Question

Assume a market with two firms 1 and 2 supplying slightly differentiated products competing against each other in what is known as Bertrand oligopoly model. If firms 1 and 2 choose prices $P_1$ and $P_2$, respectively, the quantity that consumers demand from firm 1 is $Q_1 = A - P_1 + bP_2$ and for firm 2 is $Q_2 = A - P_2 + bP_1$ where $b > 0$ reflects the extent to which firm $i$'s product is a substitute for firm $j$'s product ($i = 1, 2; j = 1, 2; i \ne j$). Assume further that fixed costs of production are zero and that the marginal costs are constant at $C < A$, and that the two firms choose prices simultaneously. Identify and graph the reaction functions of the two firms and explain intuitively their shapes. Find the Nash equilibrium of the game

          Assume a market with two firms 1 and 2 supplying slightly differentiated products competing against each other in what is known as Bertrand oligopoly model. If firms 1 and 2 choose prices $P_1$ and $P_2$, respectively, the quantity that consumers demand from firm 1 is $Q_1 = A - P_1 + bP_2$ and for firm 2 is $Q_2 = A - P_2 + bP_1$ where $b > 0$ reflects the extent to which firm $i$'s product is a substitute for firm $j$'s product ($i = 1, 2; j = 1, 2; i \ne j$). Assume further that fixed costs of production are zero and that the marginal costs are constant at $C < A$, and that the two firms choose prices simultaneously. Identify and graph the reaction functions of the two firms and explain intuitively their shapes. Find the Nash equilibrium of the game

Assume a market with two firms 1 and 2 supplying slightly differentiated products competing against each other in what is known as Bertrand oligopoly model. If firms 1 and 2 choose prices P1 and P2, respectively, the quantity that consumers demand from firm 1 is Q1 = A - P1 + bP2 and for firm 2 is Q2 = A - P2 + bP1 where b > 0 reflects the extent to which firm i's product is a substitute for firm j's product (i = 1, 2; j = 1, 2; i j). Assume further that fixed costs of production are zero and that the marginal costs are constant at C < A, and that the two firms choose prices simultaneously. Identify and graph the reaction functions of the two firms and explain intuitively their shapes. Find the Nash equilibrium of the game

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