Recall that the concept of economies of scale tells

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Unformatted text preview: ixed cost plus average variable cost) when the firm produces more output (by using more variable inputs): { It can be shown that if the ratio of inputs is constant along the expansion path then a firm with increasing returns has economies of scale; a firm with constant returns has constant economies of scale; and a firm with decreasing returns has diseconomies of scale6. In the graph below notice that even though the inputs expansion path is linear, the capital to labor ratio declines as : 6 Note to self: double check this claim and fix chapter 12 to say ratio of inputs must be constant along the expansion path. 20 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Labor expansion path That the ratio is not constant tells us that there is no firm connection between “returns” and “economies of scale”. By definition: As we know that and that: ( ) ( { ) ( ) Thus: ( ) ( { ( ) ) ⏟ ⏟ ⏟ ⏟ ⏟ ⏟ ( ) For example: 21 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Cost Functions: Functions Our “proof” of U-shaped curve under decreasing returns is a bit loose: how do we know that with decreasing returns falls and then rises? To show this rigorously we would have to show that when of and for small values of that for small values This is left as an exercise. Using the Cobb-Douglas as an example we can state this general result: Increasing Returns to Variable Inputs and Constant Returns to Variable Inputs functions strictly concave and Decreasing Returns to Variable Inputs functions linear and functions strictly convex As then As then constant As then As then As then constant As then As then As then and approaches Notice that in the long run, decreasing returns to scale did not yield a U-shaped decreasing returns does yield a U-shaped curve. ● From [ ⏟ As then and then curve, but in the short run ⏟ we get: 22 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Producing greater output requires more labor and with increasing returns 1% increase in output requires a less than 1% increase in labor and therefore less than 1% increase in cost; with constant returns a 1% increase in output requires a 1% increase in labor and therefore 1% increase in cost; with decreasing returns a 1% increase in output requires more than 1% increase in labor and therefore more than 1% increase in cost (you should think whether this makes intuitive sense). You should be prepared for test questions where you might be asked to work out ● As While and . the firm will use less labor to produce the same target output . In fact, you should show these elasticities: requires less labor, depending on the r...
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