ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

# You should also work out the elasticities for the us

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Unformatted text preview: . () () ), while if there are decreasing returns to scale then the cost function is strictly convex (i.e. () () ). For example: 14 Note to self: maybe this section should come earlier 42 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. “Cobb-Douglas” Cost Function ( ) Increasing RTS Constant RTS Decreasing RTS Strictly concave cost function Linear cost function Strictly convex cost function In fact, this is a general result (true of any production function). Here is a “simple” graphical proof – take a look at this ( ) with increasing returns to scale15: rather odd graph of a production function Left side Right side () Production Function ( ) 45 degree line 45 degree line If there are increasing returns to scale it means that doubling inputs more than doubles output; put another way, to produce double the output we need to less than double inputs. Now, the following graph shows the output , “optimal” cost ( ) and the cost of inputs to produce 15 Note to self: for next version do math proof. 43 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Left side Right side () ( ) Production Functio...
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