Why doesn't the theory of competitive pricing provide a completely accurate picture of real-world economics? 

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The theory of competitive pricing does not provide a completely accurate picture of economics in the real world because the conditions needed to engage in this type of pricing are not always present.  In essence, the closer that a market is to perfect competition, the more firms in that market will engage in competitive pricing.  In other situations, competitive pricing is not always the best way to go.

For example, let us imagine a situation in which the firms in a market are not really selling homogeneous products.  A small local fast food place and McDonald’s may both be selling hamburgers, but they are not really selling the same things.  McDonald’s is selling its brand whereas the local place might be selling its atmosphere and reputation and the quality of its burgers.  It would not make sense for the local place to try to base its prices on McDonald’s prices.

As another example, let us imagine a situation in which the market for a good has not yet come to equilibrium.  At that point, it is still not clear what the right price for a good is.  Firms will be wise to base their prices on internal factors such as their own costs rather than trying to copy the pricing of competitors. 

So, this kind of pricing can only really work in markets that are settled and in which the sellers are selling products that are practically identical.  At other times, firms will tend to set their prices in different ways.

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