Transcript Understanding Markets: Supply and Demand

Production, Costs, and Supply
Principles of Microeconomics
Professor Dalton
ECON 202 – Fall 2013
1
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
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, labor, 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.
3
Costs
 Costs are incurred as a result of production.
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
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.
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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.
6
Normal Profit
 In neoclassical economics, all costs should
be included:
• wages represent the cost of labor
• Rental rate of capital represents the cost of
capital
• Rental rate of land represents the cost of land
• “normal profit [π]” represents the cost of
entrepreneurial activity
 normal profit includes reward for risk-bearing
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.
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QX = f(L, K, R, technology, . . . )
QX = quantity of output
L = labor input
K = capital 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.
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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.
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Long Run
 The long run is a period that:
• is short enough that technology is unchanged.
• all other inputs [labor, capital, 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
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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 capital [K] and land [R] are fixed or constant
in the short run, labor [L] is the variable input.
Output is changed by altering the labour input.
QX = f(L) Technology, K and R are fixed or
constant.
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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.
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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 = labor input
TPL = QX = output of good X
APL = average product [TP/L]
MPL = Marginal product [DTP/ DL]
TPL
APL =
L
DTPL
MPL =
DL
Maximum of APL is at the 3 input of
labor.
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
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Production in the Short Run
Production of Good X
Notice that the APL increases as the first
three units of labor are added to the
fixed inputs of K and R. The maximum
efficiency of Labor or maximum APL , given
our technology, plant and natural
resources is with the third worker.
As additional units of labor are added
beyond the third worker the
output per worker [APL ] declines.
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
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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
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
Labor
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Given the TP , the APL can calculated:
APL =
APL
10
8
6
4
.
.
TPL
L
.
.
.
..
.
APL
2
1
..
2
3
4
5
6
7
8
TPL
L
APL
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
4
9
Labor
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
.
.
.
Output,TP
QXL
Graphically the relationship
between APL and TPL can be shown:
M
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.
.
.
.
.
.
.
..
.
1
2
3
4
5
6
7
8
9 AP is 20/3 = 6.67 or slope of line 0Z.
L
Labor
APL
1
2
3
4
5
6
7
3 units of L produces 20Q,
8
9
Labor
As additional units of L are
added, AP falls.
The maximum AP is where
the ray with the greatest
slope is tangent to the TP.
18
30
.
25
20
.
.
.
TPL
.
35
.
Output, QX
MPL was calculated as
the change in TPL given a
change in L.
The first unit of labor added
4 units of output.
“Between” the 1st and 2cd units
of labor, Q increases by 6.
.
.
. .
.
.
.
.
.
.
.
.. . . .. .
.
.
.
.
15
10
5
4
0
APL 10
1
2
3
4
8
5
6
7
8
9
Labor
Note: Where MPL = APL, APL
is a maximum.
MPL = APL
6
4
L
MPL
TPL
0
1
-4
0
4-0
4
2
6
10
3
10
20
4
5
25
5
4
3
29
6
7
8
2
1
32
34
35
0
9
35
APL
MPL Remember: MP is graphed
2
1
2
3
4
5
6
7
8
9
Labor
at “between” units of L.
19
.
.
.
Output, QX
.
25
20
TPL
.
30
.
Z
35
Useful things to notice:
1. MPL is the slope of TPL.
.
.
. .
.
.
.
.
.
.
.
.. . . .. .
.
.
.
.
15
10
5
4
0
APL 10
1
2
3
4
5
6
7
8
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.
3. The APL is a maximum when:
a. MPL = APL ,
8 9 b. the slope of the ray from origin
Labor is tangent to TPL .
6
4
4. When MPL > APL the APL is
increasing. When MPL < APL the
APL is decreasing.
APL 5. When MPL is 0, the
MPL slope of TPL is 0, and TP
2
1
2
3
4
5
6
7
8
9
Labor
is a maximum.
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To calculate AP:
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
8
15
19
15
10
7
5
3
1
-1
APL =
AP
8.0
11.5
14.0
14.25
13.4
12.33
11.28
10.25
9.22
8.2
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.
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PRODUCTION
LABOUR
CAPITAL 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
8
15
19
15
10
7
5
3
1
-1
AP
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.
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.
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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
LABOR
CAPITAL
OUTPUT
AP
MP
0
5
0
0
--
1
5
8
8
8
2
5
23
11.5
15
3
5
42
14
19
4
5
57
14.25 15
5
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
23
The price of labor [PL] is $4 per unit and the price of capital [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
LABOR
CAPITAL
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
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
$34 $3.75 $ .50 $4.25
$38 $1.30 $ .35 $1.65
$ .38
$ .35 $.734
$ .37
$ .39 $.76
$ .36
$ .43 $.79
$ .49 $.86
$ .37
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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
LABOR
CAPITAL
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
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
$34 $3.75 $ .50 $4.25
$38 $1.30 $ .35 $1.65
$ .38
$ .35 $.734
$ .37
$ .39 $.76
$ .36
$ .43 $.79
$ .49 $.86
$ .37
25
MPL
APL
The average variable cost [AVC] and marginal cost [MC] are “mirror” images
of the AP and MP functions.
APL
APL
APL
MPL
AVC =
1
xw
MPL
1
x w
APL
L
$
The maximum of the AP is consistent with
the minimum of the AVC.
MC
APL
MC =
L3
MPL
L 1 L2
MPL
AVC
AVC
APL x L2
Q
26
MC will intersect the AVC at the
minimum of the AVC [always].
$
ATC
ATC*
R
AVC*
J
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.
27
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.
28
LONG RUN COSTS
$
MC1
ATC!
MC2
Plant ATC* is the
optimal size!
ATC2
ATC3
Cmin
Q*
LRMC
ATC5
ATC*
ATC*
ATC6
LRAC
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].
There is a long run marginal cost function.
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Long Run Average Costs
 LRAC is “U-Shaped”
 The LRAC initially decreases due to “economies of
scale”
• economies of scale are due to division of labor.
 Eventually, “diseconomies of scale” begin
• usually lack of adequate information to
manage the production process
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Calculating 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.
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