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Feb25-12, 01:42 AM
P: 783
Microeconomics: What is the socially optimum price?

Hey Lugita remember me from my questions in the calculus/analysis subforums??

In economics, we do not care about how much a person needs something. If he cannot afford it, his need is meaningless. He only matters if he can afford it at a given price. This is assuming the good has no externalities, which is uncertain in the case of water. If the good has externalities, you must take into account taxes and subsidies, which I won't consider here.

To answer your question, even though the seller is not spending the money on himself, as long as at least someone is benefiting from the money, and none of the money is being wasted in the process, (there is zero cost of transporting and distributing the charity money), then it does not matter whether the seller spends the money on himself or some random orphan. In both cases, the producer surplus is still the same. If the money will be used, it does not matter who uses it. Whoever uses it is inevitably a part of "society". If that were not the case, then it is a different story. Otherwise, we will assume that "society" includes the orphans who will receive the charity money.

We can treat the problem as an ordinary one assuming that the seller is in fact motivated by self-interest.

Your goal is to find the price at which the total surplus is maximized.
The total surplus at quantity Q is given by the area between the supply and demand curves, i.e. [itex] \int^{Q}_{0}(D-S) dQ [/itex]
It is evident from the graph that this is achieved when supply equals demand, i.e. equilibrium quantity and price.

Therefore, the "optimum" price is the one at which supply and demand are at equilibrium.

Another way of looking at it is just replace the seller with the charity organization that is receiving the money. That way, you look at "self-interest" as being perfectly present in the problem.