The reaction functions for the two duopolists, firms X and Y are given by the equations \( P_t^X = 45 + 0.8 \, P_{t-1}^Y \) and \( P_t^Y = 45 +…
BBA Business Mathematics II · 2024 · Solved Question with Answer
The reaction functions for the two duopolists, firms X and Y are given by the equations \( P_t^X = 45 + 0.8 \, P_{t-1}^Y \) and \( P_t^Y = 45 + 0.8P_{t-1}^X \) , respectively. If the assumptions of the Bertrand model hold, derive a difference equation for \( P_t^X \) and calculate what \( P_t^X \) will be in time period 10 if firm X starts off in time period 0 by setting a price of 300.