## 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.

### 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:

**Step1:**Write the demand function for the market.**Step 2:**Write the cost functions for both the firm’s A and B in the market.**Step 3:**The individual reaction functions in the duopoly are found by taking the partial derivates of the profit function.**Step 4:**Assume firm A as a leader, obtain profit maximization equation for firm A substituting firm B’s profit function in firm A equation.**Step 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:

- 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

#### 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.

#### Further note

- Since the Stackelberg model follows a sequential move pattern and not simultaneous, it can be said that the leader who naturally has the first-mover advantage takes control of the output and hence, price setting.
- Following the above argument, the firms that follower the Stackelberg leader have a smaller market share and profit margins.

### 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.

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:

**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 profitability 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.

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