Consider a duopoly where firms compete for market share by setting prices. The firms produce differentiated products and face the following demand functions where q is output and P is the price in...

Consider a duopoly where firms compete for market share by setting prices. The firms produce differentiated products and face the following demand functions where q is output and P is the price in dollars.

              q₁ = 100 – 2P₁ + 2P₂           Demand Function for Firm 1

              q₂ = 120 – 4P₂ + P₁             Demand Function for Firm 2

Suppose that firm 1 is able to produce output at a constant marginal cost of $30 and that firm 2 is able to produce output at a constant marginal cost of $20. Both firms operate with no fixed costs.

1. Derive the best response function for firm 1.


2. Derive the best response function for firm 2.