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Ch 13 SR CMP

# Eco 204 s ajaz hussain do not distribute target

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Unformatted text preview: d the optimal bundle of inputs, we see that the “optimal” iso-cost line then passes through the “optimal” bundle of inputs: “Optimal” iso-cost line Target Output Fixed 0 The total cost is If from to then because the company has to produce with capital fixed at , it must continue to use the same amount of labor albeit at a higher total cost (see graph below where the new iso-cost line passes through the original optimal bundle): 17 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. Initial iso-cost line New iso-cost line Target Output Fixed 0 We will examine the impact of changes in other parameters on the optimal solution and cost below. ● Since [ ⏟ ⏟ we see that with increasing returns to labor, labor usage, , and cost have a strictly concave relationship with output; with constant returns to labor, labor usage, , and cost have a linear relationship with output; with decreasing returns to labor, labor usage, , and cost have a strictly convex relationship with output. This is one of the most important concepts in ECO 204 and in fact can be stated as a general result: Since constant, the “functional form” of the cost function must be the same as that of the vice versa) which implies: Here are some examples (recall that in corresponds to constant returns to labor, and , function (and corresponds to increasing returns to labor, corresponds to decreasing returns to labor): 18 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: for Cobb-Douglas Production Function ● Now we’ll use the Cobb-Douglas short run CMP to state some general results about the cost, total fixed cost, total variable cost, marginal cost, average cost, average fixed cost and average fixed cost function and explore the connection between “returns” and “economies of scale”. First, note that for any short run cost function: ( ) ⏟ Notice that as . Hence, the “shape” of the curve is intimately intertwined with the “shape” of the curve which in turn is linked to “returns”. Recall that “returns” tell us what happens to output when all variable inputs are increased by the same factor { For the Cobb-Douglas short run CMP we have: 19 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. ⏟ ⏟ ( ) ( { ) ( ) In fact we can also show that: ( { ( ) ( What is the relationship between and ) ) ? Notice: ⏟ Therefore: ( ) ( ( ) ) Finally, what can we say about “returns” and the “shape” of the curve which in turn reflects “economies of scale”? Recall that the concept of economies of scale tells us what happens to average cost (which now equals average f...
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