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# Differentiated Goods Duopoly

Do you think Pepsi tastes different from Coke? In other words, do you think Coke and Pepsi make them taste than different? IO theory has a stylized model to provide some intuition.

Brands compete more vigorously with brands that are close substitutes. Some brands have common characteristics that other brands lack. Before we go on let us provide a little bit of intuition to what we mean by close substitues. More importantly, what are not close substitutes? Salt and sugar definitely aren't substitutes - think of putting salt in your cup of coffee! What are close substitutes? How about a hamburger and a turkey-burger. For most they would probably be close substitutes, that is if one is unavailable you can do with the other.

Now consider a line, where the ends represent stark opposites in the taste of some product, say biscuits. That is one end means you have a salty biscuit and the other end represents a biscit which is very sweet. In other words each product is "located" at a particular point in product characteristics space. So in this linear stretch biscuits produced in the middle are a bit salty and a bit sweet. The same idea of product characterestics can be viewed as "location theory", where instead of choosing the product characterestics the firm decides where in the linear stretch would they put there store. So, consider products sold at nearby stores that are close substitutes. The following lays out a sketch of models that deal with such problems.

Consider, a long street that is of a fixed length, like the boardwalk in Atlantic city which stretches along the beach. Suppose that the consumers are distributed evenly along the beach and that they prefer to buy from the nearest vendor. Some ice cream vendors with pushcarts want to sell ice cream on the boardwalk. If two ice cream vendors are given the rights to sell ice cream here, and the price that they sell at is fixed, where would they locate?

Suppose we put one vendor a quarter of the way along the boardwalk and the other vendor at three quarters of the way along the boardwalk. So the consumer half way along the boardwalk will be indifferent between the two ice cream vendors. Also each vendor has one half of the market share of consumers.

But do the vendors have an incentive to stay in these locations? Suppose the vendor L moves a bit to the right. It will then have some of the other vendor's consumers without losing any of his own. Vendor R can reason exactly the same way and would like to move a bit to his left. So continuing this way the only "equilibrium" is for both vendors to locate in the middle of the linear stretch.

The story above can serve as a metaphor for the original product differentiation problem as well. It suggests that "monopolistic competition" would result in too little product differentiation in such an environment and would induce firms to make their products similar to that of the other firm. In terms of the biscuit characterestics, it would mean that both the firms would like to produce biscuits which taste quite similar and can be close substitutes of each other.

The argument above should convince some of you fence sitters that Coke and Pepsi might not taste all that different and are in fact close substitutes. If there are still some left who could swear that Coke and Pepsi are very different, they should consider the following situation. You go to a local restaurant for a glass of Coke. The store-keeper replies that he is out of Coke, and so he can offer you Pepsi or root beer! Now what would you order?