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Can anyone tell me the difference between economies of scale and increasing returns to scale. It seems to me that observationally they would be equivalent.

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Economies of scale are normally understood to refer to a situation in which, as output is increased, the cost per unit of producing that output falls (see here and here).

Increasing returns to scale are normally understood to refer to a situation in which, as all inputs are increased k-fold, output increases more than k-fold (see here and here). This is equivalent to saying that a k-fold increase in output can be achieved by increasing all inputs less than k-fold. The difference from economies of scale is that returns to scale are about the relation between inputs and output and nothing is implied about costs.

If a firm producing a good X is a price-taker in the markets for all the inputs it uses to produce X, and if those markets do not offer any form of discount for bulk purchases, then a k-fold increase in input quantities will imply a k-fold increase in cost, and vice versa. In those circumstances, the firm will benefit from economies of scale if and only if it enjoys increasing returns to scale.

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