Stackelberg Model

What is the Stackelberg Model?

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

In simple words, let us assume a market with three players – A, B, and C. If A is the dominant force, then it will set the price of the product first up. Firms B and C will follow the price set and will accordingly adjust their production basis supply and demand patterns.

Stackelberg Model

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Source: Stackelberg Model (wallstreetmojo.com)

Key Takeaways
  • Clearly, the first two scenarios will result in 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. It can be expected such a loggerhead stance can be eliminated only 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 it. This gives rise to the Cournot condition.

Assumptions in the Stackelberg Model

  • A duopolist can sufficiently recognize market competition to be 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 not always hold true in real markets. While one firm may choose to follow Stackelberg principles, the other might not thus be creating a situation of complexity.

Stackelberg Model Step By Step Calculations

Following steps can help in solving a basic problem based on Stackelberg model:

  1. Write the demand function for the market.

  2. Write the cost functions for both the firm’s A and B in the market.

  3. The individual reaction functions in the duopolyDuopolyWhen there are two market leaders in any industry or service, this is referred to as a duopoly. Such companies have complete control of the market, earning high profits and gains in a specific sector or service. In the credit card industry, for example, Visa and MasterCard have a duopoly.read more are found by taking the partial derivates of the profit function.

  4. Assume firm A as a leader, obtain profit maximization equation for firm A substituting firm B’s profit function in firm A equation.

  5. Solve for firm B as being the follower.

Possible Scenarios of Stackelberg Model

Following circumstances are possible if two firms A and B participate in a duopolistic competition:

  1. Firm A chooses to be the leader and B wants to be the follower
  2. Firm B chooses to be the leader and A wants to be the follower
  3. Both A and B want to be the leaders
  4. Both A and B choose to be followers

Further note

Understanding the Stackelberg Graphically

An important genesis of this model is that one of the Stackelberg leaders produces more output than it would have produced under the Cournot equilibrium. Similarly, the follower in the Stackelberg model produces less output than that in the Cournot model. In order to demonstrate this, look at the graphical representation below:

Assuming the x-axis represents the production of firm A and y-axis for the production of firm B. The quantities Qc and Qs indicate a point of equilibrium for Cournot and Stackelberg conditions respectively.

Understanding the Stackelberg Graphically

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

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

Stackelberg vs Other Models

Comparison of the Stackelberg model to the other models:

ParametersStackelbergCournotBertrand
QuantityMediumLowHigh
PriceMediumHighLow
Type of MoveSequentialSimultaneousSimultaneous

The similarity to the Cournot Model 

  • Both models assume quantity to be the basis of competition.
  • Both models assume homogeneity of products as opposed to the Bertrand model which also includes theory on differentiated products.

Conclusion

Stackelberg model remains an important strategic model in economics. This model is useful to a firm when it realizes prospects of 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 under the first-mover advantage concept. A practical instance where commitment to the first move is shown by leaders is capacity expansion. It is assumed that the action can not be undone. In principle, Stackelberg strategy is important where the first mover, the leader, acts irrespective of what the action of the follower is going to be.

This has been a guide to what is a Stackelberg model and its definition. Here we discuss the assumptions and various consequences of the Stackelberg model along with its comparison to other models. You can learn more about finance from the following articles –