Please help with the question below.

3. (25) .Consider the model of demand externalities and multiple equilibria of Diamond (1982). a. The welfare maximization problem is W* = max R,e -(1 - e)n So cF'(c) de + ex(e)v, s.t. ex(e) = (1 - e)nF(R) Write down the Lagrangean L associated with the above problem, using / to denote the Lagrange multiplier. . b. The optimality conditions for the maximization problem are dc dR 0, dc de = 0, dc du = 0. Take the derivatives of the Lagrangean with respect to R, e and M. c. Use the optimality conditions to characterize the solution to the welfare maximization problem in terms of 2 equations in the 2 unkowns R and e. d. Write down the equilibrium conditions for R and e at B = 1. Where is the difference between the condi- tions for efficiency and the conditions for equilibrium? What are the consequences of this difference