How do you find the equilibrium price for a duopoly?

How do you find the equilibrium price for a duopoly?

Once you know the optimal demand and optimal revenues for the market as a whole, you can now calculate the point of equilibrium for either company’s production, disregarding any collusion between the two using this formula: π = P(Q) q − C(q). In this formula: π is the individual company’s profit.

How the equilibrium is determined under Cournot’s model?

The Cournot model of oligopoly assumes that rival firms produce a homogenous product, and each attempts to maximize profits by choosing how much to produce. All firms choose output (quantity) simultaneously. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium.

Is Cournot equilibrium Pareto efficient?

Comparison with competitive equilibrium We conclude that the firms’ outputs and the price are different in a Nash equilibrium than they are in a competitive equilibrium. An implication is that, as for a monopoly, the Nash equilibrium outcome in a Cournot duopoly is not Pareto efficient.

How do you calculate equilibrium profit?

The monopolist’s profit maximizing level of output is found by equating its marginal revenue with its marginal cost, which is the same profit maximizing condition that a perfectly competitive firm uses to determine its equilibrium level of output.

Is Stackelberg equilibrium Pareto efficient?

Bi-level optimization problems arise in hierarchical decision making, where players of different ranks are involved. The situation is described by the so-called Stackelberg game. We derive conditions under which we show that a Stackelberg equilibrium is indeed a Pareto optimum.

At what point is the Cournot equilibrium achieved?

The Cournot Equilibrium is found at the intersection point between the two reaction curves as represented in Fig. 6.12-8.

How do you solve Nash equilibrium?

To find the Nash equilibria, we examine each action profile in turn. Neither player can increase her payoff by choosing an action different from her current one. Thus this action profile is a Nash equilibrium. By choosing A rather than I, player 1 obtains a payoff of 1 rather than 0, given player 2’s action.

How does the Cournot equilibrium work in a duopoly?

Each member of the duopoly must produce a homogenous good, control the market over the production of that good and not collude for the Cournot equilibrium to apply in their case. The Cournot equilibrium is used to calculate the peak profit point for one member of the duopoly based on the expected production of the other member.

How does duopoly lead to increase in consumer surplus?

DUOPOLY Thus competition leads to an increase not only in consumer surplus but in total surplus: the gain in consumer surplus (256 − 144 = 112) exceeds the loss in total profits (278 − 236 = 42). In the above example we assumed that the two firms had the same cost function

How does revenue depend on the output of a duopolist?

For a duopolist, however, revenue depends on both its own output and the other firm’s output. The solution we apply to this game is that of Nash equilibrium.

How to calculate the point of equilibrium for a company?

Once you know the optimal demand and optimal revenues for the market as a whole, you can now calculate the point of equilibrium for either company’s production, disregarding any collusion between the two using this formula: π = P (Q) q − C (q). π is the individual company’s profit. Q is the level of total market output.