Download 29 (b) Efficiency in Production

29 (b) Efficiency in Production
Production is a process of transforming inputs into outputs. The production function defines the
relationship between inputs and outputs. It defines the maximum amount of output that can be
produced using a given set of inputs (Baye 2006). Mathematically, the production function is as
follows:
Q = F (K, L)
Where Q = Quantity produced
K = Capital
L = Labor
Labor and Capital are considered as factors of production. In short run, Capital is considered as a
fixed factor of production i.e. amount of capital for production cannot be adjusted in order to
change the amount of output. Whereas in the long run all factors of production are considered
variable.
Productivity and Efficiency
According to Farrell (1957), economic efficiency has two components: Technical efficiency and
Allocative efficiency. Technical or productive efficiency focuses on levels of inputs relative to
levels of outputs. To be technically efficiency, a firm must either maximize its output for a given
level of inputs or minimize its inputs without sacrificing output levels. Productivity is a term
used to define the Technical efficiency of factors of production in a production function.
Different terms such as Total Product (TP), Average Product (AP) or Marginal Product (MP)
could be used for measuring productivity. The AP and MP of Labor and Capital can be
expressed as follows:
Q
Q
APL 
MPL 
L
L
Q
Q
APK 
MPK 
K
K
In many instances, Managers prefer to use Average Product for productivity measurement (Baye,
2006).
On the other hand, Allocative efficiency reflects the firm’s ability to allocate and use the
resources or inputs in optimal proportions based on reactions to market prices. These two
measures form Economic Efficiency. A productively efficient firm may not be economically
efficient because productive efficiency considers only inputs and outputs but economic
efficiency requires market price data in addition. According to Thomas F. Siems and Richard S.
Barr, allocative efficiency is about doing the right things, productive efficiency is about doing
things right and economic efficiency is about the doing the right things right.
As it was mentioned earlier, production function describes the relationship among input and
output variables. If we assume that, the inputs are constant then the target is to maximize the
outputs for a given level of inputs. Alternatively, we can consider the outputs as constants and
then the target is to minimize the inputs for that given level of output. Inefficiency is measured
by the amount of deviation from the optimal production level.
Figure 1: Technical Production Efficiency of Labor
600
500
Increasing
Marginal
Returns
400
300
Negative
Marginal
Returns
Diminishing
Marginal
Returns
TPL
200
100
APL
0
1
-100
2
3
4
5
6
7
8
9
10
11
12
MPL
13
Labor
In the following graph we see that, MPL is increasing upto 5 labor units. From 5 to 10 units is
MPL is decreasing but positive. After 10 units of labor, MPL is negative. When the firm inputs
less than 5 units of labor, it should continue to increase labor inputs because MPL is increasing,
hence the TPL. After 10 Units of labor it should not increase labor because more labor actually
reduces the TPL. So the production efficiency lies somewhere between 5 to 10 units of labor.
Continuous increase in the amount of a factor of production (such as Labor), will eventually lead
to a decrease in the marginal product of that factor. So we have to determine the optimal usage
of factors of production so that maximum profit could be achieved. The principle for maximizing
profit is
Marginal Benefit (MB) = Marginal Cost (MC)
So profit maximizing input usage for Labor VMPL (P X MPL) = w ; w =wage rate
And profit maximizing input usage for Capital VMPK (P X MPK) = r ; r = rent
Graphically,
Figure 2: Profit maximizing labor usage
w
Profit
maximizing
point
wo
VMPL
0
L
Lo
Another approach to determine the factors of production level is by minimizing cost. In this
analysis, the concept of Isocost and Isoquant are used. Isoquant defines the different
combinations of inputs (L, K) that produce the same level of output. Isocost defines the different
combinations of inputs (L, K) at same cost. The cost minimizing input rule suggests that,
optimal combinations of factors of production should be at that point where
Slope of Isocost = Slope of Isoquant
Mathematically
MPL w

MPK r
Graphically,
K
Point of Cost
Minimization
Slope of Isocost
=
Slope of Isoquant
Isoquant curve
K0
Q
Isocost lines
0
L0
L
From the graph we see the firm can produce Q units in different Isocost lines. But cost will be
minimized at point E where slope of Isocost and Isoquant are equal.