Competition in a Spatially-Differentiated Product Market with Negotiated Prices

Research Question

How does individually negotiated pricing — where buyers make discrete choices among differentiated products and negotiate transaction-specific prices — affect market power and merger effects in oligopoly markets, and how do these effects differ from the uniform-pricing benchmark?

Data and Setting

The paper estimates the model using 13,788 transactions between the four main UK brick manufacturers and national house-building firms over 2003–2006. For each transaction (defined as a unique buyer-variety-destination-year combination), the data record the chosen product, negotiated price, production and delivery locations, volume, transport costs, and brick characteristics. The market is highly concentrated: four manufacturers held an 85% share of brick sales, with a two-firm concentration ratio of 0.60 and an HHI of 2,113. Spatial differentiation is a central feature — transport costs vary substantially by project location, and prices for the same brick product vary across the different projects of the same buyer depending on local competitive conditions.

Model

The paper develops an empirical model that adapts the Berry, Levinsohn, and Pakes (1995) differentiated-products framework to individually negotiated pricing. In the model, each buyer negotiates simultaneously and bilaterally with the sellers of the first-best and runner-up products (defined by surplus — value minus cost). The equilibrium first-best markup equals the minimum of (i) the unconstrained Nash bargaining solution, bj(wj(1) − w0), and (ii) the first-best seller’s surplus advantage over the runner-up, (wj(1) − wj(2)). Runner-up and lower-ranked sellers earn zero markups in equilibrium. This outcome is shown to be consistent with a range of non-cooperative bargaining models (Binmore 1985, Bolton and Whinston 1993, Manea 2018) and lies in the core of the associated coalition game. The TIOLI posted-price model is nested as the special case where seller bargaining skill equals one. A tractable likelihood for the joint probability of observed product choice and negotiated price is derived under the assumption that idiosyncratic taste terms follow a Generalized Extreme Value (GEV) distribution.

Main Findings

The estimated mean seller bargaining skill is b̄ = 0.41 (s.e. 0.03), and a likelihood ratio test rejects the TIOLI restriction with a chi-squared statistic of 847 (p < 0.001), confirming that buyer bargaining power is economically and statistically significant. The model-implied price-cost margins (Lerner index) are low on average — mean of 0.08 — but vary widely across transactions (coefficient of variation of 0.78). Project location matters: sellers extract higher margins from buyers that are relatively close, taking advantage of their transport-cost proximity. Multi-product ownership also affects markups, but its relevance varies by project.

Switching from negotiated to uniform pricing raises average markups by 34% at the observed market structure. However, effects are heterogeneous: approximately 15% of transactions see markup decreases. Buyers who benefit from uniform pricing are those with relatively little runner-up competition — precisely the buyers who face weak bargaining positions under negotiated pricing, and for whom the seller’s ability to use that position is constrained under a uniform rule.

Under negotiated pricing, a merger affects a transaction’s markup only if it brings the first-best and runner-up products for that transaction under joint ownership. A demerger to single-product manufacturers reduces total manufacturer surplus by 25%. The merger of the two largest firms increases total manufacturer surplus by 19%, but with highly unequal transaction-level effects. Comparing the same mergers across pricing regimes, negotiated pricing abates average markup-increasing merger effects but worsens them for a minority of transactions — those where the merger creates a first-best/runner-up pairing.

Scope Conditions

The model applies to complete-information settings where prices are negotiated transaction-by-transaction, buyers single-source for each discrete purchase occasion, and sellers have multiple spatially differentiated products. It is most directly applicable to business-to-business markets where individual transaction values are large enough to justify project-level negotiation.

Q: What is the fundamental difference between negotiated pricing in this paper and the standard Nash-in-Nash (NiN) bargaining framework? A: In standard NiN (Horn and Wolinsky 1988), a buyer negotiates one price per product and trades positive quantities of all products with negotiated prices, so all negotiated prices are observed in transaction data. In this paper, buyers make discrete single-sourcing choices — each project uses exactly one product — so only the chosen product’s price appears in data; the runner-up product and its counterfactual price are unobserved. Additionally, under NiN, prices are set at the buyer level and apply uniformly to all the buyer’s needs, whereas here prices are negotiated separately for each project, generating intra-buyer cross-project price variation.

Q: What is the equilibrium markup formula, and what determines whether the Nash bargaining solution or the TIOLI constraint binds? A: The equilibrium first-best markup is ρ*j(1) = min[bj(1)(wj(1) − w0), (wj(1) − wj(2))], the minimum of the unconstrained Nash bargaining solution and the first-best seller’s surplus advantage over the runner-up. The TIOLI constraint (surplus advantage) binds when the seller’s bargaining skill is sufficiently high that the unconstrained NBS would exceed the surplus advantage — that is, when bj(1)(wj(1) − w0) > (wj(1) − wj(2)). Runner-up and all lower-ranked sellers earn zero markups in equilibrium because competition from the first-best drives their outside-option constraint to bind.

Q: Why do third-best and lower-ranked sellers have no effect on equilibrium outcomes? A: Because the most attractive offer any seller below the runner-up could make is a zero markup, and the runner-up already offers a zero markup due to competition from the first-best. Since the runner-up at zero markup already offers the buyer at least as much utility as any third-best product, the third-best cannot improve the buyer’s position. Proposition 1 (part iii) shows that the equilibrium markup and choice are invariant to N for N in {2, …, N̄}.

Q: How does the paper address the econometric challenge that the runner-up product and its price are unobserved? A: The paper derives a tractable closed-form likelihood for the joint probability of the observed product choice and the observed negotiated price, integrating out the unobserved idiosyncratic taste terms along with their implications for the identity and surplus of the unobserved runner-up product. The GEV distributional assumption on taste terms is crucial: it ensures that (1) choice probabilities have a closed form, (2) the surplus advantage can be expressed in terms of observed surpluses and GEV terms, and (3) the probability that the NBS is constrained has a closed form. This reduces the full problem to a lower-dimensional numerical integral over the normally distributed random effects.

Q: What empirical evidence motivates the negotiated pricing model over simpler alternatives? A: Four data patterns motivate the model. First, prices vary across projects even after controlling for product identity and buyer identity — intra-buyer cross-project variation that is inconsistent with standard NiN where prices are set at the buyer level. Second, prices are lower, other things equal, when there is greater local competition from manufacturers not chosen for a project — inconsistent with standard NiN where excluded products play no competitive role. Third, buyers have many projects and make a discrete single-sourcing choice for each. Fourth, sellers are multi-product firms with products differentiated spatially and in other dimensions.

Q: What do the price regressions reveal about price determinants? A: Adding year effects to a simple regression explains only a small share of price variation (R² rises from 0.000 to 0.118 for the full sample). Adding variety-year effects raises R² to 0.775 and adding buyer-variety-year effects to 0.918, but still leaves substantial unexplained variation. Panel B regressions show that prices decrease with quantity, increase with input prices (gas price coefficient 27.2, wage coefficient 8.3), decrease with buyer-to-seller size ratio (coefficient −2.51), and decrease with greater local competition (a distance advantage indicator raises price by about 0.48–2.20 and N(DST) count reduces price by about 1.49–1.53 depending on specification).

Q: What do the parameter estimates imply about spatial differentiation and buyer preferences? A: Transport costs have a strongly negative effect on value (coefficient on distance is −1.27, s.e. 0.04), and the interaction of distance with fuel costs is also negative and significant. The nesting parameter σJ is estimated at 0.47, indicating substantial within-group taste correlation across products from the same firm. Product characteristics matter: red and wire-cut bricks are preferred, and there are significant interactions between weather conditions and technical brick characteristics (frost positively interacts with strength; rainfall negatively interacts with absorption), indicating that buyers value bricks whose technical performance is suited to their project’s climate.

Q: How is the mean seller bargaining skill estimated, and how is the TIOLI model rejected? A: The mean seller bargaining skill b̄ is estimated at 0.41 (s.e. 0.03), substantially below one. The TIOLI restriction corresponds to b̄ = 1 (all markup determined by surplus advantage). A likelihood ratio test rejects this restriction with a chi-squared statistic of 847 (p < 0.001), providing strong statistical evidence that buyer bargaining power — not just competitive pressure — constrains markups below the TIOLI level.

Q: What are the main findings regarding the distribution of price-cost margins? A: Price-cost margins (Lerner index form) are low on average, with a mean of 0.08, but vary widely across transactions, with a coefficient of variation of 0.78. Sellers set higher margins to buyers located relatively close to them (lower transport costs make the seller more attractive to the buyer, strengthening the seller’s position). Multi-product manufacturer portfolios also affect markups, but the relevance of multi-product ownership varies across projects depending on whether different products from the same firm compete as first-best and runner-up for a given project.

Q: What does the uniform pricing counterfactual show, and how does it differ from the Hotelling benchmark? A: Switching from individually negotiated to uniform pricing raises average markups by 34% at the observed market structure. However, effects are heterogeneous: approximately 15% of transactions see markup decreases. Buyers who benefit from the switch are those in transactions with relatively weak runner-up competition — who had weak bargaining positions under negotiated pricing — and who gain because uniform pricing prevents sellers from exploiting that weakness. This contrasts with the result from the simple Hotelling linear city model (Thisse and Vives 1988), where switching to uniform pricing raises all markups.

Q: How does the demerger counterfactual quantify multi-product effects? A: Decomposing the observed market to single-product manufacturers reduces total manufacturer surplus by 25%. This large reduction reflects the role of multi-product ownership in determining who the runner-up is for each transaction: when a manufacturer owns multiple products, it can avoid internal competition between its own first-best and runner-up products, preserving its surplus advantage. The impact is highly unequal across individual transactions, however, because the relevance of multi-product effects depends on whether any of a manufacturer’s other products would have been the runner-up for a given project.

Q: What does the merger of the two largest firms imply for markups and surplus? A: The merger of the two largest firms (by market share) increases total manufacturer surplus in the industry by 19%. Markup increases are very unequal across transactions: the merger affects only those transactions for which the merging firms jointly become the first-best and runner-up, which is the mechanism highlighted in the 2010 US Merger Guidelines for negotiated pricing markets. The heterogeneity of effects means that aggregate market-level concentration measures (such as HHI changes) can be poor proxies for merger effects in these markets.

Q: How does the pricing regime interact with merger effects? A: Comparing the same mergers under negotiated versus uniform pricing, negotiated pricing abates the average markup-increasing effects of mergers. However, for a minority of transactions — specifically those where the merger creates a first-best/runner-up pairing that did not exist pre-merger — negotiated pricing makes the merger’s markup effect worse than it would be under uniform pricing. This implies that the direction of the pricing-regime effect on merger harm is not uniform across buyers, and that transaction-level analysis is required for accurate antitrust assessment.

Q: How does the paper relate to the Competition Commission’s 2007 assessment of the Wienerberger/Baggeridge merger? A: The CC (2007) found the market highly concentrated (HHI 2,113, implied HHI increase of 390 from the merger, both exceeding guideline thresholds) but approved the merger, judging profitability to be at or below average for comparable industries and competition to be more intense than the concentration level alone would suggest. This paper’s model provides formal underpinning for that assessment: with negotiated pricing and buyer bargaining power, markups are constrained by the runner-up competitive threat at the transaction level, not by market-wide concentration, and the low mean Lerner index of 0.08 is consistent with the CC’s profitability finding.

Q: What external validity evidence supports the model’s cost specification? A: The paper compares the marginal costs implied by the estimated model to plant-month level production cost data that were not used in estimation. A good match between the two provides external validation of the cost specification and supports the model’s structural interpretation of the markup decomposition.

First-best and runner-up products: Defined at the project level in terms of surplus (value minus cost). The first-best product j(i,1) is the inside good yielding the highest surplus for project i; the runner-up j(i,2) is the highest-surplus inside good not sold by the first-best seller. These two products — and only these two — determine the equilibrium markup and buyer choice; third-best and lower-ranked products are irrelevant.

Surplus advantage: The difference wj(i,1) − wj(i,2) ≥ 0 between the first-best product’s surplus and the runner-up’s surplus for a given project. This is the competitive constraint on the first-best seller’s markup under TIOLI pricing and the binding ceiling on the negotiated markup whenever the unconstrained Nash bargaining solution would exceed it.

Negotiated pricing: A pricing arrangement in which buyers negotiate prices specific to the individual purchase occasion (here, each construction project), as opposed to uniform pricing where the pre-transport price is the same for all buyers. Prices are determined bilaterally between buyer and competing sellers, with the buyer’s outside option — buying the runner-up at its anticipated negotiated price — serving as the competitive constraint.

Outside option principle (Binmore et al. 1989): The principle that a rival offer (outside option) has no effect on a bilateral Nash bargaining problem unless it would leave the receiving party better off than the Nash bargaining solution — i.e., it constrains rather than shifts the disagreement point. In the paper’s model, the runner-up seller’s zero-markup offer serves as the first-best seller’s constraining outside option when seller bargaining skill is high.

GEV (Generalized Extreme Value) taste distribution: The distributional assumption on project-product idiosyncratic match terms that makes the joint likelihood of observed product choice and negotiated price tractable. The GEV structure yields closed-form choice probabilities (nested logit) and allows the surplus advantage — which depends on unobserved runner-up surplus — to be expressed analytically, enabling joint estimation from transaction-level data.

Price-cost margin (Lerner index): Markup (price minus cost) divided by price, used here at the transaction level. The estimated mean Lerner index is 0.08 with a coefficient of variation of 0.78, reflecting wide dispersion driven by spatial variation in local competition and first-best surplus advantage across transactions.

Nash-in-Nash (NiN) vs. single-sourcing bargaining: NiN (Horn and Wolinsky 1988) applies when a buyer trades positive quantities of all products with negotiated prices (multi-sourcing); the paper’s model applies when a buyer makes a discrete single-sourcing choice per occasion, so only the chosen product’s price is observed. The distinction generates different data observability and different competitive mechanisms — in NiN, excluded products play no role; in this paper, the runner-up’s potential zero-markup offer disciplines the first-best seller’s markup.