Now suppose the firm is in the short run and capital

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Unformatted text preview: n CMP above we saw that . Now suppose the firm is in the short run and capital is fixed: it may be that or it may be that . If the solution to the short run CMP will be the same as the solution to the long run CMP (albeit, with fixed the firm won’t be able to substitute inputs in response to changes in, for example, price of inputs). For example, suppose a company in the short run uses the Cobb-Douglas production function where to produce a target output in the short run: Short run CMP Target output Long run = Short run iso-cost 2 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 this case since we see that the short run are equal to the long run On the other hand, if the solution to the short run CMP will not be the same as the solution to the long run CMP. For example, suppose a company in the short run uses the Cobb-Douglas production function where to produce a target output in the short run: Short run CMP Target output Long run iso-cost Short run iso-cost Notice that the short run long run and that the short run long run (since the short run iso-cost line has a larger intercept than the long run iso-cost line). This simple example shows that in order to produce a target output the short run cost of production is always greater than or equal to the long run cost of production (why didn’t we say that the short run amounts of variable inputs are always greater than or equal to the long run amounts?). Having developed an intuitive feel for long vs. short run CMPs we now discuss how to setup, solve and interpret short run CMPs. 2. (General) Short Run Cost Minimization Problems Before we do short run CMPs for specific production functions let us look at the general short run CMP to develop an intuitive understanding of the analytical techniques and results. The optimal mix of inputs required to produce a strictly positive and exogenously given target output level in the short run is found by solving the short run cost minimization problem (here, the variable inputs must be greater than or equal to zero; of course, it’s possible that in some CMP, variable inputs be greater than or equal to a positive number): ⏟ Where in the short run CMP do we say that some inputs are fixed? There are two ways to list fixed inputs which we show through an example. Suppose a company in the short run uses the Cobb-Douglas production function where to produce a target output in the short run. The first way to show that capital is fixed is by listing it as a constraint (note the in the production function): 3 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. The second way is to set production function): in the “output produced = target output” constraint (note the small ( in the ) In ECO 204 short run CMPs, we will denote fixed inputs in the production function (rather than listing it as...
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