Consider a variant of the Cournot model we studied in class. A single good is produced by two firms and these two firms compete with each other through outputs. Each firm produces it's output qi via the following production technology q = 1". I denotes units of labor and n is a parameter. The firms are price takers in the labour market and pay a wage w1 = w2 = w for each unit of labor. The inverse demand function is piece wise linear, that is P(Q) = a - Q if Q s a if Q > a where Q represents total output in the market. a) [ 2 Points | Formally write this as a strategic game. b) [ 8 Points ] Suppose n = 1/2 and is common across firms (both firms have the same production technology). Find a Nash equilibrium of this Cournot game. Be sure to specify the complete best response functions of both firms. Is this equilibrium unique? You do not need to prove this mathematically, simply argue one way or the other. c) [8 Points] Suppose firm 2 discovers some new innovation that changes it's production technology to q2 = zl2 where z > 1. Think of this as a total factor productivity increase specific to firm 2. Firm 1's production technology remains the same. Both firms are still price takers in the labor market (they both face the same wage w). Assuming n = = as in part b, solve for the Nash Equilibrium under this new setting. Specify the optimal labour choices for firms 1 and 2 as well as the complete best response functions of both firms. d) [ 4 Points ] Does Firm 1 hire more or less labour in the Nash equilibrium in part c compared to the one in part b? You do not need to say anything about firm 2's action