Question

Describe the process to attain the Reaction Curve (Response Function) of a dupolist. Also explain how a stable quantity in a duopolistic market is arrived at, with the help of a Reaction function.

Answer 1

Process of attaining the reaction curve:

Step 1: Take the inverse demand functions of all the firms included in the game

Step 2: Take the profit function of first firm and plug the inverse demand function as a function of quantity of goods

Step 3: Apply first order condition. Take the derivative of this profit with respect to firm's output and equate it to zero

Step 4: Derive firm's output as a function of other firms output.

This is the best response function of firm 1. We do the similar exercise to derive the best responses of other firms in the game.

Stability:
After determining the best response functions, we plot them on a C-2 plane with firm1 output on Xaxis and firm 2 output on Y-axis. The stable equilibrium is determined by the intersection of two best response curves. This occurs at point E in below figure. Any other point other than point E would not be a stable equilibrium.

Let Firm A chooses to fix its quantity at A1, firm B's best response to this is to produce B1 quantity. Now, Firm A will think that firm B will fix this quantity and would not deviate. In this anticipation, firm A increases its quantity to A2. To this, firm B then react by reducing the quantity to B2. This whole process will continue till point E where both firms are in stable equilibrium and no one has any incentive to deviate from this position.