currency unit, , to capture the entire market demand, . Therefore, firm ’s best response is: Diagram 1 illustrates firm 1’s best response function, , given the price set by firm 2. Note, in the diagram stands for marginal cost, . The Nash Equilibrium () in the Bertrand model is the mutual best response; an equilibrium where neither firm has an incentive to deviate from it. As illustrated in the Diagram 2, the Bertrand-Nash equilibrium occurs when the best response function for both firm’s intersects at the point, where . This means both firms make zero economic profits. Therefore, if rival prices below marginal cost, firm ends up making losses attracting extra demand and is better of setting price level to marginal cost. Important to note, Bertrand’s model of price competition leads to a perfect competitive outcome. This is known as the Bertrand paradox; as two competitors in a market are sufficient to generate competitive pricing; however, this result is not consistent in many real world industries. If one firm has lower average cost (a superior production technology), it will charge the highest price that is lower than the average cost of the other one (i.e. a price just below the lowest price the other firm can manage) and take all the business. This is known as "limit pricing". Critical analysis of the Bertrand model The Bertrand model rests on some very extreme assumptions. For example, it assumes that consumers want to buy from the lowest priced firm. There are various reasons why this may not hold in many markets: non-price competition and product differentiation, transport and search costs. For example, would someone travel twice as far to save 1% on the price of their vegetables? The Bertrand model can be extended to include product or location differentiation but then the main result – that price is driven down to marginal cost – no longer holds. With search costs, there may be other equilibria apart from the competitive price – the monopoly price or even price dispersion may be equilibria as in the classic "Bargains and Rip-offs" model. The model also ignores capacity constraints. If a single firm does not have the capacity to supply the whole market then the "price equals marginal cost" result may not hold. The analysis of this case was started by Francis Ysidro Edgeworth and has become known as the Bertrand–Edgeworth model. With capacity constraints,