Question

12-Allstate Insurance and Aetna are fierce rivals in the insurance industry. The output of insurance policies issued by Allstate is an important factor in Aetna’s decision of how many policies to issue (the number of policies that maximize profits). Similarly, the output of insurance policies issued by Aetna is an important factor in Allstate’s decision of how many policies to issue (the number of policies that maximize profits). The reaction function for Allstate can be expressed as: Qallstate = 100 – 0.5(Qaetna). The reaction function for Aetna is: Qaetna = 50 – 0.25(Qallstate).

a-Graph both reaction functions. Be sure you indicate numerically the points at which each function intersects the horizontal and vertical axes

. b-At which output quantities do the reaction functions intersect?

Answer 1

The two equations are Qallstate = 100 – 0.5(Qaetna) and Qaetna = 50 –
0.25(Qallstate).
Use the first equation and place its value in the second
Qaetna = 50 – 0.25(100 - 0.5Qaetna)
Qaetna = 50 - 25 + 0.125Qaetna
Qaetna = 25/0.875 =28.57and Qallstate = 100 - 0.5*28.57 = 85.71
The graph is provided below