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returns to scale
As we saw in Lecture 8, it’s assumed that firms have a Ushaped longrun 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 longrun 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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 Fall '10
 willis

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