Chapter 6 Production and Costs

Report
Production and Costs in the
Short Run
1
Overview
In this section we want to
1) Think about how production might occur and change
as different amounts of inputs are used in the
production process, and
2) Translate the production data into cost data. In other
words, we will want to understand how the cost of
producing various units of output might change as
different amounts of inputs are used.
2
Fixed/variable inputs
Inputs can be classified as either fixed or variable.
A variable input is one that can be changed as the level
of output is changed .
A fixed input is one that can not be changed as the level
of output is changed.
We often think of labor as a variable input and capital or
land as a fixed input.
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Short run/long run
The notion of a fixed or variable input is related to the
time frame of production.
The short run is that period of time when at least one
input is fixed in amount.
The long run is that period of time in which all inputs
are variable.
As an example of this consider fast food in Wayne.
About any store in town could remodel and increase
floor space in about 3 months. So after 3 months we
have the long run, all inputs can vary - even floor space.
But less than three months is the short run because there
is only so much floor space to use.
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example to illustrate some
ideas
Quantity of L
TP or Q
MPL
APL
0
0
1
5
5
5
2
12
7
6
3
21
9
7
4
28
7
7
5
33
5
6.6
6
36
3
6
7
37
1
5.285714
5
example continued
In the example, the relationship between the labor used
and the total product (TP) is called the short run
production function. Behind the scenes we assume there
is a given amount of capital.
The marginal product of labor is the additional output
forthcoming from the additional unit of labor. Note the
first unit of labor has a marginal product of 5.
Note that as the units of labor increases the marginal
product first increases, but then begins to diminish after
the third unit of labor is employed.
6
example continued
The marginal product curve has the pattern it does
because of the way the fixed input is used. Remember
that the variable input is used in conjunction with only
so much of the fixed input.
In the beginning, as more labor is added, specialization
of labor can occur and increasing returns to labor can
result, but eventually as more labor is added there will
be less of the fixed input to work with and thus
additions to output have to diminish.
The way output changes as the variable input is
changed, with a given amount of a fixed input, is
summarized with the phrase diminishing marginal
product.
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The average product of labor is for each amount of labor the
output produced divided by the labor amount.
The average product mimics, or follows, the marginal product. It
is just a math thing.
Next let’s look at some graphs.
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TP and MPL, APL
Marginal Product and Average Product of
Labor
40
35
30
25
20
15
10
5
0
10
MPL, APL
Total Product or Quantity
of output
TP or Q
8
6
MPL
4
APL
2
0
0
2
4
6
Units of labor given an amount of capital
8
0
2
4
6
8
Units of labor
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Notes about MPL and APL
Note
1) When the MPL is above the APL the APL rises.
2) When the MPL is below the APL the APL falls.
3) The APL continues to rise while the MPL is falling only
when the MPL is above the APL.
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short run costs
In the short run we will consider the fixed and variable
costs of production and how they change as more of the
variable input is used.
Definitions:
Total cost (TC) = Total variable cost(TVC) + Total fixed
cost (TFC).
Marginal cost(MC) = (change in TC)/(change in output).
where change in output = 1 when possible.
Average cost (AC) = TC/Q.
Average variable cost(AVC) = TVC/Q.
Average fixed cost(AFC) = TFC/Q.
Note that in the short run fixed costs must be paid
whether output is zero or 100,000 units.
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example
Let’s take the production example we had before and
translate the production data into cost data. Say the cost
of capital is $50 and the cost of labor is $15 per unit.
The next screen shows the continuation of our example.
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example to illustrate some
ideas
Q
VC
FC
TC
AVC AFC
5
15
50
65
3
12
30
50
80
2.5
21
45
50
95
2.14 2.38 4.52 1.67
28
60
50
110
2.14 1.79 3.93 2.14
33
75
50
125
2.27 1.52 3.79
3
36
90
50
140
2.5
1.39 3.89
5
37
105
50
155
2.84 1.35 4.19
15
10
AC
MC
13
3
4.17 6.67 2.14
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COST Curves
Totals
Averages and Marginal
150
VC
100
FC
TC
50
0
0
10
20
OUTPUT
30
40
Costs per unit
Dollar cost
200
16
14
12
10
8
6
4
2
0
AVC
AFC
AC
MC
0
10
20
30
40
OUTPUT
14
Idealized graph of per unit
costs
in
the
short
run
$/unit
AC
AVC
MC
Q
Note AVC and AC equal MC when AVC and AC are at
their minimum values.
15
When you look back at slide nine at the marginal product and
average product curves note that the horizontal axis is measuring
labor units used and the curves are inverted u-shaped curves.
When you look back at slide 14 at the marginal cost and various
average cost curves note that the horizontal axis is measuring
output units and the curves are u-shaped curves.
There is a relationship between these two graphs
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The marginal cost of production is the change in total cost divided
by the change in output.
The marginal product of labor is the change in output divided by
the change in labor.
MC = ▲TC/▲Q, and MPL = ▲Q/▲L, so
MC = ▲TC/(MPL ▲L) = price labor/MPL.
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