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Therefore, the sole equilibrium in the Bertrand model emerges when both firms establish a price equal to unit cost, known as the competitive price. [9] It is to highlight that the Bertrand equilibrium is a weak Nash-equilibrium. The firms lose nothing by deviating from the competitive price: it is an equilibrium simply because each firm can ...
The Bertrand–Nash equilibrium of this model is to have all (or at least two) firms setting the price equal to marginal cost. The argument is simple: if one firm sets a price above marginal cost then another firm can undercut it by a small amount (often called epsilon undercutting , where epsilon represents an arbitrarily small amount) thus ...
As a solution to the Bertrand paradox in economics, it has been suggested that each firm produces a somewhat differentiated product, and consequently faces a demand curve that is downward-sloping for all levels of the firm's price.
The Bertrand equilibrium is the same as the competitive result. [ 53 ] [ clarification needed ] Each firm produces where P = MC {\displaystyle P={\text{MC}}} , resulting in zero profits. [ 49 ] A generalization of the Bertrand model is the Bertrand–Edgeworth model , which allows for capacity constraints and a more general cost function.
Bertrand's result is paradoxical because if the number of firms goes from one to two, the price decreases from the monopoly price to the competitive price and stays at the same level as the number of firms increases further. This is not very realistic, as in reality, markets featuring a small number of firms with market power typically charge a ...
Equilibrium in perfect competition is the point where market demands will be equal to market supply. A firm's price will be determined at this point. In the short run, equilibrium will be affected by demand. In the long run, both demand and supply of a product will affect the equilibrium in perfect competition.
Price is a commonly known decreasing function of total output. All firms know , the total number of firms in the market, and take the output of the others as given. The market price is set at a level such that demand equals the total quantity produced by all firms.
The Stackelberg model can be solved to find the subgame perfect Nash equilibrium or equilibria (SPNE), i.e. the strategy profile that serves best each player, given the strategies of the other player and that entails every player playing in a Nash equilibrium in every subgame.