y1(120Taking the derivative of this profit with respect to y1 (holding y2 constant) and setting the derivative equal to zero we obtainy1
y2)
30y1.
120or2y1
y2
30 = 0,
y1 = (90Thus the best response function of firm 1 is given by b1(y2) = (90y2)/2.
Similarly, we find that the best response function of firm 2 is given by b2(y1) = (90 y1)/2. This function is superimposed on the best response function of firm 1 in the following figure.
y1 = b1(y2) and y2 = b2(y1).That is,
y1 = (90Substituting one equation in the other we obtain y1 = (90y2)/2 and y2 = (90
y1)/2.
y1(120Taking the derivative of this profit with respect to y1 (holding y2 constant) and setting the derivative equal to zero we obtainy1
y2)
y12.
120or2y1
y2
2y1 = 0,
y1 = (120Thus the best response function of firm 1 is given by b1(y2) = (120y2)/4.
Similarly, we find that the best response function of firm 2 is given by b2(y1) = (120 y1)/4.
y1 = b1(y2) and y2 = b2(y1).That is,
y1 = (120Substituting one equation in the other we obtain y1 = (120y2)/4 and y2 = (120
y1)/4.
[Solution]