Managerial Economics
Chapter 5: Production Theory & Estimation
The organization of Production
Production
Production refers into the transformation of inputs or resources into outputs of goods and
services. Production refers to all of the activities involved in the production of goods and
services, from borrowing to set-up or expand production facilities, to hiring workers,
purchasing of raw materials, running quality control, cost accounting, and so on, rather
than referring merely to the physical transformation of inputs into outputs of goods and
services.
Inputs
Inputs are the resources used in the production of goods and services. As a convenient
way to organize the discussion, inputs are classified into labor (including entrepreneurial
talent), capital, and land or natural resources. Inputs are also classified as fixed or
variable.
Fixed Inputs
Fixed inputs are those that cannot be readily changed during the time period under
consideration, except perhaps at very great expense.
Variable Inputs
Variable inputs are those that can be varied easily and on very short notice. Examples of
variable inputs are most raw materials and unskilled labor.
The time period during which at least is fixed is called the short run, while the time
period when all inputs are variable is called the long run.
The Production Function
A production function is an equation, table, or graph showing the maximum output of a
commodity that a firm can produce per period of time with each set of inputs. Both inputs
and outputs are measured in physical rather than in monetary units. Technology is
assumed to remain constant during the period of the analysis.
For simplicity we assume here that a firm produces only one type of output commodity or
service) with two inputs, labor (L) and capital (K). Thus, the general equation of this
simple production function is
Q = ƒ(L,K)
In equation the quantity of output is a function of, or depends on, the quantity of labor
and capital used in production. Output refers to the number of units of the commodity
(say, automobiles) produced, labor refers to the number of workers employed, and
capital refers to the amount of the equipment used in production.
The Production Function with One Variable Input
By holding the quantity of one input constant and changing the quantity used of the other
input, we can derive the total product (TP) of the variable input. For example, by
holding capital constant at 1 unit (i.e., with K=1) and increasing the units of labor used
from zero to 6 units, we generate the total product of labor given by the 2 column in
Table bellow.
From the total product schedule we can derive the marginal and average product
schedules of the variable input. The marginal product (MP) of labor (MPL) is the
change in total product or extra output per unit change in labor used, while the average
product (AP) of labor (APL) equals total product divided by the quantity of labor used.
That is,
MPL 
TP
L
APL 
TP
L
Production or Output Elasticity of labor (EL) This measures the percentage change in
output divided by the percentage change in the quantity of labor. That is,
EL 
% Q
% L
Table: Total, Marginal, and Average Product of Labor, and Output Elasticity
(1)
(2)
(3)
(4)
(5)
Labor
TP
MP
AP
Elasticity of
Labor
0
0
1
3
3
3
1
2
8
5
4
1.25
3
12
4
4
1
4
14
2
3.5
0.57
5
14
0
2.8
0
6
12
-2
2
-1
Figure: Total, Marginal, and Average Product of Labor Curves
The top panel shows the total
product of labor curve. TP is
highest between 4L and 5L. The
bottom panel shows the marginal
and the average product of labor
curves. The MPL is plotted
halfway between successive units
of labor used. The MPL curve rises
up to 1.5L and then declines, and it
becomes negative past 4.5L. The
APL is highest between 2L and 3L.
Figure: The Law of Diminishing Returns and Stages of Production
With labor time continuously
divisible, we have smooth TP,
MP, and AP curves. The MPL
(Given by the slope of the
tangent to the TP curve) rise up
to point G/ , becomes zero at J/ ,
and is negative thereafter. The
APL (Given by the slope of the
ray from the origin to a point on
the TP curve) rise up to point H/
and declines thereafter (but
remains positive as long as TP is
positive). Stage I of production
for labor corresponds to the
rising portion of the APL. Stage
II covers the range from
maximum APL to where MPL is
zero. Stage III occurs when
MPL is negative.
Tshe Production Function with Two Variable
Inputs
Production ISOQuants
An isoquant swos the various combinations of
two inputs (say labor and capital) that the firm
can use to produce a specific level of output A
higher isoquant refers to a large output where a
lower isoquant refers to a smaller output.
Economic Region of Production
While the isoquants have positively sloped
potions, these portions are irrelevant. That is, the
firm would not operate on the positively sloped
portion of an isoquant because it could produce
the same level of output with less capital and less
labor.
Ridge lines separate the relevant (i.e., negatively
sloped) from the irrelevant (or positively sloped)
portions of the isoquants.
Marginal Rate of Technical
Substitution
The absolute value of the slope of
the isoquant is called the marginal
rate of technical substitute
(MRTS). For a movement down
along an isoquant, the marginal rate
jof technical substitution of labor for
capital is given by  K / L. We
multiply K / L by -1 in order to
express the MRTS as a positive
number. Thus, the MRTS between
points N and R on the isoquant for
12Q is 2.5. Similarly, the MRTS
between points R and is ½. The
MRTS at any point on an isoquant is
given by the absolute slope of the
isoquant at that point. Thus, the
MRTS at point R is 1.
ISOcost Lines
An isocost line shows the various combinations of inputs that a firm can purchase or hire
at a given cost. By the use of isocosts and isoquants, we will then determine the optimal
input combination for the firm to maximize profits.
Suppose that a firm uses only labor and capital in production. The total coists or
expenditures of the firm can then be presented by
C = wL + rK
Where C is total costs, w is the wage rate of labor, L is the quantity of labor used, r is the
rental price of capital, and K is the quantity of capital used. Thus, equation postulates that
the total costs of the firm © equals the sum of its expenditures on labor (wL) and capital
(rK). For example, if C = $ 100, w = $10, and r = $10, the firm could either hire 10L or
rent 10K, or any combination of L and L within the total cost of $ 100.
For each unit of capital the firm gives up, it can hire one additional unit of labor. Thus,
the slope of the isocost line is -1. By subtracting wL from both sides of Equation and then
dividing by r, we get the general equation of the isocost line is the following more useful
form:
C w
 L
r r
where C/r is the vertical intercept of the isocost line and –w/r is its slope. Thus, for
C=$100 and w = r = $10, the vertical intercept is C/r = $100/$10 = 10K, and the slope is
–w/r = -$10/$10 = -1. A different total cost y the firm would define a different but
parallel isocost line, while different relatives input prices would define an isocost line
with a different slope.
K
Returns to Scale
Returns to scale refers to the degree by which output changes as a result of a given
change in the quantity of all inputs used in production. There are three types of returns to
scale: constant, increasing, and decreasing. If the quantity of all inputs used in production
is increased by a given proportion, we have constant returns to scale if output increases
in the same proportion; increasing returns to scale if output increases by a greater
proportion; and decreasing returns to scale if output increases by a smaller proportion.
That is, suppose that starting with the general production function
Q   ( L, K )
we multiply L and K by h, and Q increases by 1, as indicated in Equation
Q  (hL, hK )
We have constant, increasing, or decreasing returns to scale, respectively, depending on
whether   h,   h, or , h.