Supply Chain Pricing

When a manufacturer sells through an independent retailer, each firm adds its own markup. The result is a retail price that exceeds the price a vertically integrated monopolist would set—reducing quantity sold, shrinking total channel profit, and harming consumers. This page examines why decentralized supply chains overprice, quantifies the efficiency loss, and explores contract designs that restore coordination.

The Vertical Pricing Problem

Most consumer goods pass through multiple stages before reaching the final customer. A semiconductor manufacturer sells chips to an electronics assembler, who sells finished devices to a retailer, who sets the shelf price. At each stage, the firm in control of the price decision marks up above its cost. When these stages are operated by independent, profit-maximizing firms, the compounding of successive markups leads to a final price that is strictly higher than the price a single vertically integrated entity would charge.

This phenomenon was first identified by Spengler (1950), who coined the term successive monopoly and showed that vertical integration benefits both the integrated firm and consumers. The modern supply chain coordination literature, surveyed comprehensively by Cachon (2003), frames the problem in terms of contract design: the manufacturer must choose a wholesale pricing mechanism that aligns the retailer’s incentive with total channel profit maximization.

The core insight is that a simple linear wholesale price creates an externality. When the retailer raises the retail price by one dollar, it captures the full marginal revenue increase but bears only a fraction of the quantity loss, because part of the lost margin accrues to the manufacturer. This misalignment of marginal incentives is the root cause of double marginalization.

Double Marginalization

Definition — Double Marginalization

Double marginalization occurs when two vertically related monopolists each impose a markup on the product. The manufacturer sets a wholesale price $w > c$ above its marginal cost $c$ , and the retailer then marks up above $w$ to set the retail price. The result is two successive monopoly markups where only one is needed, leading to a retail price that exceeds the vertically integrated optimum.

Consider a market with linear demand $q = a - b \cdot p$ , where $a$ is the demand intercept and $b$ is the price sensitivity. A vertically integrated firm with marginal cost $c$ would set the standard monopoly price.

Double Marginalization Theorem

Under linear demand $q = a - bp$ with manufacturer cost $c$ , the decentralized channel with a wholesale-price contract yields:

A retail price strictly above the integrated monopoly price: $p_d > p_I$ .
A quantity strictly below the integrated monopoly quantity: $q_d < q_I$ .
Total channel profit strictly below the integrated monopoly profit: $\Pi_d < \Pi_I$ .

In particular, the decentralized channel captures exactly 75% of the integrated monopoly profit under linear demand.

Formal Model

The manufacturer-retailer interaction is modeled as a Stackelberg game. The manufacturer moves first, choosing the wholesale price $w$ . The retailer observes $w$ and then sets the retail price $p$ to maximize its own profit.

Integrated Benchmark

A single integrated firm maximizes $\Pi = (p - c)(a - bp)$ . The first-order condition yields:

p_I = \frac{1}{2}\left(\frac{a}{b} + c\right)

with quantity $q_I = \frac{a - bc}{2}$ and profit $\Pi_I = \frac{(a - bc)^2}{4b}$ .

Decentralized Channel

Given wholesale price $w$ , the retailer maximizes $(p - w)(a - bp)$ , yielding the retailer’s best-response price:

p^*(w) = \frac{1}{2}\left(\frac{a}{b} + w\right)

The manufacturer anticipates this reaction and maximizes $(w - c) \cdot q(p^*(w))$ . Substituting and optimizing:

w^* = \frac{1}{2}\left(\frac{a}{b} + c\right)

The resulting retail price is:

p_d = \frac{3a}{4b} + \frac{c}{4} = \frac{1}{2}\left(\frac{a}{b} + w^*\right)

This price is strictly above the integrated price $p_I$ . The total decentralized channel profit is:

\Pi_d = \frac{3(a - bc)^2}{16b} = \frac{3}{4}\,\Pi_I

The 25% profit loss is a direct consequence of the retailer’s inability to internalize the manufacturer’s margin when setting its price. As Tirole (1988) notes, the problem generalizes to any number of vertical stages, with each additional markup further inflating the final price.

Numerical Example: Consumer Electronics

Suppose a tablet manufacturer faces demand $q = 1000 - 10p$ with production cost $c = \$10$ per unit.

Integrated: The optimal price is $p_I = (100 + 10)/2 = \$55$ , selling $q_I = 450$ units for a profit of $\Pi_I = 45 \times 450 = \$20{,}250$ .
Decentralized: The manufacturer sets $w^* = \$55$ . The retailer then prices at $p_d = \$77.50$ , selling only $q_d = 225$ units. Total channel profit is $\Pi_d = \$15{,}187.50$ , exactly 75% of the integrated benchmark.
Consumer harm: Consumer surplus drops from $\$10{,}125$ under integration to $\$2{,}531$ under decentralization. Both the firms and consumers are worse off.

Interactive Channel Comparison

The visualization below displays integrated and decentralized outcomes side by side. Adjust the demand parameters and manufacturing cost to see how the profit rectangles and deadweight loss change.

Each panel plots the demand line with price on the horizontal axis. Shaded rectangles represent profits: a single rectangle for the integrated firm, and two stacked rectangles (manufacturer in blue, retailer in green) for the decentralized channel. The red region is deadweight loss.

Coordination Contracts

Since the wholesale-price contract leaves 25% of channel profit on the table, the question becomes: can the manufacturer design a contract that induces the retailer to set the integrated price? The supply chain coordination literature, reviewed by Cachon (2003), offers several mechanisms.

Revenue-Sharing Contracts

Under a revenue-sharing contract, the retailer keeps a fraction $\phi \in (0, 1)$ of revenue and pays a reduced wholesale price $w = \phi \cdot c$ . Cachon and Lariviere (2005) show that this contract coordinates the channel: the retailer’s first-order condition becomes:

\max_p \; \phi \cdot p \cdot (a - bp) - w \cdot (a - bp)

Substituting $w = \phi c$ , the optimal retail price satisfies:

p^*_{RS} = \frac{1}{2}\left(\frac{a}{b} + c\right) = p_I

The retailer sets exactly the integrated monopoly price regardless of $\phi$ . The parameter $\phi$ determines only how profits are split between the two parties. When $\phi$ is high, the retailer keeps most of the revenue; when $\phi$ is low, the manufacturer captures more through the revenue share.

This result holds exactly under linear demand. In practice, revenue-sharing contracts are widespread in industries such as video rental (the Blockbuster-studio arrangement analyzed by Cachon and Lariviere, 2005), digital media licensing, and franchise agreements.

Buyback Contracts

An alternative coordination mechanism is the buyback contract, studied by Pasternack (1985). The manufacturer offers to repurchase unsold inventory at a predetermined buyback price. While buyback contracts are primarily designed for settings with demand uncertainty (where the retailer bears inventory risk), they can also mitigate double marginalization by lowering the effective wholesale cost perceived by the retailer. Under certainty, they reduce to a transfer payment that shifts the profit split without affecting the retail price, achieving coordination when combined with the appropriate wholesale price.

Interactive Contract Explorer

The grouped bar chart below compares three contract structures across retail price, total channel profit, and consumer surplus. Adjust the revenue-share fraction $\phi$ and market parameters to explore how coordination improves efficiency.

The wholesale-price contract always yields the lowest profit and highest retail price. Under revenue sharing, the retail price matches the integrated benchmark exactly, and channel profit reaches 100% efficiency. The $\phi$ parameter only redistributes profit between manufacturer and retailer.

The key managerial takeaway, emphasized by Phillips (2021), is that the choice of channel contract can have a larger impact on total profit than the choice of demand model or cost estimation method. A firm that negotiates a coordinating contract effectively captures the full integrated monopoly profit and then negotiates the split, rather than leaving 25% of profit uncaptured.

Capstone: Channel Negotiation

In Play mode, you negotiate wholesale prices and revenue-sharing terms as either manufacturer or retailer in a decentralized channel. See how your choices compare to the integrated monopoly benchmark and measure the efficiency loss from double marginalization. In Design mode, sweep contract parameters to find the coordinating terms that recover the full channel profit.

References

Cachon, G. P. (2003). Supply Chain Coordination with Contracts. In Handbooks in Operations Research and Management Science, 11, 227–339.
Cachon, G. P. & Lariviere, M. A. (2005). “Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations.” Management Science, 51(1), 30–44.
Pasternack, B. A. (1985). “Optimal Pricing and Return Policies for Perishable Commodities.” Marketing Science, 4(2), 166–176.
Phillips, R. L. (2021). Pricing and Revenue Optimization, 2nd ed.. Stanford University Press.
Spengler, J. J. (1950). “Vertical Integration and Antitrust Policy.” Journal of Political Economy, 58(4), 347–352.
Tirole, J. (1988). The Theory of Industrial Organization. MIT Press.