Consider a setting of two competing firms F1 and F2. Both firms maximize their profits and provide a homogeneous ouput qi with (i = 1, 2) at market price p. Assume market clearing prices and...

Consider a setting of two competing firms F1 and F2. Both firms maximize their profits and provide a homogeneous ouput qi with (i = 1, 2) at market price p. Assume market clearing prices and non-negative outputs. Assume further, that the firms engage in quantity competition.

The inverse market demand function is: p(q) = 41 - q, where q = q₁ + q₂. The cost functions are: C₁
= 2q_1
,
C₂
= q₂
². Assume F2 is the dominant firm.

a) Should F2 prefer to play Cournot duopoly or Stackelberg competition in a one shot game?