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Exercise: market failure

An industry for good X faces the following demand and marginal cost functions:

  • What output will the industry choose to produce? And what will be the consumer and producer surplus at that quantity?

Since the MC or supply curve is constant is must be the case that the producer surplus must be zero, as the suppliers can only sell their goods for one price only. The consumer surplus is equal to:
 
  • Pollution costs are represented by the marginal externality cost (MEC) function. From society's stand point, how many units of good X should be produced?

To find society's optimal output let the MSC equal MPB:

  • The industry is required to adopt a less polluting technology which raises the marginal cost, MC=$12. Find the output the industry choose to produce and calculate the new consumer and producer surplus.
Just as before, the producer surplus is still equal to zero. The consumer surplus on the other hand is now equal to:
  • The total benefit of reducing pollution with this new technology is estimated to be $90. Is the reduction in pollution worth its costs to the producers and consumers?
The cost the consumers face is equal to the difference between the old consumer surplus and the new consumer surplus: 


We can clearly see that it costs consumers more to switch to this technology than the reduction in pollution this technology brings.

Let's graph the problem:


Source: the problem were inspired by the exercises on pages 359-360 in Study Guide For Microeconomics, 8th edition (2013) by J.Hamilton, and V.Suslow.
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Location: New York, NY, USA

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