1. (20 points) Consider the following one period model inhabited by the two agents Amanda and Brian. Their preferences are given by the following utility functions and UA(C,L) (1-0)ln(C) + In(L) UB(C,L) = 0 In(C) + In(L) where A refers to Amanda and B refers to Brian. Both individuals work for a firm (Himalaya industries) and they get dividend from the firm, depending on their share of labour input (s). The production function of the firm is Y=F(K,N)=zK0.5 No.5 Assume that K = 1 and z = 1 and h = 24, and in a twist of good fortune, there is no government in this economy. a) Find total labour supply and demand functions. b) What is the equilibrium wage (w*)? c) For what values of 0 will they split the revenue from the firm evenly? d) Assume another worker enters the labour force (let's call him Clevant). Clevant has the same labour function as Brian except that he gets none of the profits from the firm. Does your answer in the previous question change? Explain fully.