ajaz_eco_204_2012_2013_chapter_11_producer_theory_basics

Eco 204 s ajaz hussain do not distribute in

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Unformatted text preview: bor (doubling labor (by the way, this production function has increasing () ( ) ( ) 23 ECO 204 Chapter 11: Producer Theory— the Basics (this version 2012-2013) 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 2012-2013) 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 2012-2013)...
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