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Unformatted text preview: Cobb-Douglas long run CMP has a linear inputs expansion path tells us
that if the firm has increasing returns to scale then it has economies of scale, etc. Let’s show this. Recall that: By definition, the cost per unit or average cost is:
( By definition, the cost of the next (marginal) unit, or marginal cost ) is:
( The functional form of the
functions as well whether
constant, or decreasing returns to scale: ) depends on whether there are increasing, Long run Cobb-Douglas CMP
Increasing RTS Constant RTS () () () ( As Economies of scale Strictly convex cost function () ) As 12 () Linear cost function Strictly concave cost function Decreasing RTS () (
As constant As
constant Constant economies of scale ) As As Diseconomies of scale Note to self: do the math proof for next ECO 204 class.
38 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 Production Function and RTS
Cost Functions ( ) Marginal Cost and Average Cost Functions In particular, notice that the long run Cobb-Dougl...
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- Fall '14