Talk:Bertrand paradox (economics)
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Hi, please consider the 2 entries in wikipedia (I am refering to the Bertrand's Paradox entry and the Bertrand Paradox entry). Are they refering to the same paradox? Or did Bertrand came up with 2 different paradoxes. I search for Bertrand's paradox on google and it appears that the paradox on probability is the more common find: that is what is the probability that a randomly picked chord of a circle will have a length greater than the side of an equilateral triangle inscribed in the circle.
Here is a start at translating the material from the German Wikipedia entry (as requested on the page for BertrandParadox). Feel free to add to this - this is just the first paragraph, but the text is not long.
Bertrand model of price competition
In a market with a homogeneous good (e.g. water), there are two suppliers, A and B (duopoly). These suppliers compete solely through the simultaneous announcement of their prices. Al consumers buy only from the supplier with the lowest price. This suplier then satisfy the entire demand. If both suppliers offer the same price, they share the market, i.e. 50% of the consumers go to supplier A, with the rest going to supplier B. The fixed costs are negligible.
Claim
There exists a unique "Nash equlibrium" , in which the following holds: Price of supplier A = Price of supplier B = marginal cost.
Proof
(sorry, it is not marginal cost. It is smallest possible cost larger than zero-profit). Assume that Price of A = Price of B at any price greater than no profit.
Now, for either company, decrease of price will increase profit for that company. However, the other company will do likewise.
Neither company will reduce to the zero-profit level, because that actually decreases profit rather than increases it.
So, the price will decrease to zero-profit plus epsilon. Unlike pure mathematics, where epsilon is arbratrarly small, in economics, epsilon is finite.
The limits of epsilon involve smallest available monetary unit and granularity of measurements, and must be calculated separately for every such situation.
[edit] Wikification
I've wikified the article and removed the wikify tag at the top. Also cleaned up the translation a bit (thanks for the translation in the first place, by the way!). Ryan McDaniel 23:24, 22 February 2006 (UTC)
