Sometimes
a fifth category is added, entrepreneurial and management skills, a subcategory
of labour services. Capital goods are those goods that have previously undergone
a production process. They are previously produced means of production. Some textbooks
use "technology" as a factor of production.
In
the “long run” all of these factors of production can be adjusted by
management. The “short run” however, is defined as a period in which
at least one of the factors of production is fixed. A fixed factor of production
is one whose quantity cannot readily be changed. Examples include major pieces
of equipment, suitable factory space, and key managerial personnel. A variable
factor of production is one whose usage rate can be changed easily. Examples include
electrical power consumption, transportation services, and most raw material inputs.
In the short run, a firm’s “scale of operations” determines the
maximum number of outputs that can be produced. In the long run, there are no
scale limitations.
Total,
average, and marginal product
Total
Product Curve
The
total product (or total physical product) of a variable factor of production identifies
what outputs are possible using various levels of the variable input. This can
be displayed in either a chart that lists the output level corresponding to various
levels of input, or a graph that summarizes the data into a “total product
curve”. The diagram shows a typical total product curve. In this example,
output increases as more inputs are employed up until point A. The maximum output
possible with this production process is Qm. (If there are other inputs used in
the process, they are assumed to be fixed.)
The
average physical product is the total product divided by the number of units of
variable input employed. It is the output of each unit of input. If there are
10 employees working on a production process that manufactures 50 units per day,
then the average product of variable labour input is 5 units per day.
Average
and Marginal Physical Product Curves
The
average product typically varies as more of the input is employed, so this relationship
can also be expresses as a chart or as a graph. A typical average physical product
curve is shown (APP). It can be obtained by drawing a vector from the origin to
various points on the total product curve and plotting the slopes of these vectors.
The
marginal physical product of a variable input is the change in total output due
to a one unit change in the variable input (called the discrete marginal product)
or alternatively the rate of change in total output due to an infinitesimally
small change in the variable input (called the continuous marginal product). The
discrete marginal product of capital is the additional output resulting from the
use of an additional unit of capital (assuming all other factors are fixed). The
continuous marginal product of a variable input can be calculated as the derivative
of quantity produced with respect to variable input employed. The marginal physical
product curve is shown (MPP). It can be obtained from the slope of the total product
curve.
Because
the marginal product drives changes in the average product, we know that when
the average physical product is falling, the marginal physical product must be
less than the average. Likewise, when the average physical product is rising,
it must be due to a marginal physical product greater than the average. For this
reason, the marginal physical product curve must intersect the maximum point on
the average physical product curve.
Diminishing
marginal returns
These
curves illustrate the principle of diminishing marginal returns to a variable
input (not to be confused with diseconomies of scale which is a long term phenomenon
in which all factors are allowed to change). This states that as you add more
and more of a variable input, you will reach a point beyond which the resulting
increase in output starts to diminish. This point is illustrated as the maximum
point on the marginal physical product curve. It assumes that other factor inputs
(if they are used in the process) are held constant. An example is the employment
of labour in the use of trucks to transport goods. Assuming the number of available
trucks (capital) is fixed, then the amount of the variable input labour could
be varied and the resultant efficiency determined. At least one labourer (the
driver) is necessary. Additional workers per vehicle could be productive in loading,
unloading, navigation, or around the clock continuous driving. But at some point
the returns to investment in labour will start to diminish and efficiency will
decrease. The most efficient distribution of labour per piece of equipment will
likely be one driver plus a fractional worker for other tasks (1.25 workers per
transport vehicle, say).
Resource
allocations and distributive efficiencies in the mix of capital and labour investment
will vary per industry and according to available technology. Trains are able
to transport much more in the way of goods with fewer "drivers" but
at the cost of greater investment in infrastructure. With the advent of mass production
of motorized vehicles, the economic niche occupied by trains (compared with transport
trucks) has become more specialized and limited to long haul delivery.
Many
ways of expressing the production relationship
The
total, average, and marginal physical product curves mentioned above are just
one way of showing production relationships. They express the quantity of output
relative to the amount of variable input employed while holding fixed inputs constant.
Because they depict a short run relationship, they are sometimes called short
run production functions. If all inputs are allowed to be varied, then the diagram
would express outputs relative to total inputs, and the function would be a long
run production function. If the mix of inputs is held constant, then output would
be expressed relative to inputs of a fixed composition, and the function would
indicate long run economies of scale.
Rather
than comparing inputs to outputs, it is also possible to assess the mix of inputs
employed in production. An isoquant (see below) relates the quantities of one
input to the quantities of another input. It indicates all possible combinations
of inputs that are capable of producing a given level of output.
Rather
than looking at the inputs used in production, it is possible to look at the mix
of outputs that are possible for any given production process. This is done with
a production possibilities frontier. It indicates what combinations of outputs
are possible given the available factor endowment and the prevailing production
technology.
Isoquants
There
are many ways of producing a given level of output. You can use a lot of labour
with a minimal amount of capital, or you could invest heavily in capital equipment
that requires a minimal amount of labour to operate, or any combination in between.
For most goods, there are more than just two inputs. For example in agriculture,
the amount of land, water, and fertilizer can all be varied to produce different
amounts of a crop. An isoquant, in the two input case, is a curve that shows all
the ways of combining two inputs so as to produce a given level of output. In
the three input case it will be a surface. Iso is Latin for equal and quant is
short for quantity. Movement along an isoquant depicts a constant rate of output,
but a changing input ratio. A unique isoquant can be constructed for every level
of output, and a family of isoquants can be created to represent various output
levels. Isoquants further from the origin represent greater amounts of output.
Isoquants are usually considered to be everywhere dense, meaning an infinite number
of them could be plotted in any two input space.
Isoquant
A
typical isoquant is illustrated in the diagram to the right. At point A in the
diagram Ka unit of capital is combined with La units of labour to produce 100
units of output. It is downward sloping, convex to the origin, and non-intersecting
(additional isoquants, not shown, would be drawn parallel to this one). A complete
isoquant is actually a closed curve, but only the “down sloping to the right”
portion makes economic sense. The upward sloping parts of isoquants, for example,
indicate that that level of output could be produced by less of both inputs so
this section is of little interest to decision makers. The economic section of
the isoquants is defined by a pair of lines called ridge lines.
The
“downward to the right” slope of the economic region of an isoquant
is due to the possibility of substituting one input for another in the production
process while keeping the level of output constant.
The
marginal rate of technical substitution
Isoquants
are typically convex to the origin reflecting the fact that the two factors are
substitutable for each other at varying rates. This rate of substitutability is
called the “marginal rate of technical substitution” (MRTS) or occasionally
the “marginal rate of substitution in production”. It measures the reduction
in one input per unit increase in the other input that is just sufficient to maintain
a constant level of production. For example, the marginal rate of substitution
of labour for capital gives the amount of capital that can be replaced by one
unit of labour while keeping output unchanged.
Marginal
Rate of Technical Substitution
To
move from point A to point B in the diagram, the amount of capital is reduced
from Ka to Kb while the amount of labour is increased only from La to Lb. To move
from point C to point D, the amount of capital is reduced from Kc to Kd while
the amount of labour is increased from La to Lb. The marginal rate of technical
substitution of labour for capital is equivalent to the absolute slope of the
isoquant at that point (change in capital divided by change in labour). It is
equal to 0 where the isoquant becomes horizontal, and equal to infinity where
it becomes vertical.
The
opposite is true when going in the other direction (from D to C to B to A). In
this case we are looking at the marginal rate of technical substitution capital
for labour (which is the reciprocal of the marginal rate of technical substitution
labour for capital).
It
can also be shown that the marginal rate of substitution labour for capital, is
equal to the marginal physical product of labour divided by the marginal physical
product of capital.
In
the unusual case of two inputs that are perfect substitutes for each other in
production, the isoquant would be linear (linear, a straight line, with a function
y = a - bx). If, on the other hand, there is only one production process available,
factor proportions would be fixed, and these zero-substitutability isoquants would
be shown as horizontal or vertical lines.
See
also
production,
costs, and pricing
production functions
long-run cost and production functions
production possibility frontier
cost-of-production theory of value
isoquant
Economics,
Banking & Finance
