Lecture15 - Lecture#15 Recall at the end of last class we...

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Lecture #15 Recall at the end of last class we calculated a quota example. An insightful student has asked me “What if the quota was appropriate because if the market produced more x there might be environmental damage…” or some other externality? Then society is not experiencing a DWL due to the quota but rather a gain …right? While this question is beyond the scope of our analysis in this course (it belongs in an environmental or cost-benefit analysis framework), I think that this is a useful example to show you the difference between private MC and this is a useful example to show you the difference between private MC and social MC. So, let’s suppose that the government is thinking of imposing a quota on a market that produces a good with a toxic pollutant resulting as a byproduct of their production process. Of course, the firm considers only their private marginal costs when determining their output level (i e P = d = MR = MC) Left to their own devices P S (i.e. P = d F = MR = MC). Left to their own devices, the firm would produce x C under perfectly competitive conditions (at P C ), using their private MC to determine optimal firm output levels. This is the situation that we discussed in the last class A P C the situation that we discussed in the last class. Industry output is (n · x C ) if there are n identical firms in the industry. x D n · x C
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Now, remember that under perfectly competitive conditions the representative firm makes “normal profits” representative firm makes normal profits . P MC P The firm’s output level is x C under perfect MR = d F ATC P C competition and each representative firm makes zero economic profits. Note: MC P = private marginal costs x x C Now, suppose the social MC is higher than the private marginal cost because society must repair the damage caused by the toxic emissions created by this industry, say SO 2 . P MC P ATC MC S ATC MR = d F P C A B If firms were to use MC S (social marginal costs) when determining their output level then the socially desirable equilibrium would occur at P and x (point B) MR = d F P S x x C x S S S (point B).
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So, since the representative firm uses private marginal costs and the government wants them to use social marginal costs, the government regulation needs to either increase the polluting firms’ ATC (and MC) to the same level as ATC (and MC S ) or restrict output to the socially desirable level…by putting a quota in place. They could increase the representative firm’s cost structure by taxing They could increase the representative firm s cost structure by taxing emissions, implementing pollution permit programs, etc. For our purposes, we want to see how a quota works, so… P Now, S q represents the quota “supply” that induces the socially desirable price and quantity (P S and n · x S ) since this equilibrium was calculated using social MC (and thus “covers” the S A S q B P S calculated using social MC (and thus covers the costs of repairing the environment while simultaneously reducing the amount of the production which causes the emissions).
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