29 (b) Efficiency in Production
By Mohammad Aminul Karim


Production and Production Function
Production is a process of transforming inputs into outputs. The production function describes 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, p. 157). 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 the 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 efficient, a firm must either maximize its output for a given level of inputs or minimize its inputs without reducing output levels. On the other hand, Allocative efficiency reflects the firm’s ability to allocate and use the 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 (1998), allocative efficiency is about doing the things right , productive efficiency is about doing right things and economic efficiency is about the doing the right things right. There are four major methods for measuring efficiency (Coelli, Rao, O’Donnell & Battese, 2005, p. 6): These are

1. Least squares econometric production models
2. Total factor productivity (TFP) indices
3. Data envelopment analysis (DEA) and
4. Stochastic frontiers analysis (SFA)

Discussions of these methods are beyond the scope of this article.

Sometimes two terms; Productivity and Efficiency are used interchangeably. But they are not precisely the same. Productivity is the slope of a certain point in a feasible production set (a set of all input-output combinations). On the other hand, an input-output combination will be said technically efficient if it is on the production frontier (Production frontier represents the maximum output possible for a given set of input). A firm may be technically efficient but may still be able to improve it’s productivity by exploiting scale economies (Coelli, Rao, O’Donnell & Battese, 2005, p. 4). So to achieve optimum productivity, firm must be technically efficient and but not all technically efficient input-output combinations provide the optimal productivity.

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:

Equation.gif

In many instances, Managers prefer to use Average Product for productivity measurement (Baye, 2006, p. 159).

It was mentioned earlier that 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 given level of inputs. Alternatively, we can consider the output as constant 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

Figure-1---New.gif

From the above graph we see that, MP of Labor is increasing upto 5 labor units. From 5 to 9 units MP of Labor is decreasing but positive. After 9 units of labor, MP of Labor is negative. When the firm's labor input is less than 5 units, it should continue to increase labor inputs because MP Labor is increasing, hence the TP of Labor. After 9 Units of labor it should not increase labor because more labor actually reduces the TP of Labor. So the production efficiency lies somewhere between 5 to 9 units of labor.

If we consider the costs of inputs and price of output, this measure is Allocative efficiency. Allocative efficiency will be discussed in following sections from the view point of profit maximization and cost minimization.

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. 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 can be derived when

Equation3.gif

Here w = wage rate

And profit maximizing input usage for Capital could be derived when
Equation4.gif
Here r = rent

Graphically,
Figure 2: Profit maximizing labor usage
Figure-2.gif
Another approach to determine the efficient 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) where cost is same. 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
Equation2.gif
Alternatively, Marginal Rate of Technical Substitution (MRTS) = w/r

Graphically,
Figure 3: Optimum production level: Cost Minimization Rule.
Figure-3.gif

From the graph we see that the firm can produce Q units in different Isocost lines. But cost will be minimized at point E where slopes of the Isocost and the Isoquant are equal.

Input Substitution and Production Efficiency
What happens to production efficiency when the price of an input (such as labor) increases? If one input factor can be substituted for another and the firm continues to use the same combination of inputs after the price increase, then production efficiency may not be achieved. So the price change of one input (such as labor) may lead to the use of another input (such as capital) more and this is called Input Substitution. According to the optimal input substitution rule, to minimize the cost of production for a given level of output, the firm should use less of an input whose price rises and more of the other input (Baye 2006, p. 176). Usually when labor wages increase, firms try to lay off more workers and employ more automation (capital) to back to the efficient production level. Worker layoff at GM can be an example of input substitution and GM’s effort to achieve production efficiency. GM and Ford’s per hour wage rates were $45 and $43 respectively. Workers at GM and Ford produce an average of 27.9 and 33.2 vehicles per year respectively. To minimize the cost of production, GM should use less of it’s high priced labor and more of it’s capital so that it can achieve similar efficiency as Ford. In order to achieve that, GM reduced it’s work force by about 40,000 over a four year period (Baye, 2006 p. 156).

Social Welfare and Production Efficiency
Maximum social welfare and production efficiency could be achieved in a perfectly competitive market where marginal cost pf production is equal to the price of a product (Baye 2006, p. 279). If an industry produce output such that price exceeds marginal cost, it would be inefficient and social welfare could be improved expanding output until marginal cost of production is equal to price. Besides, in the long run competitive equilibrium, price equals the minimum point in the average variable cost curve. That means firm exhausted all economies of scale further improvement in production efficiency is not possible (Baye 2006, p. 280).

There are other factors rather than mere inputs can affect the efficiency in production. Technological advancement is such a factor (Jayasuriya & Wodon, 2005, p.121-140). Technological advancement could shift the Isocost, Isoquant or production frontier in a positive way. As a result, cost of production could be lower or amount of output could be higher or both could be achieved. There are other factors such as distribution efficiency, quality and flexibility in production can also affect the production efficiency.

Production efficiency could be used to compare intra-firm efficiency, inter-firm efficiency or even the efficiency among countries. In the later case, macroeconomic stability, market quality, urbanization and inflation rate may also affect productive efficiency (Jayasuriya & Wodon, 2005, p.121-140).

References
  1. Baye M., (2006), “Managerial Economics & Business Strategy”, New York: McGraw-Hill.
  2. Farrell, M.J. (1957) “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society 120(3):253-290.
  3. Siems T. F. and Barr R. S. (1998). “Benchmarking the productive Efficiency of U.S. Banks” Financial Industry Studies, Federal Reserve Bank of Dallas.
  4. Coelli T. , Sao D. S., O’Donnell C. & Battese G., (2005), “An Introduction to Efficiency and Productivity Analysis”, New York: Springer.
  5. Jayasuriya R. and Wodon Q. (2005). “Measuring and Explaining the Impact of Productive Efficiency on Economic Development”. The World Bank Economic Review. 19(1):121-140; 10/22/2007, http://wber.oxfordjournals.org/cgi/reprint/19/1/121


Multiple Choice Questions

1. Which of the following factor (s) of production is considered fixed in the short run?

a. Labor
b. Capital
c. Both
d. None

2. Which of the efficiency concept consider price or cost?

a. Technical efficiency
b. Allocative efficiency
c. None
d. Both

3. Managers prefer to use ___product for productivity measurement.

a. Total
b. Average
c. Marginal
d. None

4. Point of cost minimization is the point where slopeof isoquant is equal to slope of

a. Indifference curve
b. Isocost line
c. Budget constraint
d. None

5. Which of the following is NOT a method of measuring efficiency?

a. Least squares econometric production models
b. Total factor productivity (TFP) indices
c. Data envelopment analysis (DEA)
d. Capital Asset Pricing Model (CAPM)
e. Stochastic frontiers analysis (SFA)

Answers to Multiple Choice Questions
  1. b. Capital - It cannot be adjusted in the short run.
  2. b. Allocative efficiency - It considers input prices for efficiency measurement.
  3. b. Average Product - Average product provides a better view of efficiency than Marginal product. At a certain stage Marginal product could be higher but due to inefficiency in earlier stage Average product could be lower. So it provides better information for managers (Baye p. 159).
  4. b. Isocost line.
  5. d. CAPM - It measures risk return relationship rather than efficiency.