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* Determinar la produccion optima del agente 1: Para hacer esto debemos encontrar donde los beneficios marginales se igualan con los costos marginales. El costo marginal (c) se asume que es constante. La curva de beneficios marginales es <math>r_1(q_2)</math> con el doble de la pendiente de <math>d_1(q_2)</math> y con
* Determine firm 1’s optimum output: To do this we must find where marginal revenue equals marginal cost. Marginal cost (c) is assumed to be constant. Marginal revenue is a curve - - with twice the slope of <math>d_1(q_2)</math> and with the same vertical intercept. The point at which the two curves (<math>c</math> and <math>r_1(q_2)</math>) intersect corresponds to quantity <math>q_1''(q_2)</math>. Firm 1’s optimum <math>q_1''(q_2)</math>, depends on what it believes firm 2 is doing. To find an equilibrium, we derive firm 1’s optimum for other possible values of <math>q_2</math>. Diagram 2 considers two possible values of <math>q_2</math>. If <math>q_2=0</math>, then the first firm's residual demand is effectively the market demand, <math>d_1(0)=D</math>. The optimal solution is for firm 1 to choose the [[monopoly]] quantity; <math>q_1''(0)=q^m</math> (<math>q^m</math> is monopoly quantity). If firm 2 were to choose the quantity corresponding to [[perfect competition]], <math>q_2=q^c</math> such that <math>P(q^c)=c</math>, then firm 1’s optimum would be to produce nil: <math>q_1''(q^c)=0</math>. This is the point at which marginal cost intercepts the marginal revenue corresponding to <math>d_1(q^c)</math>.
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