Find the sub game perfect Nash equilibrium of the following problem:

Consider an economy with a Union and a Firm. Union has exclusive control on the wages (denoted by w) and Firm has exclusive control over employment (denoted by L). Union's utility function is (,)=+ where is the wage the Union demands, is the employment, > 0 and > 0. Firm's profit function is (, ) = ()- where () = ln() is the revenue of the firm when employment is and > 0. The union makes a wage demand . The firm observes and then chooses employment .