In microeconomics, the production function is a representative of the relationship between the quantity of factor inputs and the yields that result from the production process. There are three measures of productivity namely total product; aggregate output, average product; output per unit of labor and marginal product; change in output as a result of a change in a unit of factor input (Hubbard & O’Brien, 2008). In defining the production function, it can be either short run or long run.
In the short run function, the assumption is that at least one-factor input is in fixed supply. Thus, only the quantity of one-factor input can be varied (Hubbard & O’Brien, 2008). In the short run production function, the three stages of production are defined by the interrelationship between marginal, average and total costs. Presented graphically, the first stage has a positive slope of average product curve up to the point where the marginal costs curve intersects with the average cost curve. The second stage of the production function continues up to the peak of the total product curve which corresponds with a marginal product curve with a slope equal to zero. The third stage is defined by a negatively sloped total product curve.
The law of diminishing marginal returns argues that as more units of a variable production factor input are combined with the fixed unit, it reaches a point where the marginal returns start to diminish (López, 2013). In the first stage of increasing marginal returns, the fixed factor is underutilized thus marginal productivity is increasing. In the second stage, marginal productivity is rising but at a decreasing rate meaning that additional units of the variable factor produce lower returns progressively. In the third stage, the cost of adding an extra unit of variable input outweighs the yields and thus generates negative marginal returns.
As seen from the above excel worksheet, marginal return increase up to the point where the number of fishermen is equal to three but then begin to diminish after that. Thus, the point of diminishing marginal return is where number of employees is equal to 4.
As show in the above excel worksheet, stage one of the short run production function characterized by increasing average product is between one unit of labor and three units of labor. The second stage continues up to the point where marginal product is positive beyond which the production function enters into the third stage.
At a market price of $3.5 and wage rate of $100 per unit of labor, the company should hire 7 fishermen since the yield the highest profits of $1995.
If the price for tune were to fall to $2.75 or rise to $5, the company would not change the number of fishermen employed because 7 fishermen would still yield the maximum profitability. It is important to note that so long as the company breaks even at the prevailing market price for tune, it will continue production so long as marginal product of an additional fisherman is positive.
In the above analysis, a crew size of above seven, irrespective of the market demand yields negative marginal productivity. Consequently, even in the case where the demand calls for a boat to catch at least 1000 pounds of fish, the company would still operate optimally with a crew of 7 fishermen.
The economic concept of diminishing marginal returns is a critical part of the theory of the firm, consequently, it is important to have an understanding of the concept for effective decision making. Identifying the defining characteristics of the three stages of the production function is relevant to business decisions for two reasons; First, managers with an understanding of the stages will be aware of how to change the units of labor to increase productivity and fully exploit the potential of a fixed factor of production(López, 2013). Second, understanding the three stages helps in determining the stages of production in an enterprise that is likely to yield the greatest profits. Moreover, managers can use the information to know when they must reduce the units of labor if the production process has become inefficient and wasteful.
The question on increasing the units of labor to meet market demand for a product is not relevant to business decisions because it is addressed once the optimal number of labor units is determined(Singh, 2013). Once a manager ascertains the optimal labor units, he is aware that increasing the units due to increased demand for a product will just add inefficiencies to the production process.
A firm’s efficiency is affected by size provided that the expansion of the firm is in tandem with productive efficiency. Therefore, I disagree with the statement that operating a large plan inefficiently is better than operating a small firm efficiently. The primary measure of efficiency is the ability to keep the costs of production low and not necessarily the increase in the size of a firm(Singh, 2013). Consequently, it is possible to have a small firm operating at maximum efficiency being more profitable than a big firm operating at less than maximum efficiency.
While economies of scale accrue from a firm’s increase in size, inefficiency can lead to diseconomies of scale and erode the advantages that would come with size. An inefficient firm, despite its big size would be characterized by high long run average costs which would erode profitability. On the other hand, a small firm operating efficiently would be characterized by low long tern average costs which would accelerate profitability.
I would agree with this statement for several reasons. First, it is true that as a company increases in size, fixed costs remain the same and do not vary with size. Therefore, increasing output would be accompanied solely by variable costs but would also derive lower average costs for the firm which has the potential to increase profitability(Singh, 2013). Second, economies of scale are synonymous with operational efficiency which means that additional units of output would be produced with greater efficiency which would gradually lower the average costs. Moreover, if a company has not fully exploited the potential of the fixed assets, retaining production at the current level would place a greater opportunity cost on the firm and prevent the firm from increasing its profitability.
Hubbard, R. & O’Brien, A. (2008). Economics. Upper Saddle River, N.J.: Pearson Prentice Hall.
López, A. (2013). Outsourcing and firm productivity: a production function approach. Empirical Economics, 47(3), 977-998. http://dx.doi.org/10.1007/s00181-013-0770-x
Singh, S. (2013). Micro economics. New Delhi: APH Pub. Corp.