Calculating the general case for n players is easy to do with symmetric marginal costs. Going back to the last video, the first order condition for Firm 1 was a - 2q_1 - q_2 - c = 0. So rather than think of just q_2, imagine instead that it was q_2 + q_3 + ... Looking for a symmetric equilibrium where each produces the same q and substituting with n firms that makes the first order condition a - 2q - (n - 1)q - c = 0, or q = (a - c)/(n + 1). So, with two firms, you would have (a - c)/3, like in this video. The profits are easy to calculate from there. Maybe I will do a video on this before going to Stackelberg.
Profit? More like these videos are a “perfect fit” for my thirst for economics knowledge. Thanks for making them!
What will be the profits, if the firms utilize a trigger strategy? Is it advisable to use a grim trigger strategy in Cournot competitions?
9:13 did you mean to say (a-c)^2/4 and not (2a-c)^2/4?
Ah, the glories of the English language. "You get to (a-c)^2/4."
What would be the profit and production quantity of an n-opoly?
Calculating the general case for n players is easy to do with symmetric marginal costs. Going back to the last video, the first order condition for Firm 1 was a - 2q_1 - q_2 - c = 0. So rather than think of just q_2, imagine instead that it was q_2 + q_3 + ...
Looking for a symmetric equilibrium where each produces the same q and substituting with n firms that makes the first order condition a - 2q - (n - 1)q - c = 0, or q = (a - c)/(n + 1). So, with two firms, you would have (a - c)/3, like in this video.
The profits are easy to calculate from there.
Maybe I will do a video on this before going to Stackelberg.
the algebra is so painful