Why Identical Products Have Different Prices

Search for an HDMI cable on any marketplace and you will find prices ranging from $8 to $45 for functionally identical products. Standard economic theory predicts that competition among sellers of homogeneous goods drives price to marginal cost—the law of one price. Yet persistent, substantial price dispersion is one of the most robust empirical regularities in economics. The resolution lies in the cost of search: when comparing prices takes time and effort, sellers gain local market power, and the law of one price breaks down.

The Puzzle of Price Dispersion

Price dispersion exists in virtually every market. Gasoline prices vary by 20–30% across stations within a few miles of each other. Airline tickets for identical itineraries differ by hundreds of dollars depending on the seller. Retail electronics, prescription drugs, and professional services all exhibit persistent variation in posted prices for functionally identical offerings.

The internet was expected to eliminate this dispersion by reducing search costs to near zero. Early predictions held that comparison shopping engines and marketplace platforms would enforce the law of one price across digital markets. The empirical evidence tells a different story: substantial price dispersion persists online, often at levels comparable to offline markets. baye2006 document persistent dispersion across online retailers over multiple years, finding price ranges of 40% or more for identical consumer electronics.

The key insight is simple but powerful: as long as search is not completely free, some sellers can charge above the competitive price and retain customers who have not searched enough. The models that follow formalize this intuition and characterize the resulting equilibrium price distributions.

Stigler’s Search Model

Definition — Sequential Search

In sequential search, a consumer samples firms one at a time, each sample costing

c > 0

. After each sample, the consumer decides whether to accept the lowest price found or to search one more time. The optimal policy is a reservation price

r

: accept the first price at or below

r

, continue searching otherwise.

Stigler (1961) introduced the economics of information by modeling a consumer who faces $N$ firms, each drawing prices from a distribution $F(p)$ . Each price sample costs $c$ , and the consumer’s optimal strategy is to continue searching as long as the expected marginal benefit exceeds the search cost.

The optimal reservation price $r$ satisfies the indifference condition:

\int_0^r (r - p) \, dF(p) = c

The left side is the expected savings from one more search, given that the consumer currently faces price $r$ . The consumer searches until this marginal benefit exactly equals the search cost $c$ .

Reservation Price Comparative Statics

Three results follow directly from the indifference condition:

As $c \to 0$ , $r$ falls to the minimum of the price support—the consumer searches until finding the lowest possible price (competitive outcome).
As $c \to \infty$ , $r$ rises to the maximum of the price support—the consumer accepts the first price seen without searching at all.
Higher search costs mean consumers search less, giving firms more pricing power. The reservation price is monotonically increasing in $c$ .

The Diamond Paradox

Diamond Paradox (Diamond, 1971)

If all consumers have the same positive search cost $c > 0$ , and firms set prices simultaneously, the unique Nash equilibrium is for all $N$ firms to charge the monopoly price $p^m$ —regardless of how many firms exist or how small the search cost is.

The logic: if all firms charge price $p$ , no consumer searches (since all prices are the same). But then any firm can raise its price by up to $c$ without losing any customers—the consumer would need to pay $c$ to discover a cheaper alternative, which is not worth it for a saving less than $c$ . This unraveling continues until all firms charge $p^m$ .

p^{\text{Diamond}} = p^m \quad \text{for any } c > 0, \; N \ge 2

The Diamond paradox is devastating because it implies that even infinitesimal search costs destroy competition entirely. A market with 1,000 firms produces the same price as a monopoly if every consumer faces any positive search cost. This result clearly overpredicts—real markets with search costs do not produce monopoly pricing—which motivates the search for a resolution.

Resolution: Mixed-Strategy Equilibrium

The Diamond paradox assumes all consumers are identical searchers. Burdett and Judd (1983) resolve the paradox by introducing consumer heterogeneity in search behavior. Specifically, they assume a fraction $\mu$ of consumers are comparison shoppers who sample two or more firms, while the remaining fraction $(1 - \mu)$ are loyal shoppers who visit only one firm.

Definition — Comparison Shoppers

Comparison shoppers (fraction

\mu

of the market) sample at least two firms and purchase from the cheapest. Loyal shoppers (fraction

1 - \mu

) visit one firm at random and buy at whatever price they find. The presence of comparison shoppers creates competitive pressure that prevents the Diamond paradox.

In equilibrium, firms play a mixed strategy over prices. No pure-strategy equilibrium exists because:

If all firms charge a high price, a firm could undercut slightly and capture all comparison shoppers.
If all firms charge low, a firm could raise price and still keep its loyal shoppers.

Burdett-Judd Equilibrium

With $N$ firms, fraction $\mu$ comparison shoppers, and marginal cost $c$ , the equilibrium price CDF is:

F(p) = 1 - \left(\frac{(1 - \mu)(p^m - p)}{\mu(p - c)}\right)^{1/(N-1)}

for $p \in [p_L, \, p^m]$ , where $p^m$ is the monopoly price and $p_L$ is the lower bound of the price support, determined by the firm’s indifference condition. Key comparative statics:

As $\mu \to 0$ (no comparison shoppers): $F$ degenerates to the monopoly price (Diamond result).
As $\mu \to 1$ (all comparison shoppers): $F$ degenerates to marginal cost (Bertrand result).
Higher $\mu$ shifts the price distribution leftward (lower average prices).
More firms (higher $N$ ) increases price dispersion.

Interactive Explorer

The visualization below shows the equilibrium price distribution under different search cost regimes. Adjust the fraction of comparison shoppers $\mu$ and the number of firms to watch the equilibrium shift between the Diamond paradox (monopoly pricing) and perfect competition.

When $\mu = 0$ , all firms charge the monopoly price (Diamond paradox). As $\mu$ increases, price dispersion emerges as firms randomize between high prices (capturing loyal shoppers) and low prices (capturing comparison shoppers). At $\mu = 1$ , all firms price at marginal cost.

Search in the Digital Age

How Technology Reduces Search Costs

Search engines, comparison shopping sites (Google Shopping, Kayak, PriceGrabber), and marketplace platforms (Amazon with “sort by price”) directly reduce $c$ and increase $\mu$ . The Burdett-Judd model predicts that average prices should fall and dispersion should narrow as a result. Empirical evidence confirms lower average prices online relative to offline channels, but dispersion persists at substantial levels.

Strategic Obfuscation

Firms can counteract low search costs by deliberately increasing complexity. Ellison and Ellison (2009) document four strategies that raise the effective search cost $c$ :

Add-on pricing—advertise a low base price, then charge expensive extras (shipping, warranties, accessories).
Drip pricing—reveal fees late in the checkout process, after the consumer has invested search effort.
Complex tariff structures—create incomparable bundles so that price comparison requires nontrivial computation.
Bait-and-switch—advertise a low price to attract search, then redirect consumers toward higher-margin products.

These tactics strategically raise the effective search cost, partially restoring pricing power that technology eroded. The equilibrium prediction is that firms invest in obfuscation up to the point where the marginal cost of added complexity equals the marginal revenue from reduced price competition.

Platform Design and Search Costs

Marketplace designers directly control effective search costs through UI choices. Default sort order, filter options, price display format, and review visibility all determine how easily consumers can compare prices. A platform that makes price comparison easy (high $\mu$ ) pushes seller prices down—good for buyers but reduces marketplace take rates. A platform that makes comparison difficult (low effective $\mu$ ) allows sellers to maintain higher margins, which can attract seller participation but erodes consumer trust.

Platform designers must balance consumer surplus against seller participation. The Burdett-Judd framework provides the analytical foundation: the choice of $\mu$ (which the platform influences through design) determines the entire equilibrium price distribution, and with it the division of surplus between buyers and sellers.

Key Insights

1. Search Costs Create Market Power

Even small search costs give sellers pricing power over consumers who have not compared alternatives. The Diamond paradox shows this in its starkest form: any positive search cost, no matter how small, can support monopoly pricing.

2. Heterogeneity Resolves the Paradox

Real markets avoid monopoly pricing because some consumers do compare. The fraction of comparison shoppers $\mu$ is the key parameter determining how competitive the market is. Even a small share of comparison shoppers disciplines prices substantially.

3. Price Dispersion Is an Equilibrium Phenomenon

Firms do not charge different prices because they are different—they randomize as part of a mixed-strategy equilibrium. Dispersion is a feature, not a bug, of markets with search frictions. The variance of prices is a predictable function of $\mu$ and $N$ .

4. The Digital Paradox

The internet dramatically reduced search costs but did not eliminate price dispersion. Strategic obfuscation, information overload, and platform design choices all maintain effective search costs even in digital markets. The models predict that dispersion narrows but does not vanish as long as any friction remains.

References

Burdett, K. & Judd, K. L. (1983). “Equilibrium Price Dispersion.” Econometrica, 51(4), 955–969.
Diamond, P. A. (1971). “A Model of Price Adjustment.” Journal of Economic Theory, 3(2), 156–168.
Ellison, G. & Ellison, S. F. (2009). “Search, Obfuscation, and Price Elasticities on the Internet.” Econometrica, 77(2), 427–452.
Stigler, G. J. (1961). “The Economics of Information.” Journal of Political Economy, 69(3), 213–225.