microbook_3e-page121 - returns to scale As we saw in...

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returns to scale As we saw in Lecture 8, it’s assumed that firms have a U-shaped long-run average cost curve. At low output levels, firms face increasing returns to scale. At high output levels, they face decreasing returns to scale. At the minimum point on the long-run average cost curve, they face constant returns to scale. If a firm facing constant returns to scale doubles all of its inputs, then its output will exactly double. For example, if a firm’s production function is given by: X = K 2/3 *L 1/3 then if it doubles its inputs of capital and labor, its output doubles. 2X = (2K) 2/3 *(2L) 1/3 = 2 2/3 *K 2/3 *2 1/3 *L 1/3 2X = 2*K 2/3 *L 1/3 Similarly, you can easily see that when a firm doubles all of its inputs, its output: x more than doubles when it faces increasing returns to scale x less than doubles when it faces decreasing returns to scale . increasing returns to scale: X = K 2/3 *L 2/3 2X < (2K) 2/3 *(2L) 2/3 < 2 2/3 *K 2/3 *2 2/3 *L 2/3 2X < 2 4/3 *K 2/3 *L 2/3 decreasing returns to scale:
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