## Cost Elasticities and Economies of Scale

It is often easy to calculate scale economies by considering cost elasticities. Cost elasticity, eC, measures the percentage change in total cost associated with a 1 percent change in output. Algebraically, the elasticity of cost with respect to output is e^ =

Percentage Change in Total Cost (TC) Percentage Change in Output (Q)

ATC/TC AQ/Q

Cost elasticity is related to economies of scale as follows:

Then

Which Implies

Percentage change in TC < Percentage change in Q ec < 1

Percentage change in TC = Percentage change in Q ec = 1 Percentage change in TC > Percentage change in Q ec > 1

Economies of scale (decreasing AC) No economies of scale (constant AC) Diseconomies of scale (increasing AC)

With a cost elasticity of less than one (eC < 1), costs increase at a slower rate than output. Given constant input prices, this implies higher output-to-input ratios and economies of scale. If eC = 1, output and costs increase proportionately, implying no economies of scale. Finally, if eC > 1, for any increase in output, costs increase by a greater relative amount, implying decreasing returns to scale. To prevent confusion concerning cost elasticity and returns to scale, remember that an inverse relation holds between average costs and scale economies but that a direct relation holds between resource usage and returns to scale. Thus, although eC < 1 implies falling AC and economies of scale, because costs are increasing more slowly than output, recall from Chapter 7 that an output elasticity greater than 1 (eQ > 1) implies increasing returns to scale, because output is increasing faster than input usage. Similarly, diseconomies of scale are implied by eC > 1, diminishing returns are indicated when eQ < 1. 