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(by the way, this production function has increasing () ( ) ( )
23 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. ( ) ( ) ( ) In Wolfram Alpha type plot (10/L^1)^(1/1), (14.14214/L^1)^(1/1) , (20/L^1)^(1/1) from L=0,5 K=0,5 There are several reasons why economists are interested in returns to variable inputs:
● It may help a firm decide whether to produce more output by building a new identical facility versus doubling variable
inputs at the existing facility. If the cost of doubling variable inputs at the existing facility is the same as the cost of
building another identical facility then:
If there are increasing returns to variable inputs, the firm should double variable inputs at the existing facility because
this more than doubles output whereas building another identical facility doubles output
If there are constant returns to variable inputs, the firm can either double variable inputs at the existing facility or build
another identical facility because either option doubles output and costs the same.
If there are decreasing returns to variable inputs, the firm should build an identical facility as this doubles output
whereas doubling the variable inputs at existing facility less than doubles output
● We may want to know what happens to average variable cost (
) when the firm expands all variable inputs: does
rise, fall, or stays the same when
due to all variable inputs being increased by the same factor
(simplest
example: when all variable inputs are doubled). We will show that under some conditions:
Returns to Variable Inputs and Behavior of
Increasing returns to variable inputs
Constant returns to variable inputs
Decreasing returns to variable inputs when due to firm expanding variable inputs
as
constant as
as 24
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. To prove this, assume uniform variable input prices so that the total variable cost of
production is: variable inputs used in ∑ Now the average variable cost is:
∑ Suppose the firm doubles all variable inputs. Then, with twice as many variable inputs as before and uniform prices, the
total variable cost must also double:
{ ∑ } Since doubling all variable inputs always doubles total variable 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 variable inputs are
doubled. If there are increasing returns to variable inputs, then doubling all variable inputs more than doubles output so
that: With increasing returns as then If there are constant returns to variable inputs, then doubling all variable inputs doubles output so that: With constant returns as then stays the same If there are decreasing returns to variable inputs, then doubling all variable inputs less than doubles output so that: With decreasing returns as then 25
ECO 204 Chapter 11: Producer Theory— the Basics (this version 20122013)...
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