1
Introduction to Production and Resource
Use
Unit 4
2
OBJECTIVES:
•
•
•
•
•
•
List the different types of firms and the goals of the firm
Define the various revenue, production cost and profit
concepts.
Calculate revenue, production cost and profit in the short
and long run.
Explain the relationship between different production cost
concepts and the law of diminishing returns.
Draw the total, average and marginal concepts and the
average and marginal cost curves.
Explain the concepts of isocosts, isoquants and least cost
combination
1. Conditions for Perfect Competition
3
Input or product market can be classified as perfectly
competitive if the following conditions are met:
 Homogeneous product: Products sold by one business
is a perfect substitute for the product sold by the
other businesses. Meaning the buyers in the market
can choose from a number of sellers.
 No barriers of entry and exit: Business can enter
and leave the sector without encountering any
barriers of entry. Resource must be free to move into
the sector without encountering barriers to entry
(e.g. patents, licensing).
4
1. Conditions for Perfect
Competition………


Many sellers of the product: No single seller has a
disproportionate influence on the price; all sellers are
price taker.
Perfect information exist: All participants in the market
have complete information regarding prices, quantities,
qualities, sources of supply and more.
When all this four conditions are met the market structure is perfectly
competitive. Perfectly competitive business is a price taker. For
example Maize meal farmer, there are thousands of producers
producing the same product (Maize meal), each has equal access to
maize information and has no ability to control the price.
Class Activity 1
5
i.
ii.
iii.
iv.
Indicate which of the following is True(T) or False (F)
One of the requirements of perfect competition is
that there must be a large number of buyers and
sellers of the product.
In a perfect competition there are barriers of
entry and exit.
Sellers do not have perfect knowledge of the
market conditions.
All the firms supplying a specific product in the
market together form the industry.
Producer Decision Making
6
Production - a process by which resources are
transformed into products or services that
are usable by consumers.
Producer Decision Making
7
Decisions a Producer Must Make
What to Produce?
How Much to Produce?
How to Produce?
These can be resolved by input-output
relationships.
Producer Decision Making
8
Resource (input) - A factor that can be used to
produce a product that can satisfy a human want or
desire.
Physical Relationships
Land - everything you see in viewing the earth’s surface.
Labor - physical act of performing a task.
Management - the sole responsibility of decision making.
Capital - every manufactured thing that can be used to aid
or enhance production.
Producer Decision Making
9
Different quantities and combinations of these four things
will produce different amounts of the product.
 Production Function
Y = Output
X = inputs (land, labor, capital & management)
Function Y = f ( x1, x2, x3, ..., xn )
This function is used to determine the level of output given
the units of inputs.
The Production Function
10


Production function: the relationship that
describes how inputs like capital and labor are
transformed into output.
Mathematically,
Q = F (K, L)
K = Capital
L = Labor
Figure 4.0: The Production Function
11
The Production Function
12




Long run: the shortest period of time required to alter the
amounts of all inputs used in a production process.
Short run: the longest period of time during which at least
one of the inputs used in a production process cannot be
varied.
Variable input: an input that can be varied in the short run.
Fixed input: an input that cannot vary in the short run.
Returns to Scale
13



How does output respond to increases in all inputs
together?
Suppose that all inputs are doubled, would output
double?
Returns to scale have been of interest to economists
since the days of Adam Smith
Returns to Scale
14

Smith identified two forces that come into operation
as inputs are doubled
 greater
division of labor and specialization of labor
 loss in efficiency because management may become
more difficult given the larger scale of the firm
Producer Decision Making
15
Constant Returns - if all inputs were increased in
a constant ratio, the output will increase by the
same percentage as the inputs.
Increase in X’s in constant ratio, will result in
proportional increases in Y.
Figure 4.1: Producer Decision Making
16
Total Physical Product Curve
Y
TPP
X = (1 acre of land ,
$1000 of capital, 1 week
of management time)
2 X = (2 acres of land ,
$2000 of capital, 2
weeks of management
time)
X produces 5 units of output
2 X produces 10 units of output
TPP = Total Physical Product
X
Producer Decision Making
17
Changing the Level of One Input
Law of diminishing returns - as successive
amounts of a variable input are combined with
a fixed input in a production process, the
total product will rise, reach a maximum,
then eventually decline.
Producer Decision Making
18
Changing the Level of One Input
TPP
TPP
X1 X2, X3,...,Xn


19
If the relationship of input X’s are combined in different
proportions or are varied so that some are held constant
while others are varied, to result in different levels of output,
the relationship can be represented by the function:
Where inputs to the left are variable and those on the right
are fixed/constant.
X1 X2, X3,...,Xn
TPP initially increases at an increasing rate, increase at a
decreasing rate and finally decreases.
Producer Decision Making
20
Changing the Level of One Input
Marginal Physical Product - the amount added
to total physical product when another unit
of the variable input is used.The change in
output that results from changing the
variable input by one unit, holding all other
factors constant. MPP will generally rise at
low levels of input use, then begin to fall as
input use rises.
Producer Decision Making
21
Marginal Physical Product
Y
TPP
Change in Y
Change in one unit of X
X1 X2, X3,...,Xn
Producer Decision Making
22
Marginal Physical Product
MPP =
Change in output
Change in input
TPP
=
Y
=
X1
X1
Producer Decision Making
23
Average Physical Product: Tells us how
productive the variabe resource is on
average or per unit of X1.
As TPP increases, APP also increases, but
only to the point along the TPP curve where
MPP and APP are equal. From that point
on, as X increases, APP falls and becomes
only zero when TPP becomes zero.
Producer Decision Making
24
Average Physical Product
APP =
Output
Input
Y
=
X1
Diminishing Marginal Returns

25
Law of diminishing Marginal returns: As ever
larger amounts of a variable input are
combined with fixed inputs, eventually the MPP
of the variable input will decline.
Table 1: TPP, APP and MPP schedule
26
Input
TPP
10
75
APP
7.5
20
30
17
14.5
40
50
12.5
13.0
60
70
MPP
6.2
10.8
Marginal Physical Product Curve


If Farmer adds another pound of fertilizer per
hectare, will maize yields increase? If yes, by how
much? Or would more fertilizer “burn out” the
crop and cause yields to decline? Does addition
of another employee expand output? All this
questions give rise to the concepts of MPP.
An important relationship exist between MPP and
TPP.
 Slope
27
of the TPP curve is approx. equal to the MPP.
 MPP measure the rate of change in output in
response to a change in the use of labour.
Relationships between
Product Curves
28





MPP reaches a maximum at inflection point
MPP = 0 occurs when TPP is maximum
MPP is negative beyond TPP max
Y
TPP
Drawing a line from the origin which is tangent to
the TPP curve gives APP max
At point where APP is max, MPP crosses APP
(MPP=APP)
X
Y



When MPP > APP, APP is increasing
When MPP = APP, APP is at a max
When MPP < APP, APP is decreasing
The relationship between TPP, APP, & MPP is
very specific.
If we have COMPLETE
information about one curve, the other two
curves can be derived.
APP
MPP is negative
MPP
X
Law of Diminishing Marginal
Physical Product
29

Law of Diminishing Marginal Physical
Product: As additional units of one input are
combined with a fixed amount of other inputs, a
point is always reached where the additional
product received from the last unit of added
input (MPP) will decline

This occurs at the inflection point
Stages of Production:
Rational & Irrational
30



The stage I of the production
function is between 0 and X1
units of X.
In stage I:
 TPP is increasing
 APP is increasing
 MPP increases, reaches a
maximum & decreases to
APP
Stage I is an irrational stage
because APP is still increasing
Y
I
TPP
X
Y
APP
0
X1
MPP
X
Stages of Production:
Rational & Irrational
31


The stage II of the production
function is between X1 and X2 units
of X.
Y
I
TPP
In Stage II:

TPP is increasing

APP is decreasing

MPP is decreasing and less than
APP, but still positive

RATIONAL STAGE BECAUSE
TPP IS STILL INCREASING
II
X
Y
APP
0
X1
X2
MPP
X
Stages of Production:
Rational & Irrational
32


Stage III of the production
function is beyond X2 level X
In Stage III:
 TPP is decreasing
 APP is decreasing
 MPP is decreasing and
negative

Y
I
TPP
II
III
X
Y
IRRATIONAL STAGE
BECAUSE TPP IS
DECREASING
APP
0
X1
X2
MPP
X
How Much Input to Use
33



Do not produce in Stage III, because more output
can be produced with less input.
Do not normally produce in Stage I because the
average productivity of the inputs continues to rise
in this stage.
Stage II is the “rational stage” of production.
Marginal Value Product
34
 total value product
MVP =
 input level
TVP = TPP × product selling price
If output price is constant:
MVP = MPP × product selling price
Marginal Input Cost
35
 total input cost
MIC =
 input level
TIC = amount of input × input price
If input price is constant:
MIC = input selling price
Table 2:Marginal Value Product, Marginal Input Cost
and the Optimum Input Level
36
Input
level
Total
physical
product
(TPP)
0
1
2
3
4
5
6
7
8
9
10
0
12
30
44
54
62
68
72
74
72
68
Marginal
physical
product
(MPP)
Total
value
product
(TVP) $
Marginal
value
product
(MVP) $
Marginal
input
cost
(MIC) $
12.0
18.0
14.0
10.0
8.0
6.0
4.0
2.0
-2.0
-4.0
0
24
60
88
108
124
136
144
148
144
136
24
36
28
20
16
12
8
4
-4
-8
12
12
12
12
12
12
12
12
12
12
input price = $12; output price = $2
The Decision Rule
37
MVP = MIC
If MVP > MIC, additional profit can be made by using more
input.
If MIC > MVP, less input should be used.
How Much Output to Produce
An alternative way to find the profit-maximizing point is to
find directly the amount of output that maximizes profit.
Producer Decision Making
38
Two - Variable Inputs and
Enterprise Selection
Three Types of Relationships Producers
Must Understand
39
1
Factor - Product relationship : This
functional relationship between
variable factor and its product.
is a
a
2
Factor - Factor relationship: Deals
with
choosing between competing factors.
Choosing the optimal proportion of the inputs
in order to efficiently produce output.
3
Product - Product relationship deals with
choosing between competing products.
Two-Variable Input Functions: Factor - Factor
40
A two production function has the the following form:
Q = f (K, L), where K and L can vary in amounts.




Different resource combinations are capable of producing a given quantity of output.
With two variable input function, reducing the quantity of one resource will reduce output
and also change MPP of the two inputs.
However, the producer does not have to accept a reduction of output as the only
possibility, because that loss of output may be regained by a compensating increase in
the quantity of the other input. This can be illustrated by the isoquant.
Different proportions of the inputs L and K can be used to produce a give amount of
output, such as Q.
Production Isoquants
41

In the long run, all inputs are variable & isoquants
are used to study production decisions
 An
isoquant is a curve showing all possible input
combinations capable of producing a given level of
output.
 Isoquants are downward sloping; if greater amounts of
labor are used, less capital is required to produce a
given output.
Typical Isoquants
42
(4.1)
Marginal Rate of Technical Substitution
43

The MRTS is the slope of an isoquant & measures
the rate at which the two inputs can be substituted
for one another while maintaining a constant level
of output
K
MRTS  
L
The minus sign is added to make MRTS a positive
number since K L , the slope of the isoquant, is
negative
Marginal Rate of Technical Substitution
44

The MRTS can also be expressed as the ratio of
two marginal products:
MPL
MRTS 
MPK
As labor is substituted for capital, MPL declines &
MPK rises causing MRTS to diminish
K MPL
MRTS  

L MPK
Input substitution
45



Resources are able to substitute for one another when the use
of one resource can be increased as a replacement for another
reduced in amount and still yield a given amount of product.
The ease or difficulty of substituting one resource for another is
made apparent by the shape of the isoquant, with its shape
determined by the rate at which resources substitute for
another.
Three basic types of relationships are discernible:

Perfect substitutes

Perfect complements

Imperfect substitutes
Perfect substitutes Fig 4.2
46
K
Perfect substitutes are able to replace one
another without affecting output.
For every unit decrease in one input a
constant unit increase in the other input will
hold output at the same level.
They have a constant slope or MRTS.
Example : Water From Well 1 and Water
from Well 2
Q
L
Perfect complements Fig 4.3
47
K
They are right angled implying that the
two inputs K and L must be used in fixed
proportion and they are not substitutable.
MRTS= 0.
Example: Tractor and Plow.
Q
L
Imperfect Substitutes Fig 4.4
48
K
The most common problem faced by
producers. Factors will substitute for one
another, but not at a constant rate. MRTS
diminishes as the amount of one input
increases. Successive equal incremental
reductions in one input, must be matched
by increasingly larger increases in the
other input in order to hold output
constant.
Example: Land and Fertilizer
As we decrease available land, we must use
increasingly more fertilizer to make up for
the lost land.
Q
L
Isocost
49
Isocost lines represent all combinations of
two inputs that a firm can purchase with
the same total cost.
C  wL  rK
C w
K  L
r r
C  Total Cost
w  Wage Rate of Labor ( L)
r  Cost of Capital ( K )
Isocost
50
•
Slope of an isocost curve is the negative
of the input price ratio (  w r )
• K -intercept is C r

Represents amount of capital that may be purchased if zero
labor is purchased
Optimal Combination of Inputs Fig 4.5
51
Isocost Lines
AB
C = $100, w = r = $10
A’B’
C = $140, w = r = $10
A’’B’’
C = $80, w = r = $10
AB*
C = $100, w = $5, r = $10
Optimal Combination of Inputs
52
• Minimize total cost of producing Q by
choosing the input combination on the
isoquant for which Q is just tangent to an
isocost curve
Two slopes are equal in equilibrium
 Implies marginal product per dollar spent on last unit of
each input is the same

MPL w

MPK
r
or
MPL MPK

w
r
53
Optimal Input Combination to Minimize Cost for
Given Output
(Figure 4.6)
Optimization & Cost
54

Expansion path gives the efficient (least-cost) input
combinations for every level of output
 Cost
minimization occurs at the point of tangency.
Expansion Path
55
(Figure 4.7)
Returns to Scale
56
f(cL, cK) = zQ

If all inputs are increased by a factor of c & output
goes up by a factor of z then, in general, a
producer experiences:



Increasing returns to scale if z > c; output goes up
proportionately more than the increase in input usage
Decreasing returns to scale if z < c; output goes up
proportionately less than the increase in input usage
Constant returns to scale if z = c; output goes up by the same
proportion as the increase in input usage
Sources of increasing returns to scale
57


Indivisibilities: Some technologies can only be
implemented at a large scale of production.
Subdivision of tasks: Larger scale allows increased
division of tasks and increases specialization.
Sources of decreasing returns to scale
58


Coordination inefficiencies: Larger organizations
are more difficult to manage.
Incentive problems: Designing efficient compensation
systems in large organizations is difficult.
59
THE VARIOUS MEASURES OF COST

Costs of production may be divided into fixed costs
and variable costs.
 Fixed
costs are those costs that do not vary with the
quantity of output produced.
 Variable costs are those costs that do vary with the
quantity of output produced.
Fixed and Variable Costs
60

Total Costs
 TC
= TFC + TVC
 Consider the following TC function:
TC= 30+18Q – 2.7Q2 + 0.15Q3
What is the TFC and TVC from this function?
Derive the Marginal cost function?
Fixed and Variable Costs
61

Average Costs
Average costs can be determined by dividing the firm’s costs
by the quantity of output it produces.
 The average cost is the cost of each typical unit of product.


Average Costs
Average Fixed Costs (AFC) = TFC/Q
 Average Variable Costs (AVC)= TVC/Q
 Average Total Costs (ATC) = AFC + AVC

Average and Marginal Costs
62

Marginal Cost
Marginal cost (MC) measures the increase in total cost that
arises from an extra unit of production.
 Marginal cost helps answer the following question:


How much does it cost to produce an additional unit of output?
(change in total cost) TC
MC 

(change in quantity)
Q
Class activity
63
a)
If a firm has the following total cost function: TC=
30+18Q-2.7Q2+0.15Q3.
Calculate the TC, VC, ATC, AVC and MC if this firm
is producing quantities that vary from 0-15.
Tabulate your values.
Total Revenue
64
TR = P x Q
E.g. N$20 x Q = 20Q
MR = ?
AR= 20Q / Q = 20
MR=P=D
IDENTIFICATION OF COSTS. WHAT
ARE COSTS?
65

Total Revenue


Total Cost



The amount a firm receives for the sale of its output.
The market value of the inputs a firm uses in production.
Profit is the firm’s total revenue minus its total cost.
Profit = Total revenue - Total cost
Costs as Opportunity Costs
66


A firm’s cost of production includes all the
opportunity costs of making its output of goods and
services.
Explicit and Implicit Costs
A
firm’s cost of production include explicit costs and
implicit costs.
 Explicit
costs are input costs that require a direct outlay of
money by the firm.
 Implicit costs are input costs that do not require an outlay of
money by the firm.
Economic Profit versus Accounting Profit
67


Economists measure a firm’s economic profit as total
revenue minus total cost, including both explicit and
implicit costs.
Accountants measure the accounting profit as the
firm’s total revenue minus only the firm’s explicit
costs.
Economic Profit versus Accounting Profit
68


When total revenue exceeds both explicit and
implicit costs, the firm earns economic profit.
Economic profit is smaller than accounting profit.
Figure 4.8 Economists versus Accountants
69
How an Economist
Views a Firm
How an Accountant
Views a Firm
Economic
profit
Accounting
profit
Revenue
Implicit
costs
Explicit
costs
Revenue
Total
opportunity
costs
Explicit
costs
Long-Run Costs
70

Long-run total cost (LTC) for a given level of output
is given by:
LTC = wL* + rK*
Where w & r are prices of labor & capital, respectively, &
(L*, K*) is the input combination on the expansion path that
minimizes the total cost of producing that output
Long-Run Costs
71

Long-run average cost (LAC) measures the cost per
unit of output when production can be adjusted so
that the optimal amount of each input is employed
is U-shaped
 Falling LAC indicates economies of scale
 Rising LAC indicates diseconomies of scale
 LAC
LTC
LAC 
Q
72
Long-Run Average Cost as the Planning Horizon
(Figure 4.9)
Self-study (Students to present in class)
73




Loss minimization and the shut-down rule
Short run supply curve
Long run equilibrium and economic efficiency
Consumer and producer surplus
NB: Make your own notes!! Page 109-113 study
guide.
74
The End!
QUESTION ?