Consider the following duopoly market: Inverse of demand function: P^D(Q)=A^D-B^DQ (D is superscript) Production function of firm i:qi=AiLi (i is subscript) Note: Ai is a parameter such that A1>A2>0 and Li is the amount of labor employed by firm i Assume firms compete using Bertrand rules a) Write down the rules of a Bertrand game b) Compute the nash equilibrium of this game c) Define an equilibrium for this economic environment d) Solve for the equilibrium e) Assume the government wants to buy X units from this market. Define the equilibrium for this environment f) Solve for the equilibrium you defined in part e g) Perform a cost benefit analysis for the project defined in part (e).