5. In the Cournot oligopoly model of section 2.1: (a) find the total output Y1TS that maximizes the total surplus (and hence is Pareto efficient). (b) show that the number of firms that achieves Y1=Y1TS is J. (c) find the total output Y1PS that maximizes the producer surplus. (d) find the number of firms that achieves Y1=Y1PS. 2.1 Cournot Oligopoly producer j 's profit maximization problem (indirect method step 2): maxy1j:j=p1y1jz2(y1j),s.t.:X1(p1)=Y1=y1j+l=jy1l,given:{y1l}l=j. differences from perfect competition: - firm j knows that its own output y1j affects p1 through (14) - firm j knows that rivals' outputs {y1l}l=j affect p1 through (14) - Cournot assumption: firm j takes {y1l}l=j as given (14) inverse demand function: p1=X11(Y1)p1(Y1);p1(Y1)=1/X1(p1(Y1))0jz2(y1j)=c>0=abY1;a>c,b>0p1(Y1)=b0 welfare implications of the Cournot equilibrium: - equilibrium: marginal benefit = price > marginal cost - efficient: marginal benefit = price = marginal cost ( see (11),(13)) - equilibrium total output 0jz2(y1j)=c>0=abY1;a>c,b>0p1(Y1)=b0 welfare implications of the Cournot equilibrium: - equilibrium: marginal benefit = price > marginal cost - efficient: marginal benefit = price = marginal cost ( see (11),(13)) - equilibrium total output