 1.0 1008.0

MP ΔyΔx1

750 5125 4

238

Change x1 from 1 to 2

MP ΔyΔx1

144 382 1

106

Using calculus

y f (x1 ,x2 ,x3 , ,xn)

1 200x1 20x2 40x 21 200x1x2 20x 2

2 2x 31 x 3

2

y x1

200 80x1 200x2 6x 21

y x1

200 (80)(2) (200)(1) (6)(22)

200 160 200 24

136

Graphical representation

Marginal Product of Input 1 - x2 = 1

-50050100150200250300

0 2 4 6 8 10 12 14Input - x1

Ou

tpu

t -

y

MPP 1

Average (physical) product

An average measure of the relationship betweenoutputs and inputs is given by the average product,

which is just the level of output divided bythe level of one of the inputs

APi f(x)xi

yxi

Example calculations

Average product at x1 = 5

AP1(5) yx1

7505

150

Average product at x1 = 2

AP1(2) yx1

1442

72

Input 1 Input 2 Productx1 x2 y (TPP)labor wagons bales0.00 0.00 ---1.0 1.0 38.02.0 1.0 144.03.0 1.0 306.04.0 1.0 512.05.0 1.0 750.06.0 1.0 1008.0

Graphical representation

Average and Marginal Product of Input 1

-50

0

50

100

150

200

250

300

2 4 6 8 10 12 14

Input - x1

Ou

tpu

t -

y MPP 1

APP 1

Discussion of marginal (physical) product

Increasing returns

When the marginal product rises (increases)as an input rises, we say that the marginal productof the input is increasing

When there are increasing returns, an additional unit of the input causes a larger increase in output than the previous unit.

When marginal product is increasing,total product is increasing at an increasing rate

Data with 1 tractor and wagonAverage

Total Average Marginal MarginalInput 1 Input 2 Product Product Product Productx1 x2 y (TPP) APP A MPPlabor wagons bales0.00 0.00 --- --- --- ---1.0 1.0 38.0 38.00 38.00 74.00 2.0 1.0 144.0 72.00 106.00 136.00 3.0 1.0 306.0 102.00 162.00 186.00 4.0 1.0 512.0 128.00 206.00 224.00 5.0 1.0 750.0 150.00 238.00 250.00 6.0 1.0 1008.0 168.00 258.00 264.00 7.0 1.0 1274.0 182.00 266.00 266.00 8.0 1.0 1536.0 192.00 262.00 256.00 9.0 1.0 1782.0 198.00 246.00 234.00 10.0 1.0 2000.0 200.00 218.0 200.00 11.0 1.0 2178.0 198.00 178.0 154.00 12.0 1.0 2304.0 192.00 126.0 96.00 13.0 1.0 2366.0 182.00 62.0 26.00 14.0 1.0 2352.0 168.00 -14.0 -56.00

Graphical representationTotal Product of Input 1

030060090012001500180021002400

0 2 4 6 8 10 12 14

Input - x1

Ou

tpu

t -

y

y

Average and Marginal Product of Input 1

-50

0

50

100

150

200

250

300

2 4 6 8 10 12 14

Input - x1

Ou

tpu

t -

y MPP 1

APP 1

Diminishing returns

When the marginal product falls (decreases)as an input rises, we say that the marginal productof the input is diminishing

When there are diminishing returns, an additional unit of the input causes a smaller(but positive) increase in output than the previous unit

When marginal product is decreasing,(but positive) total product is increasing at a decreasing rate.

The law of diminishing returns

The law of diminishing (marginal) returns states that as we continue to add more of any input (holding the other inputs constant), its marginal product will eventually decline.

Examples

fertilizer

hay wagons

counter workers

college administrators

Negative returns

When marginal product is negative,output actually falls with the additionof another unit of the input

Examples

fertilizer

water on a plant

cooks in a kitchen

Average, total and marginal product1. When the marginal curve is positive, the total curve will be rising

2. When the marginal curve is rising, the total curve will be rising at an increasing rate (becomes steeper)

3. When the marginal curve is positive but falling, the total curve will be rising at a decreasing rate (becomes flatter)

4. When the marginal curve is greater than the average curve, the average curve is rising

5. When the marginal and average curves are equal, the average curve does not change (is usually at a maximum or minimum point)

6. When the marginal curve is less than the average curve,the average curve is falling

7. For a production function MP and AP intersect at the maximum of APP

Intuition for average-marginal relationship

Cumulative GPA

Average test scores

The End