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# DIFFERENCES BETWEEN THE LAW OF RETURNS TO SCALE AND THE LAW OF CONSTANT RETURNS TO SCALE WITH APPROPRIATE DIAGRAMME

## DIFFERENCES BETWEEN THE LAW OF RETURNS TO SCALE AND THE LAW OF CONSTANT RETURNS TO SCALE WITH APPROPRIATE DIAGRAMME

Introduction

The terms ’returns to scale’ and economies of scale in economics are related and are usually used to describe certain outcome as the scale of production begins to increase in the long run, that is, when all input levels including physical capital usage are variable i.e. chosen by the firm. The two concepts are quite different and should not be mistakenly used interchangeably. Returns to scale as a concept comes up in the consideration of a firm’s production function. The concept also explains the influence of rate of increase in the firm’s output or production to the subsequent increase in the inputs, that is, the factors of production in the long run. All factors of production in the long run are variable and subject to change due to a given increase in the scale or size.

THE LAWS OF RETURNS TO SCALE

The law of returns is often confused with the law of returns to scale. The law of returns operates in the short period. It explains the production behavior of the firm with one factor variable while other factors are kept constant. Whereas the law of returns to scale operates in the long period. It explains the production behavior of the firm with all variable factors.

The laws of returns to scale operate in the long period. It explains the production behavior of the firm with all variable factors.

There is no fixed factor of production in the long run. The law of returns to scale describes the relationship between variable inputs and output when all the inputs or factors are increased in the same proportion. The law of returns to scale analyses the effects of scale on the level of output. Here we find out in what proportions the output changes when there is proportionate change in the quantities of all inputs. The answer to this question helps a firm to determine its scale or size in the long run. The law of returns to scale is a set of three inter-related and chronological laws or stages viz:

• The law of increasing returns to scale: for example, if the amount of inputs are doubled and the output increases by more than double, it is said to be an increasing returns to scale. When there is an increase in the scale of production, it leads to lower average cost per unit produced as the firm enjoys economies of scale.
• The law of constant returns to scale: for example, if a firm doubles inputs, it doubles output. In case, it triples output. The constant scale of production has no effect on average cost per unit produced.
• And the law of decreasing/ diminishing returns to scale: for example, if a firm increases inputs by 100% but the output decreases by less than 100%, the firm is said to exhibit decreasing returns to scale. In case of decreasing returns to scale, the firm faces diseconomies of scale. The firm’s scale of production leads to higher average cost per unit produced.

The diagramme of returns to scale

Figure 1.

The figure 1 shows that when a firm uses one unit of labor and one unit of capital, point a, it produces 1 unit of quantity as is shown on the q = 1 isoquant. When the firm doubles its outputs by using 2 units of labor and 2 units of capital, it produces more than double from q = 1 to q = 3.

So the production function has increasing returns to scale in this range. Another output from quantity 3 to quantity 6. At the last doubling point c to point d, the production function has decreasing returns to scale. The doubling of output from 4 units of input causes output to increase from 6 to 8 units increases of two units only.

If output increases by less than that proportional change in inputs, there are decreasing returns to scale (DRS). If output increases by more than that proportional change in inputs, it means there are increasing returns to scale (IRS). In the mainstream microeconomics, the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions (i.e., conclusions about returns to scale are derived from the specific mathematical structure of the production function in isolation).

The production function of a firm could display different types of returns to scale in different degrees of output. Typically, there could be increasing returns at relatively low output levels, decreasing returns at relatively high output levels, and constant returns at one output level between these ranges. Example, when all inputs increase by a factor of 2, new values for output will be:

• Twice the previous output if there are constant returns to scale (CRS)
• Less than twice the previous output if there are decreasing returns to scale (DRS)
• More than twice the previous output if there are increasing returns to scale (IRS)

LAW OF CONSTANT RETURNS TO SCALE

With the addition of successive units of variable inputs to fixed amount of other factors, there is a proportionate increase in total output. In other words, when the units of variable factors are increased with the units of other fixed factors, the marginal productivity remains constant. It is called constant return.

A given proportional change in all resources in the long run results in the same proportional change in production. Constant returns to scale exists if a firm increases ALL resources–labor, capital, and other inputs–by 10 percent, and output also increases by 10 percent. This is one of three returns to scale. The other two are increasing returns to scale and decreasing returns to scale.

Constant returns to scale results if long run production changes are greater than proportional changes in all inputs used by a firm.

Suppose, for example, that The Wacky Willy Company employs 1,000 workers in a 5,000 square foot factory to produce 1 million Stuffed Amigos (those cute and cuddly armadillos, tarantulas, and scorpions) each month. Constant returns to scale exists if the scale of operation expands to 2,000 workers in a 10,000 square foot factory (a doubling of the inputs) and production increases to exactly 2 million Stuffed Amigos.

The anticipated pattern for most production activities is that increasing returns to scale emerge for relatively small levels of production, which is then following by constant returns to scale and decreasing returns to scale.

Returns to scale are the flip side of economies and diseconomies of scale. Although economies and diseconomies of scale focus on changes in average cost, returns to scale focus on production. One way to view constant returns to scale is the quantity of production or the range or production in which the forces underlying increasing returns to scale exactly balance the forces underlying decreasing returns to scale.

The Diagramme of Constant Returns to Scale

Figure 2

The unit of labor and capital (variable inputs) are measured on X-axis, while marginal productivity of these inputs on Y-axis. By schedule, we have taken A, B, C and D points. Marginal productivity curve of constant returns is obtained by joining these points. This curve has zero slope and parallel to X-axis. This law operates for a very short period when the marginal returns move towards optimum level of production and remains constant for short period, then begins to decline.

CONCLUSION

Assuming that the factor costs are constant that is, that the firm is a perfect competitor in all input markets, a firm experiencing constant returns will have constant long-run average costs, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs. However, this relationship breaks down if the firm does not face perfectly competitive factor markets (i.e., in this context, the price one pays for a good does depends on the amount purchased). For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input’s per-unit cost, then the firm could have diseconomies of scale in that range of output levels. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.

Formally, a production function F (K, L) is defined to have:

• Constant returns to scale if (for any constant a greater than 0)

F (aK, al) = aF (K, L),

• Increasing returns to scale if (for any constant a greater than 1)

F (aK, aL) > aF (K, L),

• Decreasing returns to scale if (for any constant a greater then 1)

F (aK, aL) < aF (K, L)

Where K and L are factors of production–capital and labour respectively.

REFERENCES

Gelles, Gregory M.; Mitchell, Douglas W. (1996). “Returns to scale and economies of scale: Further observations”. Journal of Economic Education 27 (3): 259–261. JSTOR 1183297.

Frisch, R. (1965). Theory of Production. Dordrecht: D. Reidel.

Ferguson, C. E. (1969). The Neoclassical Theory of Production and Distribution. London: Cambridge University Press. ISBN 0-521-07453-3.

Susanto Basu (2008). “returns to scale measurement,” The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

James M. Buchanan and Yong J. Yoon, ed. (1994) The Return to Increasing Returns. U.Mich. Press. Chapter-preview links.

John Eatwell (1987). “returns to scale,” The New Palgrave: A Dictionary of Economics, v. 4, pp. 165-66.

Joaquim Silvestre (1987). “economies and diseconomies of scale,” The New Palgrave: A Dictionary of Economics, v. 2, pp. 80-84.

Spirros Vassilakis (1987). “increasing returns to scale,” The New Palgrave: A Dictionary of Economics, v. 2, pp. 761-64.

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