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. (0.1) The firm's profit function is given by: (w, L) = 55L L 2 2 wL, (0.2) where wL is the wage bill and 55L L 2 2 is the revenue that the firm can earn by employing L workers. Suppose the timing of the game is as follows: (1) the union makes a wage demand, w; (2) the firm observes (and accepts) w and then chooses employment, L; (3) payoffs are U(w, L) and (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 L corresponding to that w (chosen by the union)?

(iii) Let w and L denote answers to part (ii). (1 mark) Find (w , L ) and U(w , L ) (1 mark) Are there values of (w, L) such that firm's profit is strictly higher than (L , w ) and union's utility is strictly higher than U(L , w )? Suggest one such value and verify