Question: Consider the following demand function, p = a-bQ, Q = q1 + q2 + q3, where qi denotes Firm i's output, i = 1; 2;

Consider the following demand function, p = a-bQ, Q = q1 + q2 + q3, where qi denotes Firm i's output, i = 1; 2; 3; a and b are positive parameters. The three firms choose prices simultaneously and non cooperatively (Bertrand competition). Firm i's marginal cost of production is constant and equal to ci > 0. Assume that c1 = c2 = c3 = c.

a) Derive the best response function of each firm.

Assume now that c1 < or equal to c2 and that c1 < or equal to c3.

b) Find the Bertrand-Nash equilibrium price.

c) Show that, if c1 < c2 and c1 < c3, firm 1 makes higher profits than the other firms.

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