Production function
No matter the objective of any business organization, achievement of efficiency in production or cost minimization for a given production activity appear to be one of the prime concern of the managers In the manager’s effort to minimize production costs, the fundamental questions he or she faces are:
- How can production be optimized or costs minimizes?
- What will be the behavior of output as inputs increase?
- How does technology help In reducing production costs?
- How can the least-cost combination of Inputs be achieved?
- Given the technology, what happens to the rate of return when more plants are added to the firm?
The Theory of Production Production theory generally deals with quantitative relationships, that is, technical and technological relationships between inputs, especially labor and capital, and between inputs and outputs. An Input Is a good or service that goes Into the production process. As economists refer to It, an Input Is simply anything which a firm buys for use In Its production process. An output, on the other hand, is any good or service that comes out of a production process.
Economists classified inputs as
- labor;
- capital;
- land;
- raw materials;
- time.
These variables are measured per unit of time and once referred to as flow variables. In recent times, entrepreneurship has been added as part of the production Inputs, though this can be measured by the managerial expertise and the ability to make things happen. Inputs are classified as either fixed or variable Inputs. Fixed and variable inputs are defined in both economic sense and technical sense. In economic sense, a fixed input is one whose supply is inelastic in the short run.
In technical sense, a fixed input is one that remains fixed (or constant) for certain level of output. A variable input is one whose supply in the short run is elastic, example, labor, raw terrestrial, and the like. Users of such inputs can employ a larger quantity in the short run. Technically, a variable Input Is one that changes with changes In output. In the long run, all Inputs are variable
3. 1 The Production Function
Production function is a tool of analysis used in explaining the input-output relationship. It describes the technical relationship between inputs and output in physical terms.
In its general form, it holds that production of a given commodity depends on certain specific Inputs. In Its specific form, it presents the quantitative relationships between Inputs and outputs. A production function may take the form f a schedule, a graph line or a curve, an algebraic equation or a mathematical model. The production function represents the technology of a firm. An empirical production function is generally so complex to include a wide range of inputs: land, labor, capital, raw materials, time, and technology.
These variables form the Independent variables In a firm’s actual production function. A firm’s long- run production function Is of the form: where Old = land and building; L = labor; K = capital; M = materials; T = technology; and, t = time. For sake of convenience, economists have reduced the number of variables used in a reduction function to only two: capital (K) and labor (L). Therefore, in the analysis of input-output relations, the production function is expressed as: Q = f(K, L) (3. 1. 2) Equation (3. 2) represents the algebraic or mathematical form of the production function. It is this form of production function which is most commonly used in production analysis. As implied by the production function (equation (3. 1. 2)), increasing production, Q, will require K and L, and whether the firm can increase both K and L or only L will depend on the time period it takes into account for increasing production, that is, whether he firm is thinking in terms of the short run or in terms of the long run.
Economists believe that the supply of capital (K) is inelastic in the short run and elastic in the long run. Thus, in the short run firms can increase production only by increasing labor, since the supply of capital is fixed in the short run. In the long run, the firm can employ more of both capital and labor, as the supply of capital becomes elastic over time. In effect, there exists two types of production functions: The short-run production function; and, The long-run production function
