Economies of scale is related to and can easily be confused with the theoretical economic notion of returns to scale. Where economies of scale refer to a firm’s costs, returns to scale describe the relationship between inputs and outputs in a long-run production function. A production function has constant returns to scale if increasing all inputs by some proportion results in output increasing by that same proportion. Returns are decreasing if, say, doubling inputs results in less than double the output, and increasing if more than double the output. If a mathematical function is used to represent the production function, and if that production function is homogeneous, returns to scale are represented by the degree of homogeneity of the function. Homogeneous production functions with constant returns to scale are first degree homogeneous, increasing returns to scale are represented by degrees of homogeneity greater than one, and decreasing returns to scale by degrees of homogeneity less than one.
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If the firm is a perfect competitor in all input markets, and thus the per-unit prices of all its inputs are unaffected by how much of the inputs the firm purchases, then it can be shown that at a particular level of output, the firm has economies of scale if and only if it has increasing returns to scale, has diseconomies of scale if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale. In this case, with perfect competition in the output market the long-run equilibrium will involve all firms operating at the minimum point of their long-run average cost curves at the borderline between economies and diseconomies of scale .
If, however, the firm is not a perfect competitor in the input markets, then the above conclusions are modified. 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.
In essence, returns to scale refer to the variation in the relationship between inputs and output. This relationship is therefore expressed in “physical” terms. But when talking about economies of scale, the relation taken into consideration is that between the average production cost and the dimension of scale. Economies of scale therefore are affected by variations in input prices. If input prices remain the same as their quantities purchased by the firm increase, the notions of increasing returns to scale and economies of scale can be considered equivalent. However, if input prices vary in relation to their quantities purchased by the company, it is necessary to distinguish between returns to scale and economies of scale. The concept of economies of scale is more general than that of returns to scale since it includes the possibility of changes in the price of inputs when the quantity purchased of inputs varies with changes in the scale of production.