Production and Cost Analysis in the Short Run

The table below shows the Average and Marginal product of labor for a hypothetical firm:

Amount of labor ( units) Amount of capital(No. of machines) The output of parts(Q, hundreds of parts) Average product (Q/L) Marginal product(∆Q/∆L)
0 5 0
1 5 49 49 49
2 5 132 66 83
3 5 243 81 111
4 5 376 94 133
5 5 525 105 149
6 5 684 114 159
6.6 5 792.59 120.09 108.59
7 5 847 121 163
8 5 1008 126 161
9 5 1161 129 153
10 5 1300 130 139
11 5 1419 129 119
12 5 1512 126 93
13 5 1573 121 61
14 5 1596 114 23
14 5 1575 105 -21

In the short run, it is not possible for accompany to vary the amount of all the inputs as there are fixed factors of production, namely capital. On the other hand, in the long run, each factor of production becomes variable. Hence, the firm can use different amounts of inputs to produce its output as well as alter the entire scale of production. The concept of returns to scale plays an important role in determining the average cost of a firm. Returns to scale are defined as the rate of change in output with respect to a change in the use of input. When the output increases more than the increase in the inputs, then it leads to Increasing Returns to Scale while a Decreasing Returns to Scale occurs when the rate of increase in output is less than the increase in inputs. Hence, it is evident that when Increasing Returns to Scale occurs, the average cost of production decreases. Similarly, when a firm undergoes decreasing returns to scale, the average total cost evidently rises, that is, there exist diseconomies of scale. When the change in output is the same as the change in inputs, then there exist Constant Returns to Scale (Lipsey and Chrystal, 2007, p. 156).

Using the table above Short-run average product (AP) curve and Short-run marginal product (MP) curve will be as shown below:

From the graph

From the graph and the table above three stages can be identified include:

  • Stage one. As the number of laborers is increased from 1 to 7 the average and marginal product increases (Increasing Returns to Scale).
  • Stage two: when the number of workers is increased and average product increases but marginal product remains the same (Constant Returns to Scale).
  • Stage three. This is when an increase in the number of workers increases average product but marginal product decrease (decreasing returns to scale).

There is only one stage in the short run because the company cannot increase its plant’s size or the number of factories. The only thing it can do to increase the production of its products is to increase the labor force. This is typical of a short-run phenomenon where capital is fixed and labor is variable. Hence, the company above will employ more workers to increase its production. This shows that the cost of the plants is considered a fixed cost. In the long run, that is, over a period of few years, the company can increase the number and size of its factories as well as shut down the old plants and build up new ones. This implies that the cost of plants is variable in the long run. Thus for the company, a time span of few months is akin to a short run whereas the time span of several years corresponds to the long run. This horizon varies from company to company. As the company moves along the average cost curve, it modifies the size of the plant according to the quantity of production (Mankiw, 2008, p. 280-281)

The company experiences economies of scale at low levels of output where the LRAC falls with a rise in output. At interim levels of output, it experiences constant returns to scale and when the long-run average cost rises at the increased level of output, it experiences diseconomies of scale. The economies of scale take place mainly due to specialization. This means that it occurs when the increase in the number of workers leads to specialization in their jobs. This is based on the division of labor concept of Adam Smith. (Dhamee, 1995, p. 2-3)Each worker experiences an increase in her/ his efficiency. For instance, if Ford hires a higher number of employees and manufactures a greater number of cars, it will experience a reduction in its costs by using technologically upgraded assembly-line production (Mankiw, 2008, p. 281). At lower levels of output, specialization would be beneficial because the coordination problems do not shoot up severely. Thus the long-run average cost of production falls at low levels of production in the absence of coordination problems due to an increase in specialization. At higher levels of output, there occur diseconomies of scale because the gains from specialization have already been accrued. There arises the severity of coordination problems at higher levels of production because of the increase in the size of the firm and management problems. This ultimately leads to diseconomies of scale (Mankiw, 2008, p. 280-281).

In the short run, when the company tries to increase its output, it does so by increasing the number of employees in its medium-sized plant. This will result in an increase in the average total cost because of the diminishing returns to scale. Again, in the long run, the firm is able to enlarge its plant size and also increase the number of factories as well as the labor force. This will result in the lowering of the average total cost and help in developing efficiencies. When there is an increase in a variable factor of production and the factor This is governed by the law of diminishing returns which states that as you add some successive units of one factor of production to a fixed amount of other factors the increment in total output with at first rise then decline. This law is true considering that the variable cost varies as per the production. The law of diminishing returns has a number of limitations this includes the method that is used in production, the amount of capital, and the raising in prices in factors of production.

References

Dhamee, Y. (1996). Adam Smith and the Division of Labour. The Victorian Web. Web.

Lipsey, R. G., & Chrystal, K. A. (2007). Economics. Oxford: Oxford University Press.

Mankiw, G. (2008). Economics Principles and applications. New Delhi: Cengage Learning India Private ltd.

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