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This is a PowerPoint presentation on the production
process and associated costs.
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R. Larry Reynolds 1997
Production
· Production is an activity where
resources are altered or changed and
there is an increase in the ability of
these resources to satisfy wants.
· change in physical characteristics
· change in location
· change in time
· change in ownership
Fall ‘ 97
Principles of Microeconomics
Slide -- 2
Production and Cost
·
Production is a technical relationship between a set of inputs
or resources and a set of outputs or goods.
QX = f( inputs
[land, labour, capital], technology, . . . )
[Legal and social/cultural institutions influence the production
function.]
·
·
Cost functions are the pecuniary relationships between
outputs and the costs of production;
Cost = f(QX {inputs, technology} , prices of inputs, . . . )
Cost functions are determined by input prices and
production relationships. It is necessary to understand
production functions if you are to interpret cost data.
Fall ‘ 97
Principles of Microeconomics
Slide -- 3
Costs
· Costs are incurred as a result of production. The
important concept of cost is opportunity cost
[marginal cost]. These are the costs associated
with an activity. When inputs or resources are
used to produce one good, the other goods they
could have been used to produce are sacrificed.
· Costs may be in real or monetary terms;
· implicit costs
· explicit costs
Fall ‘ 97
Principles of Microeconomics
Slide -- 4
Implicit Costs
· Opportunity costs or MC should include all costs
associated with an activity. Many of the costs are
implicit and difficult to measure.
· A production activity may adversely affect a
person’s health. This is an implicit cost that is
difficult to measure.
· Another activity may reduce the time for other
activities. It may be possible to make a
monetary estimate of the value.
Fall ‘ 97
Principles of Microeconomics
Slide -- 5
Explicit Costs
· Explicit costs are those costs where
there is an actual expenditure in a
market. The costs of labour or
interest payments are examples.
· Some implicit costs are estimated and
used in the decision process.
Depreciation is an example.
Fall ‘ 97
Principles of Microeconomics
Slide -- 6
Normal Profit
· In neoclassical economics, all costs
should be included:
·
·
·
·
wages represent the cost of labour
interest represents the cost of Kapital
rent represents the cost of land
“normal profit [ P ]” represents the cost
of entrepreneurial activity
· normal profit includes risk
Fall ‘ 97
Principles of Microeconomics
Slide -- 7
Production Function
· A production function expresses the
relationship between a set of inputs and
the output of a good or service.
· The relationship is determined by the
nature of the good and technology.
· A production function is “like” a recipe for
cookies; it tells you the quantities of each
ingredient, how to combine and cook, and
how many cookies you will produce.
Fall ‘ 97
Principles of Microeconomics
Slide -- 8
QX = f(L, K, R, technology, . . . )
QX = quantity of output
L = labour input
K = Kapital input
R = natural resources [land]
Decisions about alternative ways to produce good X require
that we have information about how each variable influences
QX.
One method used to identify the effects of each variable on
output is to vary one input at a time. The use of the ceteris
paribus convention allows this analysis.
The time period used for analysis also provides a way to
determine the effects of various changes of inputs on the
output.
Fall ‘ 97
Principles of Microeconomics
Slide -- 9
Technology
· The production process [and as result, costs]
is divided up into various time periods;
· the “very long run” is a period
sufficiently long enough that technology
used in the production process changes.
· In shorter time periods [long run, short
run and market periods], technology is a
constant.
Fall ‘ 97
Principles of Microeconomics
Slide -- 10
Long Run
· The long run is a period that:
· is short enough that technology is unchanged.
· all other inputs [labour, kapital, land, . . . ] are
variable, i.e. can be altered.
· these inputs may be altered in fixed or variable
proportions. This may be important in some
production processes.
· If inputs are altered, the output changes.
· QX = f(L, K, R, . . . ) technology is constant
Fall ‘ 97
Principles of Microeconomics
Slide -- 11
Short Run
· The short run is a period in which at least
one of the inputs has become a constant
and at least one of the inputs is a variable.
· If kapital [K] and land [R] are fixed or
constant in the short run, labour [L] is the
variable input. Output is changed by
altering the labour input. QX = f(L)
Technology, K and R are fixed or constant.
Fall ‘ 97
Principles of Microeconomics
Slide -- 12
Market Period
· When Alfred Marshall included time
into the analysis of production and
cost, he included a “market period” in
which inputs, technology and
consequently outputs could not be
varied.
· The supply function would be
perfectly inelastic in this case.
Fall ‘ 97
Principles of Microeconomics
Slide -- 13
Production in the Short Run
Consider a production process where K, R and technology are
fixed: As L is changed, the output
Production of Good X
changes, QX= f(L)
L = labour input
TPL = QX = output of good X
APL = average product [TP/L]
MPL = Marginal product [DTP/ DL]
L
DL = 1
TPLL
APLLL===
AP
L
DTPL
MPL =
DL
TPL
output
APL =
= Efficiency
=
L
input
Maximum of APL is at the 3 input of
labour.
Fall ‘ 97
Principles of Microeconomics
TPL
APL
0
1
0
0
DTPL=4
4
4
2
10
MPL
-4
5
6
3
20 6.67
10
4
25 6.25
5
5
29
5.8
6
32
5.3
4
3
7
34 4.87
8
35 4.37
2
1
9
35 3.89
0
Slide -- 14
Production in the Short Run
APL =
TPL
output
=
L
input
= Efficiency of
labour
Notice that the APL increases as the first
three units of labour are added to the
fixed inputs of K and R. The maximum
efficiency of Labour or maximum APL , given
our technology, plant and natural
resources is with the third worker.
As additional units of labour are added
beyond the third worker the
output per worker [APL ] declines.
Fall ‘ 97
Principles of Microeconomics
Production of Good X
L
TPL
APL
MPL
0
1
0
4
0
--
4
4
2
10
5
6
3
20
6.67
10
4
25
6.25
5
5
29
5.8
6
32
5.3
4
3
7
34 4.87
8
35 4.37
2
1
9
35 3.89
0
Slide -- 15
Graphically TPL can be shown:
TPL initially increases at an increasing
rate; it is convex from below.
.
.
.
.
.
.
.
.
.
.
TPL
Output, QX
35
Maximum
30 output
25
20
15
10
5
1
Fall ‘ 97
2
3
L
TPL
0
1
0
4
2
10
3
20
4
25
After some point it
then increases at a
decreasing rate and
reaches a maximum
level of output,
and declines
5
29
6
32
7
34
8
35
4
9
35
5
6
7
8
9
Labour
Principles of Microeconomics
Slide -- 16
Given the TP , the APL can calculated:
TPL
L
APL
TPL
= output = Efficiency of
L
labour
input
0
4
0
1
0
10
2
5
20
3
6.67
25
4
6.25
29
5
5.8
32
6
5.3
34
7 4.87
35
8 4.37
35
9 3.89
APL =
APL
10
8
6
4
.
.
.
.
.
.
.
APL
2
1
Fall ‘ 97
. ..
2
3
4
5
6
7
8
4
9
Labour
Principles of Microeconomics
Slide -- 17
30
25
20
15
.
.
5
4
0
APL 10
8
6
.
2
Z
The APL is the
slope of a
ray from
the origin
to the
TPL .
10
4
.
.
.
.
.
35
.
.
M
.
Output, QX
TPL
Graphically the relationship
between APL and TPL can be shown:
1 unit of L produces 4Q, APL is 4/1 = 4 or the
slope of line 0H.
H
2 units of L produces 10Q,
APL is 10/2 = 5 or the slope of line 0M.
3 units of L produces 20Q,
APL is 20/3 = 6.67 or the slope of line 0Z.
.
.
.
.
.
.
..
.
1
Fall ‘ 97 1
2
3
4
5
6
7
8
9
Labour
4 units of L produces 25Q,
APL is 25/4 = 6.25 or
the slope of line 0W.
As additional units of L are added,
the AP falls.
The maximum AP is where
APL the ray with the greatest
slope is tangent to the TP.
2
3
4
5Principles
6 7of Microeconomics
8 9
Labour
Slide -- 18
30
.
25
20
.
.
.
TPL
.
35
.
Output, QX
Given TPL , the APL was
calculated and graphed.
MPL was calculated as
the change in TPL given a
change in L.
The first unit of labour added
4 units of output.
“Between” the 1st and 2cd units
of labour, Q increases by 6.
.
.
. .
.
.
.
.
.
.
.
.. . . .. .
.
.
.
.
15
10
5
4
0
APL 10
1
2
3
8
MPL = APL
6
4
5
6
7
8
9
Labour
Note: Where MPL = APL, APL
is a maximum.
4
MP
APLL
TPL
0
1
-0
44
0
4-0
4
2
65
10
3
10
6.67
20
4
5
6.25
25
5
4
5.8
3
5.3
29
6
7
8
2
4.87
1
4.37
32
34
35
0
9 3.89
35
APL
MPL Remember: MP is graphed
2
Fall ‘ 97 1
L
2
3
4
at “between” units of L.
5Principles
6 7of Microeconomics
8 9
Slide -- 19
Labour
.
.
.
Output, QX
.
25
20
TPL
.
30
.
Z
35
Useful things to notice:
1. MPL is the slope of TPL.
2. When TPL increases at an increasing
rate, MPL increases. At the inflection
point in the TPL , MPL is a maximum.
When TPL increases at a decreasing rate,
MPL is decreasing.
.
.
. .
.
.
.
.
.
.
.
.. . . .. .
.
.
.
.
15
10
5
4
0
APL 10
1
2
3
4
8
5
6
7
3. The APL is a maximum when:
a. MPL = APL ,
b. the slope of the
8 9 ray from origin is tangent to
Labour TPL .
4. When MPL > APL the APL is increasing.
When MPL < APL the APL is decreasing.
6
4
APL
MPL
2
Fall ‘ 97 1
2
3
4
5Principles
6 7of Microeconomics
8 9
Labour
5. When MPL is 0, the
slope of TPL is 0, and TP
is a maximum.
Slide -- 20
Summary: TPL , MPL and APL
In many production processes
Q initially increases at an
increasing rate. This is due to
Z
TPL
division of labour and a “better”
mix of the variable input with the
fixed inputs.
At the
inflection
point
As Q [TPL ]increases at an increasing
rate, MP increases.
As Q [TPL ]increases at a
decreasing rate, MPL decreases.
Where 0Z is tangent to TPL , APL is a
maximum; APL = MPL .
0
MPL
APL
MPL is
a max
Fall ‘ 97
{MP> AP, AP rises}
Principles of Microeconomics
Diminishing
marginal
product
L
{MP< AP,
AP falls}
APL
When TPL is a maximum, MPL is zero.
When TPL is decreasing, MPL is
negative.
TPL
MPL
L 1 L2
L3
Slide -- 21
L
To calculate AP:
PRODUCTION
LABOUR
0
1
2
3
4
5
6
KAPITAL OUTPUT
5
DL= 1
5
DL= 1
0
8
5
23
5
42
DL= 1
DL=5 1
DL=5 1
DL=5 1
57
67
74
7
5
79
8
5
82
9
5
83
10
5
82
MP
APL =
AP
DTPL = 8
8 DTP8.0
L = 15
11.5
15DTP
L = 19
19 14.0
DTPL = 15
15DTP
14.25
L = 10
10 DTP
13.4
L= 7
7 12.33
5 11.28
3 10.25
1
9.22
-1
8.2
0 0 = ?
8 1 = 8
23 2 = 11.5
42 3 = 14
574 = 14.25
67 5 = 13.4
TPL
L
AP is a maximum
when L = 4.
Note that MP is
15 between 3rd & 4th
units of L, it is 10
between 4th & 5th,
so it equals
AP = 14.25 at L=4.
To calculate MP:
DTPL
MPL =
DL
MP is a maximum between 2cd and 3rd unit of L.
Fall ‘ 97
Principles of Microeconomics
Slide -- 22
PRODUCTION
LABOUR
KAPITAL OUTPUT
0
5
0
1
5
8
2
5
23
3
5
42
4
5
57
5
5
67
6
5
74
7
5
79
8
5
82
9
5
83
10
5
82
MP
AP
8
15
19
15
10
7
5
3
1
-1
0
8.0
11.5
14.0
14.25
13.4
12.33
11.28
10.25
9.22
8.2
Diminishing Marginal Productivity begins
with the 4rth unit of L.
Fall ‘ 97
As L is added to production
process, output per worker [AP]
increases. to a maximum
“efficiency” [output/input which
occurs at L = 4.
MP increases to a max between
the 2cd & 3rd units of L.
When MP > AP the output per
worker is increasing.
Division of Labour and a more
efficient mix of L, K & R causes
AP to increase.
Output per worker decreases
after the 4th worker. “Too
many” workers for K, R & tech,
MP< AP.
Principles of Microeconomics
Slide -- 23
The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6
per unit. Calculate the cost functions for this production process.
TFC = PK x K = $6K = 6 x5 = $30, This cost does not change in the short run.
TVC = PL x L = $4L, as L changes TVC and Output change.
PRODUCTION AND COST
LABOUR
KAPITAL
OUTPUT
AP
MP
=
0 x $4 5
0
0
--
=
1 x $4 5
8
8
8
=
2 x $4 5
23
11.5
15
=
3 x $4 5
42
14
19
=
4 x $4 5
57
14.25 15
=
5 x $4 5
67
13.4
10
6
5
74
12.33
7
7
5
79
11.28
5
8
5
82
10.25
3
9
5
83
9.22
1
10
5
82
8.2
-1
TFC
TVC
TC = TVC+TFC
TC
AFC
AVC
ATC
$30 + $ 0
+ $4
$30 =$30
+ $8
$30 =$34
+ $12
$30 =$38
$30 =$42
+ $16
$30 =$46
+ $20
=$50
$30 +
$24 =$54
$30 + $28
$30 =$58
+ $32
$30 =$62
+ $36
$30 =$66
+ $40
=$70
Fall ‘ 97
Principles of Microeconomics
Slide -- 24
The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6
per unit. Calculate the cost functions for this production process.
ATC = AVC + AFC = TCQ
AFC = TFCQ = $30Q
AVC = TVC Q
PRODUCTION AND COST
LABOUR
KAPITAL
OUTPUT
AP
MP
0
5
0
0
--
1
2
5
5
8
23
8
11.5
8
15
3
4
5
5
42
57
14
19
15
5
6
5
5
67
74
7
8
5
5
79
82
11.28
9
10
5
5
83
82
9.22
Fall ‘ 97
14.25
13.4
12.33
10.25
8.2
10
7
5
3
1
-1
TFC
TVC
TC
AFC
AVC
ATC
$30
$30
$30
$0
$4
$8
$30
$12
$30
$16
$30
$30
$20
$24
$42 $ .71 $ .29 $1.00
$46 $ .53 $ .28 $.81
$50 $ .45 $ .30 $.75
$54 $ .41 $ .32 $.729
$30
$28
$32
$36
$40
$58
$62
$66
$70
$30
$30
$30
$30
Principles of Microeconomics
$34 $3.75 $ .50 $4.25
$38 $1.30 $ .35 $1.65
$ .38
$ .35 $.734
$ .37
$ .39 $.76
$ .36
$ .43 $.79
$ .49 $.86
$ .37
Slide -- 25
Things to note . . .
As AP increases, AVC decreases.
When AP is a maximum, AVC is a minimum.
AFC declines so long as Q or output increases.
{Up to the point where TP becomes negative.}
Since AFC declines, it will “pull”
the ATC down as Q increases
beyond the minimum of the AVC.
PRODUCTION AND COST
LABOUR
KAPITAL
OUTPUT
AP
MP
0
5
0
0
--
1
2
5
8
8
8
5
23
11.5
15
3
4
5
42
14
19
5
57
14.25
15
5
6
5
67
13.4
10
5
74
12.33
7
7
8
5
79
11.28
5
5
82
10.25
3
9
10
5
83
9.22
1
5
82
8.2
-1
Fall ‘ 97
TFC
TVC
TC
AFC
AVC
ATC
$30
$30
$30
$0
$4
$8
$30
$12
$30
$16
$30
$30
$20
$24
$42 $ .71 $ .29 $1.00
$46 $ .53 $ .28 $.81
$50 $ .45 $ .30 $.75
$54 $ .41 $ .32 $.729
$30
$28
$32
$36
$40
$58
$62
$66
$70
$30
$30
$30
$30
Principles of Microeconomics
$34 $3.75 $ .50 $4.25
$38 $1.30 $ .35 $1.65
$ .38
$ .35 $.734
$ .37
$ .39 $.76
$ .36
$ .43 $.79
$ .49 $.86
$ .37
Slide -- 26
TPL is Q
TPL
TVC = L x PL
Z
When TP or Q
increases
at an
increasing
rate,
0
L1 L2
L2 x PL
TPL
L3
TVC
TVC increases at a decreasing rate.
L2 x PL
L1 x PL
L
Q* is the output
with the lowest
AVC! [Max AP]
Q*
Q
At L1 [inflection point] the MP is a maximum; the point of Diminishing Marginal
productivity begins, each additional worker increases output, but at a smaller and
smaller amount.
At L2 the AP is a maximum; output per worker is a maximum, “maximum efficiency;”
additional units of labour are less “productive.”
At L3 the TP is a maximum; this is the maximum amout of output [Q] that can
be produced given the size of the plant [fixed input K]. Additional [marginal] L is
negative.
Fall ‘ 97
Principles of Microeconomics
Slide -- 27
MPL
APL
The average variable cost [AVC] and marginal cost [MC] are “mirror” images
of the AP and MP functions.
APL
APL
APL
MPL
1
x PL
MP
1
AVC =
x PL
AP
L
$
The maximum of the AP is consistent with
the minimum of the AVC.
MC
APL
MC =
L3
MPL
L1 L2
MPL
AVC
AVC
APL x L2
Fall ‘ 97
Principles of Microeconomics
Q
Slide -- 28
MC will intersect the AVC at the
minimum of the AVC [always].
$
ATC
ATC*
AVC*
R
TC = ATC* x Q**
J
TVC = AVC* x Q*
AVC
MC will intersect the ATC
at the minimum of the ATC.
The vertical distance between
ATC and AVC at any output is
the AFC. At Q** AFC is RJ.
Q* Q**
Q
At Q* output, the AVC is at a minimum AVC* [also max of APL].
At Q** the ATC is at a MINIMUM.
Fall ‘ 97
Principles of Microeconomics
Slide -- 29
The Long Run
· The long run is a period of time where:
· technology is constant
· All inputs are variable
· The long run period is a series of short run
periods. [For each short run period there is a set of TP,
AP, MP, MC, AFC, AVC, ATC, TC, TVC & TFC for each
possible scale of plant]
Fall ‘ 97
Principles of Microeconomics
Slide -- 30
LONG RUN COSTS
$
MC1
ATC!
MC2
Plant ATC* is the
optimal size!
ATC2
ATC3
Cmin
Q*
LRMC
ATC5
ATC*
ATC*
ATC6
LRAC
There is a long run
marginal cost function.
At Q* the cost per unit are
minimized [the least inputs
used].
Q
For Plant size 1, the costs are ATC1 and MC1 :
For a bigger Plant 2, the unit costs move out and down. It is more cost
effective.
As bigger plants are built the ATC moves out and down.
Eventually, the plant size is “too large,” the ATC moves out but also up!
An “envelope curve” is constructed to represent the long run AC [LRAC].
Fall ‘ 97
Principles of Microeconomics
Slide -- 31
The LRAC
· LRAC is “U-Shaped”
· The LRAC initially decreases due to “economies of
scale”
· economies of scale are due to division of labour.
· Eventually, “diseconomies of scale” begin
· usually lack of adequate information to manage
the production process
Fall ‘ 97
Principles of Microeconomics
Slide -- 32
Calculation of LRAC
· With a little mathematics, the long
run cost functions can be calculated.
· It is easier to use equations rather
than tables and graphs.
· If consumer behavior, production and
cost is understood, you can then think
about how to achieve your objectives.
Fall ‘ 97
Principles of Microeconomics
Slide -- 33
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