CHAPTER 4: PRODUCTION THEORY
Managers make production decisions in 2 different decision making
Short run production decisions and long run production decisions.
In short run decision making situations a manager must produce
with at least some inputs that are fixed in quantity.
In a typical short run situation the manager has a fixed amount of
plant & equipment with which to produce the firm’s output.
The manager can change production levels by hiring more or less
labor and purchasing more or less raw materials but the size of the
plant is viewed by the manager as essentially unchangeable or
fixed for the purposes of making production decisions in the short
Long run decision making concerns the same types of decisions
as the short run with one important distinction: the usage of all
inputs can be either increased or decreased or all inputs are
In the long run a manager can choose to operate in any size plant
with any amount of capital equipment.
Once a firm builds a new plant or changes the size of an existing
plant the manager is once again in a short run decision making
Economists think of the short run as the time period during
which production actually takes place and long run as the
planning horizon during which future production will take
After determining the demand for firms product the manager’s must
choose now the most profitable way to use the firm’s resources to
produce the good or service.
Simply stated, production issues are concerned with how scarce
resources (inputs) are used to produce the firm’s product or service
(output). A production function simply specifies the efficient
relationship between inputs and outputs.
Demand analysis gives total revenue, cost analysis gives total
cost of profit equation.
Costs evolve from production process so to understand costs
one should understand the production process.
Production is the creation of goods and services
from inputs like labor, machinery & other capital
equipment , land, raw materials, etc.
Firms have many types of inputs many of which can be grouped
into 3 broad categories:
i)Capital(K): Long-lived inputs like land, buildings(factories, stores)and equipment(machines, trucks).
ii)Labor(L): Human services such as those provided by managers, skilled workers(architects,
economists, engineers, accountants, plumbers) and less skilled workers(custodians, construction
laborers, assembly line workers).
iii)Materials(M): Raw goods(oil, water, wheat, electricity, fuel) and processed products(aluminum,
plastic, paper, steel).
1 The output can be a service such as an automobile tune-up by a mechanic or a physical product such
as a computer chip or a potato chip.
Inputs or factors of production are ingredients mixed together by a firm through its technology to
The theory of production is centered on the concept of a production function.
The Production Function for a product is a table , a graph or an equation showing
the maximum amount of output that can be produced from any specified set of inputs
given the existing technology at that time or state of the art of production.
A change in technology such as the introduction of more automated equipment or the
substitution of skilled for unskilled labor results in a new production function.
We will normally use capital and labor as the 2 inputs.
Hence the production function we will usually be concerned with is often written in a
mathematical form as: Q = f (K, L).
This states that the firm’s quantity of output depends on the respective quantity of labor(L) &
capital(K) used in production.
The Production Function with One Variable Input (Production in the
Thomas Machine Company in which there is one input whose quantity is fixed(K) and one
input(L) whose quantity is variable.
Fixed input is service of five machine tools, variable input is labor and the product is a
Table 4.1 & 4.2 and Figure 4.1 can be regarded as the production function where the
company is maximizing output of labor and machines it uses.
Numbers in Table 4.1 and Table 4.2 are derived from the relationship:
Q = 30L + 20L – L 3
The production function provides basic information concerning the nature of a firm’s production
Once the investment is made and the level of capital is fixed the firm is in the short run and
output can be changed only by varying the amount of labor employed and not plant and
It shows us the maximum total output that can be realized by using each combination of
quantities of inputs. This is Total Product.( Table 4.1 & Figure 4.1).
We will now discuss the different concepts in production theory.
Total Product(TP) is the maximum total output that can be realized by using each
combination of quantities of inputs. e.g. labor & capital.
TP rises reaches a maximum and then decreases.
The exact relationship between total product and labor called the Production function can be
illustrated by Table 4.1 & Figure 4.1 and by an equation :Q = f(L) where capital is fixed.
Returning to Thomas Machine Company we can calculate two other important concepts:
Average Product and Marginal Product of an input.
Average product of an input = total product divided by the total input used to produce this
amount of output.
Before hiring extra workers a manager may also want to know whether output will rise in
proportion to this extra labor.
Average Product(AP) of an input(labor) is the total product divided by the number of
laborers: AP of labor is the ratio of output to the number of workers used to produce that
output. AP = Q/L.
2 AP of labor which is the only variable input in this case first rises, reaches a maximum and
then declines thereafter.(Table 4.2 & Figure 4.2).
Marginal product of an input = the addition to total output resulting from the addition of the
last unit of the input when the amounts of other inputs used are held constant.
Before deciding whether to hire one more worker a manager wants to determine how much
this extra worker dL=1 will increase output dQ.
Marginal Product(MP) of an input(labor) is the additional output resulting from the use of one
additional laborer with the use of all other inputs fixed.(capital).
That is MP = dQ/dL
where ‘d’ indicates “the change in”. L stands for units of labor and Q stands for output.
Figure 4.2 shows the relationship. A definite relationship exists between the average and
marginal product curves.
When MP>AP, AP must be increasing as is shown in the figure.
If MP>AP, AP must rise.
o The Law of Diminishing Marginal Returns(LDMR): This concept is mentioned
because LDMR always occurs when there is one or more inputs that are fixed.
The law states that as the number of units of the variable input increase in equal increments,
other inputs held constant, a point will be reached beyond which the MP of the variable input
decreases.(as illustrated in Table 4.2 beyond 4 units of labor).
This law is the direct result of 1 or more input being fixed and the other input being variable (crowding
effect), applies in the short run.
o When the amount of the variable input is small relative to the fixed inputs, more
intensive utilization of fixed inputs by variable inputs may initially increase the marginal
product of the variable input as this input is increased.
o Nonetheless, a point is reached beyond which an increase in the use of the variable
input yields progressively less additional output (crowding effect).
o Each additional unit has, on average, fewer units of the fixed inputs with which to work.
o Do not confuse negative marginal product with Diminishing Marginal Product/Return.
o Example: Mel’s Hot Dog Restaurant sells hot dogs, french fries, and soft drinks. Mel’s
kitchen has one gas range for cooking the hot dogs, one deep fryer for cooking French
fries and one soft drink dispenser.
o 1)1 cook prepares 15 meals/hr combo of hot dog, fries & soft drink.
o 2)2 cooks 35 meals, MP=35-15=20 meals/hr. which is 5 more meals than first cook. 1
cook concentrates on making fries & soft drinks while the other prepares hot dogs.
o 3)3 cooks is 50 meals/hr, MP=50-35=15meals/hr. MP begins to decline.
o 4)4 cooks 60 meals/hr, MP=60-50=10 meals/hr.
o 5)5 cooks 65 meals/hr, MP=65-60=5 meals/hr.
o 6) The MP of additional cooks can even become negative. Adding a 6 cook reduces
the number of meals from 65 to 60. The MP=60-65=-5.
o Do not confuse negative MP with diminishing MP.
o Diminishing MP sets in with the 3 cook but MP does not become negative until the 6 th
cook, since output would fall.
The Optimal Level of Utilization of a Variable Input
If a firm has one fixed input(capital) and one variable input(labor), how much of the variable
input should it utilize?
To maximize profits , a firm should expand any activity as long as the marginal benefits exceed
the marginal costs.
3 This is a very important question for managers of business firms, large or small.
To maximize its profits the firm should utilize the amount of variable input labor where
MRP L= MEL
To answer this we must define the
Marginal Revenue Product(MRP L) of the variable input(labor) is the additional amount of
output that an additional unit of the variable input adds to the firm’s total revenue.
It can also be written as MRL = MR(MP L) which follows that MRP of variable input labor
equals the variable input’s marginal product(which can be few units of output) times the firm’s
So MRP L=MR(MP L).
Marginal Expenditure(ME ) is the amount that an additional unit of the variable input (labor)
adds to the firm’s total costs.
It should stop expanding it when the marginal benefiL) equals the marginal costL).
The MRP L is the amount that an additional unit of variable input adds to the firm’s total
That is, letting LRbe the marginal revenue product of input L.
Thus since dQ/dL equals MPLif follows that:
MRP L = MR(MP L) Equation 4.2
Which means that MRP L is the marginal product of the variable input labor times the marginal
revenue of the firm. The MP from 1 additional unit of labor could be few units.
The Marginal Expenditure is the amount that an additional unit of the variable input adds to the
firm’s total costs. That is, leLtbe the marginal expenditure of input L.
ME L= dTC
dL Equation 4.3
To maximize its profits the firm should set:
MRP L= ME L Equation 4.4
To maximize profits, a firm should expand any activity as long as the marginal benefits exceed the
marginal costs. It should expanding it when the marginal benefit) equals the marginal costs
Production Function With Two Variable Inputs.(Long-Run Production):
In the long run both inputs Labour(L) & Capital(K) are variable, which means, it is planning for
the future during which production will take place. No investment has taken place yet.
With both factors variable a firm can usually produce a given level of output by using:
i)a great deal of labor and very little capital,
ii) a great deal of capital and very little labor or
iii) moderate amounts of both.
That means the firm can substitute one input for another while continuing to produce the same
level of output in much the same way that a consumer can maintain a given level of utility by
substituting one good for another.
For example a lumberyard can produce
400 planks an hour with:
1)20 workers using hand saws,
2)8 workers using handheld power saws
3)4 workers using bench power saws.
Another example is an automobile assembly line can produce 2000 cars /hour by using 1)20
workers and 2 robot.
2) It can also produce 2000 cars by using only 4 workers and 6 robots.
4 To minimize the costs of producing 1000 cars the manager must determine the efficient combo
of inputs to use, to produce them.
An isoquant defines the combinations of inputs K & L that yield the producer the same level of
output. i.e. any combination of capital and labor along the same isoquant produces the same level of
In the Long- Run Production Decisions all inputs are variable.
We first develop some tools then we derive & set forth principles of
(1)cost minimization at a given level of output (output constraint)
(2)output maximization at a given level of cost.(cost constraint)
These principles follow directly from the principles o