Take the Goods and Run: Contracting Frictions and Market Power in Supply Chains

Overview

This paper studies the efficiency of self-enforced relational agreements in manufacturing supply chains when sellers have market power and contracts cannot be externally enforced. The setting is Ecuador, an upper-middle-income country with slow commercial courts (debt enforcement takes around two years even after a 2016 reform) and highly concentrated manufacturing markets (average Herfindahl-Hirschman Index of 0.6 for 6-digit economic codes, well above the 0.25 threshold used by the US Department of Justice to identify highly concentrated markets).

Research question. How efficiently do long-term trade relationships operate, period by period, when the seller can price discriminate and the buyer can opportunistically default on trade-credit debt? Does seller market power worsen or mitigate enforcement-driven inefficiencies?

Data. The paper uses three Ecuadorian government administrative databases: (1) an electronic invoicing (EI) system covering all sales of 49 large manufacturing firms in textiles, pharmaceuticals, and cement products for 2016–2017, providing product-level unit prices, quantities, and payment method for each buyer-seller pair (median seller has 600 buyers); (2) the universe of firm-to-firm VAT transactions from 2008–2015, used to measure relationship age (censored at 9 years); and (3) annual financial statements providing variable costs to proxy marginal cost.

Model. The author develops a dynamic contracting model that embeds non-linear pricing with heterogeneous buyers (following Jullien 2000 and Attanasio-Pastorino 2020) into an infinitely repeated game with limited enforcement (following Martimort et al. 2017). The seller holds all bargaining power, commits to a long-term menu of prices and quantities, and finances every transaction through trade-credit. The buyer has a privately observed, fully persistent type (willingness to pay) and can opportunistically default after delivery — “take the goods and run” — at the cost of losing the future relationship. The seller uses the value of the ongoing relationship as the enforcement instrument. The paper solves the seller’s profit-maximization problem using a recursive Lagrangian approach, yielding a modified virtual-surplus condition that governs optimal quantity allocations as a function of current and past limited-enforcement Lagrange multipliers (LE multipliers).

Six motivating empirical facts documented in the data: (1) New buyers are ~35% of pairs but account for only ~10% of total trade; relationships lasting nine or more years are less than 10% of pairs but generate over 30% of trade. (2) Trade-credit is used in approximately 65% of transactions in the first year and 70–75% in older relationships. (3) Quantities increase as relationships age. (4) A 10% increase in quantity purchased is associated on average with a 2% decrease in unit price (quantity discounts). (5) Conditional on quantity, older buyers pay up to 3% less; these price discounts appear only in trade-credit transactions, not in pay-in-advance transactions. (6) Approximately 40% of new relationships survive one additional year, 60% of relationships aged 1–3 years survive, and more than 75% of relationships aged four or more years survive.

Key structural finding. Almost all new relationships have binding enforcement constraints. The estimated LE multiplier equals 1 (unconstrained) only for the top 1% of pairs at tenure 0. As relationships age, the constraint relaxes and quantities are backloaded — consistent with the seller making promises of higher future trade to incentivize current debt repayment.

Efficiency results. New relationships operate at approximately 30% of the frictionless (first-best) surplus level. Efficiency rises to 60% at tenure 2, 75% at tenure 4, and over 80% at tenure 5. Aggregating across buyers weighted by efficient quantities: only 5% of sellers trade efficiently with new buyers, rising to 70% by tenure 2 and 84% in the long term. By sector, 68% of textiles, 88% of pharmaceutical, and 95% of cement-product sellers reach efficient aggregate output by tenure 5. Sellers capture approximately 80% of generated surplus; the median buyer captures around 25%, and the smallest buyers may capture less than 10%.

Counterfactuals reveal a second-best interaction. Fixing enforcement alone (Counterfactual a: non-linear pricing with perfect enforcement) raises surplus for 75% of buyers in the early tenures but reduces surplus for essentially all buyers in later tenures, because the threat of buyer default was the force compelling the seller to promise growing quantities over time. Fixing market power alone (Counterfactual b: uniform pricing with limited enforcement) collapses surplus to 0–40% of the baseline because the seller can no longer tailor dynamic incentives to each buyer’s enforcement constraint, causing a large share of buyers to be excluded from trade. Addressing both frictions simultaneously (Counterfactual c: uniform pricing with perfect enforcement) raises surplus for most buyers in early tenures but remains welfare-reducing for high types in later tenures; the aggregate effect depends critically on weighting: positive (~40% gain) when weighted by number of buyers, negative (surplus falls to ~58% of baseline) when weighted by quantities.

Q&A

Q1: What is the central theoretical mechanism by which limited enforcement leads to backloading of quantities in the model?

The buyer can default after delivery because payment is post-delivery (trade-credit). To prevent this, the seller must ensure the buyer’s discounted future net returns exceed the current payment obligation. This creates a forward-looking enforcement constraint: the seller must credibly promise sufficiently large future quantities at lower prices. As a result, current quantities are distorted downward (the seller delays granting full trade volumes), but quantities increase over time as past promises become binding promise-keeping constraints. The optimal contract is therefore non-stationary: total surplus generated and the buyer’s net return both increase over time even without efficiency gains in production.

Q2: How does seller market power interact with enforcement frictions — does it worsen or improve efficiency relative to a perfect-enforcement benchmark?

The paper’s key finding is that market power and enforcement constraints act as partially offsetting frictions. Seller market power creates downward quantity distortions (the seller restricts supply to extract rents). Limited enforcement, however, compels the seller to promise growing quantities to prevent buyer default, which counteracts the market-power distortion. Thus, in older relationships, the enforcement constraint effectively disciplines the seller’s rent-extraction incentives, producing trade levels that approach the frictionless first-best. This is an instance of the theory of second-best: each friction partially offsets the other, so removing only one friction can reduce total welfare.

Q3: What are the six motivating empirical facts and why do they rule out standard alternative explanations?

The six facts are: (1) heavy concentration of trade in long-established relationships; (2) widespread trade-credit even in new relationships; (3) quantities increase with relationship age; (4) quantity discounts within any age cohort; (5) older buyers pay lower prices conditional on quantity; (6) survival rates increase with quantity and relationship age. Alternative models — efficiency gains, learning, demand assurance, and supply-side enforcement issues — cannot jointly account for all six patterns under realistic assumptions. Critically, Fact 5 holds only in trade-credit transactions and not in pay-in-advance transactions, which supports limited enforcement (not learning or demand assurance) as the underlying mechanism.

Q4: How is the model identified from cross-sectional data on prices and quantities for a single seller?

Identification exploits two sources of variation. First, because the seller offers non-linear price menus that induce type revelation, cross-sectional variation in prices and quantities across buyers reveals their underlying private types. Second, for the highest-type buyer at tenure 0, the cumulative LE multiplier equals 1 by construction, so the gap between the observed marginal price and marginal cost directly reveals the current enforcement multiplier for that type; cross-sectional variation across high-type buyers then identifies the elasticity parameter β. Once β is pinned down, the multipliers for all types and tenures are recovered as unique solutions to ordinary differential equations, and buyer types are recovered semi-parametrically. The approach requires only cross-sectional data from one seller per year — no panel of individual buyers is needed.

Q5: What are the estimated magnitudes of the marginal product of capital wedge, and how do they compare to related studies?

The paper finds a wedge between the buyer’s marginal product of capital (MPK) and the transaction price of 40% for the median new relationship and 34% for the median tenure-5 relationship. These wedges are smaller than the 80% gaps estimated for Indian firms by Banerjee and Duflo (2014), and larger than the average 6% gap calculated by Blouin and Macchiavello (2019) in the international coffee market. They are also much smaller than the 300–500% gaps estimated for Mexican micro-enterprises by McKenzie and Woodruff (2008), which is consistent with the buyers in this sample being substantially larger (median yearly sales of USD 200,000).

Q6: What does Counterfactual (a) — perfect enforcement with non-linear pricing — reveal about the intertemporal trade-off?

Counterfactual (a) shows massive short-run gains for low and middle types: surplus at tenure 0 increases to 1,508% and 628% of baseline for the bottom 10th and median buyer percentile groups respectively. However, for higher types (top 25%), perfect enforcement is immediately welfare-reducing because these buyers are already trading near efficiently and the seller loses the incentive to grow quantities over time once default is not a threat. By tenure 3 and beyond, perfect enforcement reduces surplus for essentially all buyers. The aggregate effect is negative because high-type buyers, who trade larger volumes, bear larger losses in later tenures when those tenures are weighted by quantity.

Q7: Why does uniform pricing with limited enforcement (Counterfactual b) perform so poorly?

Under uniform pricing, the seller cannot tailor the dynamic contract to each buyer’s individual enforcement constraint. Without individualized price-quantity menus, many buyers cannot credibly commit to repaying their debts — because the seller cannot offer a sufficiently personalized future stream of benefits — and are thus excluded from trade entirely. For instance, at tenure 0, 95.8% of the bottom-decile buyers and 64% of median buyers are excluded. The aggregate surplus under this regime reaches only 3–68% of baseline across different tenures and percentile groups. This implies that the seller’s price discrimination ability, while generating informational rents, also serves a second purpose: it allows each buyer’s specific enforcement constraint to be satisfied, enabling trade that would otherwise be infeasible.

Q8: What do the sector-level results suggest about the generalizability of the main findings?

All six motivating empirical facts are consistent across the three industries studied (textiles, pharmaceuticals, and cement products). The efficiency patterns also appear in all three sectors, though with heterogeneous speeds of convergence. Pharmaceutical and cement-product sellers converge faster (88% and 95% efficient at tenure 5) than textiles sellers (68% efficient at tenure 5). The finding that relationships approach efficiency in the medium and long term holds in every industry analyzed, suggesting that the underlying mechanisms — limited enforcement and seller market power — are broadly operative rather than sector-specific.

Q9: How does the paper establish that the standard non-linear pricing model without enforcement constraints does not explain the data?

The paper tests whether the LE multiplier at tenure 0 (G0) is statistically distinguishable from the null hypothesis of a standard non-linear pricing model (which would imply G0 = 1 for all buyers). Based on t-statistics from the estimated distribution of G0 across seller-year markets, the null of a standard model is rejected for 86% of the markets (seller-years) in the sample. Additionally, the dynamic price discounts conditional on quantity — which are the key signature of backloading — appear only in trade-credit transactions and not in pay-in-advance ones, ruling out alternative explanations such as learning about buyer quality or demand assurance.

Q10: What are the model’s main limitations and how do they affect the counterfactual conclusions?

The author flags three principal limitations. First, buyer types are assumed fully persistent due to data constraints (only two years of invoice-level data); a Markov type structure would require longer buyer-level panels. Second, the identification strategy relies on the seller’s first-order optimality conditions and cannot recover counterfactual dynamic quantities — the counterfactuals are therefore static comparisons of per-period surplus rather than full dynamic simulations. Third, if buyers have unobserved outside options, the counterfactual efficiency results may be biased, though the direction of the bias is uncertain and depends on the distribution of types and the curvature of the return function.

Key Concepts

Limited enforcement constraint (LE-B). The paper’s central friction: because payment is post-delivery, the buyer can default and keep the goods. In the model, the contract is “default-free” only if the buyer’s post-delivery payment is weakly less than the discounted value of all future truthful net returns. The constraint is binding when this condition is tight — the buyer is on the margin of defaulting. When binding, it forces the seller to reduce current tariffs and quantities (to lower the attractiveness of default) while promising higher future quantities (to raise the continuation value).

Limited enforcement Lagrange multiplier (LE multiplier), Gt(α). The shadow price on the buyer’s enforcement constraint at tenure t for a buyer at quantile α. It takes values in [0,1], equals 1 only when the enforcement constraint is slack (unconstrained buyer), and equals zero for the lowest type at all tenures. In the paper’s framework, the entire trajectory of Gt(α) across tenures encodes the history of past enforcement promises and is the key object identified and estimated to recover the dynamic distortions.

Backloading. The equilibrium property whereby the total surplus generated by the relationship and the buyer’s net return both increase over time. The seller achieves this by initially restricting quantities and promising growing future allocations as an enforcement device. Formally, quantities increase over time if and only if enforcement constraints are relaxed (gt+1(q) ≤ gt(q)).

Modified virtual surplus. The object that replaces ordinary virtual surplus (which appears in standard non-linear pricing models) in the seller’s first-order condition. It augments standard virtual surplus by adding shadow costs for current binding enforcement constraints and subtracting corrections for past enforcement promises. Optimal quantity allocations are determined by an inverse-markup rule applied to this modified virtual surplus.

Relational agreement / self-enforced relational contract. An informal long-term agreement sustained purely through the repeated interaction between the parties, without access to third-party (court) enforcement. In this paper’s setting, the seller disciplines the buyer’s opportunism exclusively through the threat of relationship termination; no legal recourse is available or used in equilibrium.

Quantity discounts (non-linear pricing / wholesale quantity discounts). Price schedules under which the unit price decreases with the quantity purchased, offered by a seller with market power. In the paper’s empirical setting, a 10% increase in quantity is associated with a 2% decrease in unit price, and these discounts appear at every relationship age. The model generates them as the incentive-compatibility requirement that ensures higher-type buyers truthfully reveal their demand.

Trade-credit. Seller financing of the transaction, in which goods are delivered before payment is received. In the Ecuadorian data, approximately 65% of first-year purchases and 70–75% of purchases in mature relationships are conducted via trade-credit. Because the seller bears the full cost of buyer default, trade-credit is the financial arrangement that gives rise to the limited enforcement constraint studied in the paper.

Second-best interaction of frictions. The paper’s counterfactual finding that removing a single friction (either enforcement or market power) can reduce total welfare when both frictions are present simultaneously. This occurs because the two frictions partially offset each other: enforcement constraints discipline the seller’s monopoly distortions, and market power allows the seller to price-discriminate in ways that enable enforcement in the first place. Addressing both frictions simultaneously can improve welfare, consistent with the Lipsey-Lancaster theory of second-best.