5. [20 pts] Two firms compete for hiring workers in the labour market. The equilibrium wage is w = a+ (H1 + H2), where a, B > 0 are parameters, and H; is the number of workers hired by firm i = 1, 2. Firm 's profit is (y - w) Hi, where y is the output per worker. Assume y > a. Firm i chooses H; to maximize its profit. Do the following: (a) Consider the two firms decide on H; simultaneously. Derive the Nash equilibrium. (b) Consider the two firms make decisions sequentially. Firm 1 gets to hire first, followed by firm 2. Derive the subgame perfect equilibrium