Monday, December 31, 2012

Benefits of City Council

Alzheimer's problem of the day.

There is only one doctor in the town of Erewhon. Every time he treats a patient, he must use a pair of disposable rubber gloves. He also finds it necessary to keep an X-ray machine in his office, which he rents for $500 over year. The town council has decided to help the doctor meet expenses, and is undecided between two plans. Under Plan A, the council will provide the doctor with unlimited free rubber gloves for use in his practice; under Plan B, the council will provide him with an X-ray machine. Which plan will beneļ¬t the doctor’s patients  more and why?

Plan A.  Assuming that the marginal cost of treating a patient is now zero and the doctor will treat patients up to the point where the marginal benefit equals marginal cost, society will gain because more patients will receive treatment.  In this case, the doctor will treat 9 patients.  But when he pays for the gloves he will only treat 5 patients and charge almost $4 dollars. 

Even if the gloves were a constant marginal cost of $3, then the number of patients the doctor would treat would be six.  When the marginal cost is reduced to zero, he would treat 9 patients.  

I was wondering if there would be any reason why there would be any reason why the price would be driven down to the marginal cost.  There's no Bertrand pricing or Cournot behavior.  As an imperfect competitor, this doctor might the only doctor in the area and the pricing might not change.  

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