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# Lecture%209 - Econ 208 lecture 9 page 1 Lecture 9 Cost...

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Econ 208 lecture 9 page 1 Lecture 9: Cost Curves and Equilibrium in the Long Term To review what we have done so far: 1. The derivation of rule for profit maximizing output. Produce to point where MC = MR. Under competition MR = P, so the rule is MC = P. This generates a short-run supply curve. 2. We added up individual firm supply curves to get a market supply curve. 3. Choice of technique or factor proportions. Profit-maximizing rule is MP i /w i = MP j /w j , this comes down to the rule that firms purchase inputs such that the marginal product per dollar spent on each input is the same. Since MP’s are subject to diminishing return, a reduction in the cost of an input will result in substitution towards it. We were just starting the analysis of long-run adjustment. The point to make here is that the analytic difference between the long-run and the short run turns on the variability of inputs. In the long run, all inputs are variable (to the firm); in the short run only some inputs are. The principle of diminishing returns reflects the short-run fixity of at least some of the inputs. So we now want to examine the rules for long-run adjustment. Long-run adjustments are of two types: variation in the scale of output by individual firms and variation in the number of firms in an industry. The two are related. The book mainly focuses on variation at the firm level. However, the crucial analysis occurs at the level of the industry. Long-run Principle:

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Econ 208 lecture 9 page 2 Let me begin by stating the principle, and then we will go back to prove it. The principle of long-run equilibrium is that output will expand – either by increased output of existing firms or by entry of new firms up to the point where price equals average cost. Symmetrically, output will contract to the point where price equals average cost. Since we are always in a short run, this is also where price equals marginal cost. So the condition for long-run equilibrium is P = MC = ATC. Since MC = ATC defines the minimum average total cost, this is also the level of output that minimizes average cost. Proof: 1. Start with production function: use generic input I. Q on vertical axis. Note range of increasing return and inflexion point to diminishing return. Reasoning: at low levels of output marginal additions of variable inputs increase the efficiency of utilization of the fixed inputs. Beyond the inflexion point you run into diminishing returns.
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