Why the Leader Would Not Follow: A Pricing Game Between a Ready-Mix Producer and a Rival That Also Sells It Cement
Student Name
American College of Education
ECON5003: Economics Analysis
Module 3 Assignment
Instructor Name
July 17, 2028
The Question Left Open
Module 2 found that an $8 increase in the price of Bellwether Ready-Mix's standard residential mix would add about $1.2 million a year in contribution if the market's price leader followed, but would lose about $135,000 if it did not. The decision therefore depends on the leader's response, and the leader's response depends on its own interests. This paper models that interaction as a game between the two firms. The two independent producers, which Module 1 found to be price takers, are treated as following whichever price the larger firms settle on. In a concentrated market, every price is a move in a game whether or not the players think of it that way.
The Payoffs
Each firm chooses to raise its residential price by about $8 or to hold. Payoffs are changes in annual contribution, in millions of dollars, relative to both holding. If both raise, Bellwether gains about $1.2 million, from Module 2, and the leader, with a larger residential volume, gains about $2.0 million. If Bellwether raises and the leader holds, Bellwether loses about $0.1 million as customers switch, and the leader gains from the volume it captures. That gain has two parts: about $0.9 million of ready-mix contribution on the switched volume, and about $1.4 million of additional contribution at its cement plant, which is running at 68 percent of capacity and earns a high margin on every extra ton, for a total of about $2.3 million. If the leader raises and Bellwether holds, Bellwether gains about $0.6 million from captured volume and the leader loses about $0.4 million. If both hold, both payoffs are zero.
The cement component is what makes this market unusual. Because the leader sells cement to Bellwether and also uses cement in its own concrete, it earns cement margin on almost every yard poured in the market, but more on yards it delivers itself, since it then also earns the ready-mix margin and runs its own plants closer to capacity.
Best Responses and the Equilibrium
Consider the leader's best response to each of Bellwether's choices. If Bellwether raises, the leader earns $2.0 million by also raising and $2.3 million by holding, so it holds. If Bellwether holds, the leader earns $0.4 million less by raising than by holding, so it holds. Holding is the leader's best response either way, a dominant strategy in this version of the game. Bellwether's best response depends on the leader: if the leader raises, Bellwether does better raising, $1.2 million against $0.6 million; if the leader holds, Bellwether does better holding, zero against a $0.1 million loss. Given that the leader holds, Bellwether holds, and the equilibrium is both holding.
The sequential version, in which Bellwether moves first and the leader observes and responds, gives the same answer. The leader would see Bellwether's increase and hold, capturing volume and cement sales, so Bellwether should not lead. This is exactly the pattern in Bellwether's history: when it raised prices alone two years ago, the leader did not follow for three months. The model explains that episode as a rational response, not bad luck.
Relaxing the Assumptions
Three features of the real market could change the result. The first is capacity. Kreps and Scheinkman (1983) showed that when firms first commit to capacity and then compete on price, the outcome resembles quantity competition, with prices above cost, because no firm can serve the whole market. The leader's spare capacity is what makes capturing volume attractive; if its plants were near full, holding would gain little and following would become its best response. Bellwether should expect the leader to follow price increases more readily in a construction boom, when capacity is tight, than in a slowdown.
The second is repetition. The two firms face each other every season. Axelrod and Hamilton (1981) showed that in repeated interactions, strategies that reciprocate, cooperating when the other cooperates and retaliating when it does not, can sustain cooperation that a single interaction would not. In pricing, this means a leader that captures volume after every rival increase may provoke aggressive responses in segments where the rival is stronger, such as the eastern suburbs. The third is the independents: at a price gap of $8, they would capture some switching customers too, reducing the leader's gain from holding and making following somewhat more attractive than the model suggests.
The Legal Line
Any strategy that depends on a rival's price must stay within antitrust law. Firms may observe rivals' public prices and decide independently whether to follow, which is how price leadership lawfully works in concentrated markets. They may not agree, directly or through intermediaries, on prices, bids or customers, and they should not signal intentions through channels designed to coordinate. Bellwether's sales staff must not discuss prices with the leader's staff, including in conversations about cement purchases, which bring the two firms into regular contact. The company should route cement purchasing through its procurement manager, who has no role in ready-mix pricing, and document the separation.
Competing Where Price Is Not the Weapon
If Bellwether cannot profitably lead on price, it can compete on the dimensions the price game leaves out. Ready-mixed concrete looks like a commodity, but its delivery is a service: the right mix, at the right site, at the right minute, with a driver who knows how to place it. Syverson (2008) notes that producers differ considerably in productivity and that local conditions shape how they compete, which leaves room for firms that deliver more reliably or more efficiently to earn better margins than rivals selling the same product. Bellwether's reputation for dispatch reliability is exactly such an advantage, and it is harder for the leader to match quickly than a price cut.
Three investments follow from this. Bellwether can offer residential builders guaranteed delivery windows with a credit for late trucks, turning its reliability into a visible promise. It can place a small satellite plant in the fast-growing eastern suburbs, shortening haul times where its position is strongest. And it can train its drivers to handle the finishing contractors' requests on site, which builders value and rarely receive. Each raises the cost to a customer of switching to the leader for a few dollars a yard, which in the language of the game lowers the elasticity Bellwether faces and raises the price it can charge without the leader's cooperation.
Strategy for Bellwether
The analysis supports three conclusions. First, Bellwether should not lead a residential price increase of $8 while the leader has spare capacity; the leader's best response is to hold. Second, Bellwether should follow the leader's increases promptly, since following is its best response when the leader raises. Third, Bellwether should reduce the leader's advantage over time by diversifying its cement supply, since the cement relationship both raises the leader's gain from capturing Bellwether's customers and limits Bellwether's freedom. A second cement source at a delivered cost within $5 a ton of the leader's would weaken the leader's incentive to hold and strengthen Bellwether's position in every future round of this game.
References
Axelrod, R., & Hamilton, W. D. (1981). The evolution of cooperation. Science, 211(4489), 1390-1396. https://doi.org/10.1126/science.7466396
Kreps, D. M., & Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes. The Bell Journal of Economics, 14(2), 326-337. https://doi.org/10.2307/3003636
Syverson, C. (2008). Markets: Ready-mixed concrete. Journal of Economic Perspectives, 22(1), 217-233. https://doi.org/10.1257/jep.22.1.217
How this ECON 5003 Module 3 example is structured
ECON 5003 Module 3 in many sections turns to rivalry and how a competitor's response changes yours; your classroom's instructions decide the modeling tools. This example sets up a simple two-player game with explicit payoffs, explains where each payoff comes from and solves it both as a simultaneous and a sequential game. It then relaxes the model's assumptions, considering capacity, repetition and the smaller rivals, and ends with a strategy that respects the legal line between observing a rival and coordinating with one.
ECON5003 Module 3 questions, answered
What does ECON5003 Module 3 usually ask for?
ECON5003 Module 3 in many sections asks students to analyze competitive rivalry, often using game theory to show how a competitor's likely response changes a firm's best decision. Your classroom's instructions decide whether a payoff matrix, sequential game or other tools are required.
How do I find a Nash equilibrium in a pricing game?
For each player, find the best response to each of the other player's choices. An outcome in which each player's choice is a best response to the other's is a Nash equilibrium. If one player has a strategy that is best regardless of the other's choice, it is a dominant strategy.
Is following a competitor's price increase legal?
Independently observing a rival's public prices and deciding whether to match them is generally lawful. Agreeing with rivals on prices, directly or indirectly, is illegal. Firms should keep pricing decisions independent and avoid price discussions with competitors.
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