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Unformatted text preview: because this more than doubles
output whereas building another identical facility doubles output
If there are constant returns to scale, the firm can either double the existing facility or build another identical facility
because either option doubles output and costs the same.
If there are decreasing returns to scale, the firm should build an identical facility as this doubles output whereas
doubling the existing facility less than doubles output
● We may want to know what happens to average cost when the firm expands the scale of operations: does
rise,
fall, or stays the same when
due to all inputs being increased by the same factor
(simplest example: when
inputs are doubled). We will show that under some conditions:
Returns to Scale and Behavior of
Increasing returns to scale
Constant returns to scale
Decreasing returns to scale when To prove this, assume uniform input prices so that the total cost of due to firm expanding its scale
as
constant as
as
inputs used in production is: ∑ Now the average cost is:
∑ Suppose the firm doubles all inputs. Then, with twice as many inputs as before and uniform prices, the total cost must
also double: ∑ { } 10 In next version : IRS firm can double output by less than doubling existing facility instead of building an identical facility; CRS to double output firm can either double existing facility or build an identical facility; DRS firm can double output by building an
identical facility instead of having to more than double existing facility.
19
ECO 204 Chapter 11: Producer Theory— the Basics (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Since doubling all inputs always doubles total cost, we see that whether
rises, falls, or stays the same depends on
whether output less than doubles, doubles, or more than doubles when all inputs are doubled. If there are increasing
returns to scale, then doubling all inputs more than doubles output so that: With increasing returns to scale as then If there are constant returns to scale, then doubling all inputs doubles output so that: With constant returns to scale as then stays the same If there are decreasing returns to scale, then doubling all inputs less than doubles output so that: With decreasing returns to scale as then 4. “Returns” to Variable Inputs in the Short Run
“Returns to scale” is a long run concept: it tells us for example whether, doubling all inputs more than doubles output,
less than doubles output, or exactly doubles output. In this section we discuss another important concept in producer
theory: “returns” to variable input(s) in the short run which tells us the impact on output when all variable inputs are
scaled up by a factor
For a firm in the short run with a fixed and a variable input, the only way to produce more output is for the firm to
expand inputs along one specific inputs expansion path. For example, in the following isoquants graph for a CobbDouglas production function with fixed capital (
) and variable labor, the only way to expand production is by using
more variable labor along one (and only...
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This document was uploaded on 01/19/2014.
 Fall '14

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