Tuesday, May 11, 2010

What does economics say about setting a price?

Every economist should know how prices are determined. After all, we study from (and write) textbooks with the title Price Theory. Top universities have Price Theory sequences in their graduate curricula. Economists critically examine data on every price under the sun. Indeed, if any profession should know how a price is determined, it is the economics profession.

So, what is it that we know about how prices are determined? To put it differently, how does a price come to be? Here's my blog-sized interpretation on what standard economic analysis has to say about pricing.

The Standard Theory of the Price

The standard theory of the price is the theory of price-taking individuals. That is, every individual in a market takes the market price as given. Neither buyers nor sellers can affect prices on their own. At first, this seems like a strange place to start if we want to explain price changes. It looks like we have assumed the problem away by saying that not one individual can affect the price.

But, it turns out that this model of the world can actually do a great deal to improve our understanding of prices and how they change. Imagine a world where buyers have no bargaining power because sellers can sell to the next available buyer. At the same time, sellers have no market power because if they raise the price a dime, they lose all of their business. What price will prevail in such a market (called a perfectly competitive market)?

In a competitive market, the price that prevails is the equilibrium price, which equates supply and demand. We expect this price to prevail because if there is excess supply, sellers have an incentive to decrease the price to attract buyers. If there is excess demand, buyers have an incentive to pay more (either to ensure access to the good, or to avoid waiting in line). The only price that is stable is one for which there is no excess demand or supply.

This is the theory of price that underlies the standard supply and demand diagram. If you have had an introductory economics course, you know that supply and demand speak profoundly to the nature of prices and price changes. Yet, supply and demand analysis does not speak to the rich nature of negotiation and bargaining over prices. Price is determined as an equilibrium outcome to the competitive game. And, every individual in this competitive game has absolutely no ability to affect the price.

In other words, the economist's standard off-the-shelf theory of the price does a lot to explain what prices can prevail in the marketplace, but it does not tell a satisfactory story of how the price came to be. Individuals in this model go to the market and pay the price, and there is no other price. It is what it is, and everyone takes it as it is.

The Monopoly Theory of the Price

There's another standard case that economists like to consider: The case of one seller and many buyers (or similarly, one buyer with many sellers). Economists call this type of market a monopoly. In such a world, the monopoly seller selects the price that maximizes profit, and the price is set as the result of the single firm's profit maximization problem. Hire an economist to consult on what price should be set, and the intuition (coming from the monopoly problem) is to "set the price that maximizes profit."

As you may have guessed, there is much more to the story. A monopoly need not set one price. If a seller can get away with setting one price for one group of consumers and another for a different group of consumers, it may be able to raise profits in the process. If that works, why not split the market into three segments? Or, four? Without getting into particulars, it gets really difficult to set the right price or set of prices. How do you define a market segment? Do you segment the market by offering products of different quality? If the seller's product is durable or buyers can stockpile, that adds even more complication as the seller competes with himself.

Multiple (but not many) sellers

No markets are perfectly competitive, nor are there perfect examples of monopoly. Most market interactions lie somewhere in between the two extremes. How do we predict the price that prevails in such markets? Economists have (essentially) two approaches: quantity competition and price competition.

Quantity competition is called Cournot competition. When competition is Cournot-style, sellers pick the output that is a best response to what they think the other sellers output will be. Then, whatever price prevails at the produced quantity is the price that the economist predicts. There is no active setting of the price in this style of competition. So, like perfect competition, we have a theory of the price that does not tell us how the price came to be.

So, let's turn to price (Bertrand) competition. When competition is Bertrand, sellers pick the price that is the best response to the other sellers' prices. If products are identical, this style of competition is fierce. With two competitors who compete on price, the price will be bid down until both firms are selling at cost (This is because -- in a world with many buyers -- a slightly lower price attracts the entire market). In other words, once we give the seller the option to set the price, we know that the price that prevails has to be the unit cost of producing the product.

This is also unsatisfactory, so we tweak the identical product Bertrand analysis to allow for differentiated products. Sellers' products are different, so each seller can charge a bit above the unit cost without losing too many customers. Product differentiation means that each seller has a local monopoly over the bundle of product attributes they sell. So, the analysis usually proceeds as: taking the product attributes as given, what price maximizes profit? And, that's a standard theory of price in industrial organization.

As nice as this theory is, it has problems: First, who said that the product attributes are fixed? These are surely an object that the company can choose to help increase profits. Moreover, what is the role of advertising here? These questions drive to the heart of what price ultimately prevails. Yet, it is my understanding that we don't have a complete picture of the full set of interactions between product quality, advertising, entry and exit and how each of these factors determines the price that prevails. This remains an active research area.

Few Sellers and Few Buyers

There is one final piece to the puzzle of pricing. What if there is only one buyer and one seller (or even a few buyers and sellers)? Neither has a monopoly, yet we cannot rely on competition to set the price. Necessarily, the price is going to be determined through some sort of bargain between the two individuals.

Take an example. Imagine that Tony is willing to sell something for $15, while Eric is willing to buy it for $85. What price should prevail? It doesn't take an economist to say "somewhere between $15 and $85." Beyond that, the price could be $20, $50 or $80 (or $51.01 for that matter). What price prevails depends critically on an assortment of factors. How good of a negotiator is Tony relative to Eric? What are each individuals' outside options? Is there some form of leverage that Eric can hold over Tony? Is there time pressure for either of the individuals in coming to a deal? And, so on.

A common mode of analysis that economists use to make these questions more precise is called Nash Bargaining. There is some math involved, but the intuition stems from answering an intuitive question. What factors do you expect to influence the relative bargaining power of the two individuals? And, in this particular bargain, who has more power? Economists -- specifically structural labor economists -- have developed tools to estimate the bargaining power of workers relative to firms, husbands relative to wives, and it wouldn't be hard to put these tools to use in analyzing the bargaining of unions with firms as well.

This structural labor theory of the price assumes some "bargaining parameter," which fully determines the price. Then, the economist tries to understand statistically what determines the relative bargaining power of the two parties.

To conclude, what should an economist know about the price that prevails in a market? Quite a bit! But, most of this knowledge stems from the assertion that price is an equilibrium outcome. On an intuitive level, economists' understanding of price is that it is what makes the terms agreeable to both buyers and sellers. In perfect competition, "agreeable" means no excess demand. In monopoly, "agreeable" means maximizes the seller's profits. In Nash bargaining, "agreeable" balances relative talent at negotiation with other factors like desperation and opportunity cost.

Because the world is complicated, there is always work to do to understand what price is agreeable in a particular context. If you like economics, figuring out what precisely drives a price does not feel much like work, and it is hard to put a price on that.

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