What is the Stackelberg Model?

The Stackelberg model is a leadership model that allows the firm dominant to set its price first. Subsequently, the follower firms optimize their production and cost. It was formulated by Heinrich Von Stackelberg in 1934.

Let us assume a market with three players – A, B, and C. If A is the dominant force, it will set the product’s price first. After that, firms B and C will follow the price set and adjust their production basis supply and demand patterns accordingly.

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Assumptions in the Stackelberg Model

  • A duopolist can sufficiently recognize market competition based on the Cournot model.Each firm aims to maximize its profits based on the expectation that the decisions of its competitors will not be affected by its output.It assumes perfect information for all players in the market.Note: An underlying assumption with the Cournot model is that the operating firms cannot collude and must seek to maximize profits based on their rivals’ decisions.

However, models such as Stackelberg, Cournot, and Bertrand have assumptions that do not always hold in real markets. While one firm may follow Stackelberg’s principles, the other might not. Thus, be creating a situation of complexity.

Key Takeaways

  • The first two scenarios will result in an equilibrium condition after a time-lapse where the profit maximization functions will serve as the determinants.In case 3, a warfare situation will occur as equilibrium will be difficult to establish. Therefore, it can be expected such a loggerhead stance can only be eliminated if there is a collision or failure of the weaker firm leading to a monopoly in the market.Finally, in case 4, the profit maximization expectations will not hold, and they must revise. That gives rise to the Cournot condition.

Possible Scenarios of the Stackelberg Model

The following circumstances are possible if two firms, A and B, participate in a duopolistic competition:

  • Write the demand function for the market. Write the cost functions for both firms A and B in the market. The individual reaction functions in the duopoly are found by taking the partial derivates of the profit function. Assume firm A as a leader, and obtain the profit maximization equation for firm A, substituting firm B’s profit function in firm A equation. Solve for firm B as being the follower.

  • Firm A chooses to be the leader, and B wants to be the follower.Firm B chooses to be the leader, and A wants to be the follower.Both A and B want to be the leaders.Both A and B choose to be followers.

Further note

  • The Stackelberg model follows a sequential move pattern and is not simultaneous. We can say that the leader who naturally has the first-mover advantage takes control of the output and hence, price setting.Following the above argument, the Stackelberg leader firms have a smaller market share, and profit marginsProfit MarginsProfit Margin is a metric that the management, financial analysts, & investors use to measure the profitability of a business relative to its sales. It is determined as the ratio of Generated Profit Amount to the Generated Revenue Amount. read more.

Understanding the Stackelberg Graphically

An important genesis of this model is that one of the Stackelberg leaders produces more output than it would have made under the Cournot equilibrium. Similarly, the follower in the Stackelberg model stimulates less production than that in the Cournot model. To demonstrate this, look at the graphical representation below: –

Assuming the X-axis represents firm A’s production and Y-axis for firm B’s output. Then, the quantities Qc and Qs indicate an equilibrium point for Cournot and Stackelberg conditions, respectively.

If firm A assumes itself as the Stackelberg leader and B as the follower, it will produce Qa’ quantity. Consequently, firm B follows with Qb’, which is the best it can maximize up to. Notice that Qs is the Stackelberg equilibrium point where firm A produces more than it could create at Qc, the Courton equilibrium point.

Similarly, when firm B follows after firm A has taken the output decision, it produces much less than it could have in a Courton game.

Stackelberg vs Other Models

The comparison of the Stackelberg model to the other models is given below:

The similarity to the Cournot Model 

  • Both models assume quantity to be the basis of competition.Both models assume homogeneity of products instead of the Bertrand model, including theory on differentiated products.

Conclusion

Stackelberg’s model remains an important strategic model in economics. This model is useful to a firm when it realizes profitabilityProfitabilityProfitability refers to a company’s ability to generate revenue and maximize profit above its expenditure and operational costs. It is measured using specific ratios such as gross profit margin, EBITDA, and net profit margin. It aids investors in analyzing the company’s performance.read more prospects under the first-mover advantage concept. A practical instance where leaders show commitment to the first move is capacity expansion. It is assumed that one cannot undo the action. In principle, Stackelberg’s strategy is important where the first mover, the leader, acts irrespective of the follower’s movement.

This article is a guide to a Stackelberg Model definition. We discuss the assumptions, consequences, and comparison of the Stackelberg model to other models. You can learn more about finance from the following articles: –

  • Market Share FormulaDiseconomies of Scale ExampleExamples of PEST AnalysisNeoclassical Economics Theory