Exercise 2. Wages and Employment in a Unionized Firm (6 marks) * This exercise is based on section 2.1.C in the textbook by Gibbons: Game Theory for Applied Economists. Part 1 Consider a model of firm and monopoly union where the union has exclusive control over wages (w) while the firm has exclusive control over employment (L). Union's utility function is given by: U(w, L) = (w - 15)L. (0.]) The firm's profit function is given by: *(w, L) = 55L- L- - WL (0.2) where w/ is the wage bill and 554 - is the revenue that the firm can earn by employing & workers. Suppose the timing of the game is as follows: (1) the union makes a wage demand, wx; (2) the firm ob- serves (and accepts) w and then chooses employment, L; (3) payoffs are U(w, L) and a(w, L) as specified in (0.1) and (0.2). (i) (2 marks) Find the amount of labour (L) that the firm chooses in stage 2 for a given w. Let L(w) denote firm's choice of L given w. (ii) (2 marks) Suppose union chooses w first, following which the firm chooses L. What w will union choose? What is the profit-maximizing level of & corresponding to that w (chosen by the union)? (iii) Let w* and L' denote answers to part (ii). . (1 mark) Find a(w', L') and U(w , L') . (1 mark) Are there values of (w L) such that firm's profit is strictly higher than a L', w") and union's utility is strictly higher than U(L', w')? Suggest one such value and verify