Answer to Question #228430 in Microeconomics for Dam

Question

Describe how firms determine variable input and stage of production in matimatically and graphically

Answer 1

In production process, firms introduce factors required to create finished goods. These factors are also referred to as inputs or factors of production and can be fixed or variable inputs. The former refers to inputs such Capital (K) that remain unchanged over the short run stage of production where as the latter, variable inputs, are those factors such as Labor (L), or material inputs that change over the short run as the firms tries to adjust it's output to reach optimal level.

Mathematically, the combination of these inputs is well illustrated in what is referred to as a production function as shown below;

TP = f[L,K]

In the short run, the Total Product of L (TPL) is given by TPL= f[L].

As the firm continues to adjust the units of labor in its quest to reach optimal level, it becomes imperative to determine the contribution of each additional unit of labor i.e. Marginal Product of Labor (MPL).

MPL = $\frac{\Delta TP}{\Delta L}$

Optimal level of output is reached at a point where the MPL starts to deteriorate or decline. This is in tandem with the law of diminishing returns as shown in the graphs below.

The table below show the TPL and MPL; trees lumbered at different units of laborers (lumberjacks):

Total Products of Labor (TPL) from the above table can be graphically illustrated as shown below:

Whilst, Marginal Product of Labor is illustrated graphically as shown below:

Conclusion: Optimal production level is achieved at MP = 6 after which the Law of diminishing marginal returns come to play and it becomes uneconomical for the company to employ additional lumberjacks.