Question

The inverse demand for a homogeneous good is given by P(Q) = 5 – 2Q, where Q denotes the quantity of the good. The good is produced by two quantity‐ setting firms. Firm 1 has a constant marginal cost equal to c>0. Firm 2 has a constant marginal cost equal to d∈[0,c]

1) Assume simultaneous competition. Derive price, quantities and profits in the Cournot‐Nash equilibrium.

2) Assume now sequential competition, with firm 1 taking the Stackelberg leader role. Derive price, quantities and profits in the Stackelberg equilibrium.

Answer 1

The cournot Nash equilibirium is a situation where rival firm produce homogeneous product and each attempts to maximize the profits by choosing how much to produce . all the firm choose the quantity again and again. Here Quantity is more important than price . They maximize the profits by producing large quantities of goods. They don't check the price but only focus on the quantities like how much they produce . price will be less in count nash equilibrium when compared to monopoly

Once the firm 1 has taken the stackleberg leader role. The firm 2 will follow firm 1 subsequentially. Stackleberg equilibrium refers to a situation where a firm having some competitive advantage over the other make a leader role by moving differently in all aspects. Like fixing their on price , quantities and earning profits.And then the both firms compete on quantities produced. The stackleberg leader is referred to as market leader.