Law of Returns to Scale || The Concept of Short Run || The Concept of the Long Run

Law of Returns to Scale

The law of returns is sometimes misunderstood as the law of returns to scale. The law of returns applies in a limited time frame. It describes the firm's production behaviour by changing one element while holding the others constant. The law of returns to scale, on the other hand, acts over a lengthy period. It explains the firm's production behaviour with all variable elements.

It has been found that when the amounts of inputs are changed proportionally, the behaviour of the output differs. The output may rise in a large proportion, a similar proportion, or a lesser proportion to its inputs. The behaviour of output as the scale of operation increases is referred to as growing returns to scale, constant returns to scale, and declining returns to scale.

These three rules of returns to scale are now briefly presented under distinct headings:

(1)  Increasing Returns to Scale:

When a firm's output grows more than proportionally to an equal percentage increase in all inputs, the output is said to display growing returns to scale.

For example, if the number of inputs is doubled and the output more than doubles, this is referred to as growing returns to scale. Increased production size leads to the reduced average cost per unit produced since the company benefits from economies of scale.

(2)  Constant Returns to Scale:

When all inputs are raised by a particular percentage, the output rises by the same proportion; this is referred to as the production function exhibiting constant returns to scale.
For example, if a company doubles its inputs, it also doubles its output. In this situation, the production is tripled. The constant production scale has no influence on the average cost per unit produced.

(3)  Diminishing Returns to Scale:

The phrase ‘diminishing’ returns to scale refers to a scale in which output rises in a lesser proportion than total input increases.

For example, if a company raises its inputs by 100% but its output reduces by less than 100%, the company is said to have declining returns to scale. When returns to scale decrease, the company suffers diseconomies of scale. The firm's manufacturing size results in a higher average cost per unit produced.

Graph/Diagram:

With the assistance of the graph below, the three rules of returns to scale are now explained:

Figure 11.6 indicates that when a business employs one unit of labour and one unit of capital, point a, it generates one unit of quantity, as illustrated on the q = 1 isoquant. When the business doubles its outputs by employing two units of labour and two units of capital, it produces more than twice as much from q = 1 to q = 3.

As a result, in this range, the production function exhibits rising returns to scale. Another output from number 3 to number 6. The production function has diminishing returns to scale from the latest doubling point c to point d. The doubling of output from 4 units of input results in a two-unit increase in output from 6 to 8 units.

The Concept of Short Run

·        To comprehend short-run expenses, it is critical to first grasp the idea of the short run.

·        In economics, we distinguish between the short and long term by using fixed or variable inputs.

·        Fixed inputs (plant, machinery, etc.) are production factors that cannot be modified or altered in a short amount of time due to a 'too short' period. This results in a brief run. The inputs, in this case, are of two types: fixed and changeable.

·        Over time, all of the inputs become changeable (e.g. raw materials). This means that the volume of output may be used to adjust all inputs. As a result, the idea of fixed inputs only applies in the short run.

S hort-Run Cost Function

A cost function is a functional connection that exists between cost and output. It indicates that the cost of production changes with the degree of output, as long as other factors stay constant (ceteris paribus). This may be expressed numerically as:
C = f(X)
where C is the manufacturing cost and X is the degree of output

Total Fixed Cost

·        The cost of fixed inputs is referred to as fixed cost. It is unaffected by the level of production (thus, fixed). Buildings, machinery, and other fixed inputs are examples of fixed inputs. As a result, the cost of such inputs as rent or machinery represents fixed expenses. These expenses, also known as overhead costs, supplemental costs, or indirect costs, stay constant regardless of production level.

·        As a result, if we plot the Total Fixed Cost (TFC) curve on the horizontal axis against the amount of production, we get a straight line parallel to the horizontal axis. This suggests that these expenses are constant and must be incurred even if production is zero.

Total Variable Cost

·        Total Variable Cost refers to the costs expended on variable elements of production (TVC). These expenses fluctuate according to the degree of output or production. As a result, when the production level is zero, the TVC is likewise zero.

·        As a result, the TVC curve starts at the origin.

·        The TVC has an unusual form. It is reported to be in the shape of an inverted S. This is because, in the early phases of manufacturing, there is room for increased variable factor usage while consuming less fixed factor (e.g. Workers employing machinery).

·       When a result, as the variable input utilised rises, the variable input's productive efficiency assures that the TVC increases, albeit at a decreasing pace.

·        As a result, the initial half of the TVC curve is concave.

·        As production grows, more and more variable factors are used for a given quantity of fixed input. Each variable factor's productive efficiency decreases, increasing the cost of manufacturing. As a result, the TVC rises, but at a faster rate. This is the point at which the TVC curve becomes convex. As a result, the TVC curve takes on an inverted-S form.

Total Cost

The sum of fixed and variable expenses incurred in the short run is referred to as total cost (TC). As a result, the short-run cost is stated as 

TC = TFC + TVC

In the long term, because TFC = 0, TC Equals TVC. Thus, by adding the TFC and TVC curves, we may obtain the form of the TC curve.

Fig.1

(Source: economics discussion)

The TC curve has the following characteristics:

·      The TC curve is curved like an inverted S. This is due to the TVC curve. Because the TFC curve is horizontal, the difference between the TC and TVC curves at any level of output is the same and equals TFC. This is detailed in detail below:

TFC = TC + TVC

·     The TFC curve is parallel to the horizontal axis, whereas the TVC curve is formed like an inverted S.

·      As a result, the TC curve has the same form as the TVC curve but starts at the point of TFC rather than the origin.

·    The law of changing proportions describes the form of TVC and, consequently, TC.

The Concept of the Long Run

The long-run refers to the time in which a corporation can adjust all of its production parameters. As a result, the long run is entirely made up of variable inputs, and the idea of constant inputs does not exist. In the long run, the company can expand the plant's size. As a result, there is no distinction between long-run variable cost and long-run total cost, because fixed costs do not exist in the long run.

Long-Run Total Costs

·     The minimum cost of manufacturing is referred to as the long-run total cost. It is the cheapest way to produce a given amount of production. As a result, it can be less than or equal to the short-run average costs at various output levels, but never larger.

·  The minimum points of the STC curves at different levels of output are linked to form the LTC curve visually. The LTC curve is given by the location of all these points.

Long Run Average Cost Curve

·     Long-run average cost (LAC) is the long-run average of the LTC curve or the cost per unit of production. It may be computed by dividing LTC by the amount of production.

·    LAC may be calculated graphically using the Short-run Average Cost (SAC) curves.

·    While the SAC curves apply to a specific plant since the plant is fixed in the short term, the LAC curve illustrates the potential for plant development while reducing costs.

Derivation of the LAC Curve

    · Each SAC curve in the illustration corresponds to certain plant size. This size is set, while the variable input in the short term can fluctuate. In the long term, the business will choose the plant size that will reduce expenses for a given level of output.

    · As you can see, the business should function at the plat size represented by SAC2 until it reaches the OM1 level of production. The cost would be higher if the business operated at the cost indicated by SAC2 when generating an output level OM2.

    ·  In the long run, the company will produce on SAC2 till OM1. However, until an output level indicated by OM3 is reached, the business can produce at SAC2, after which it is profitable to produce at SAC3 if the firm intends to reduce expenses.

Thus, in the long term, the best option is to produce at the smallest plant size possible. As illustrated in the image, this results in a LAC curve that connects the minimum points of all feasible SAC curves. As a result, the LAC curve is also known as an envelope curve or a planning curve. The curve lowers first, reaches a minimum, and then rises, forming a U-shape.

The form of the LAC curve may be explained using returns to scale. Returns to scale represent the change in output as a result of changing the inputs. During Increasing Returns to Scale (IRS), the output doubles while the inputs are less than doubled. As a result, LTC rises less than production rises, and LAC falls.

• In Constant Returns to Scale (CRS), double the inputs double the output, and the LTC rises proportionally to the growth in output. As a result, LAC remains constant.

• In Decreasing Returns to Scale (DRS), the output doubles by utilising more than twice the inputs, causing the LTC to grow more than proportionally to the increase in output. As a result, LAC increases. This is what gives LAC its U-shape.

Long Run Marginal Cost

·    The additional cost of creating an extra unit of output, in the long run, i.e. when all inputs are variable, is defined as the long-run marginal cost. The LMC curve is formed by the tangent points of LAC and SAC.

·  There is a significant relationship between LMC and SAC here. When LMC is below LAC, LAC falls, and when LMC is above LAC, LAC rises. LAC is constant and minimal at the point when LMC = LAC.