A firm has the production function: 1 E)=20E E? f(E) =20 200 and the product price is p = 1. 1. Derive the firm's labor demand curve. 2. Suppose the firm is bargaining with a union. The union's utility function is given by: U(w,E)=w x E. What wage would a monopoly union demand? How many workers will be employed under the union contract? (Hint: you can use a Lagrangean, or use the constraint to substitute an expression for w in terms of F in the union's utility function, then maximize that). 3. Now suppose the union's utility function is actually: U(w,E) = (ww*) X E, where w* = 8 is the competitive market wage. What wage would a monopoly union demand? How many workers will be employed under the union contract? 4. Contrast your answers from parts (b) and (c). Can you explain why they are different? 5. Draw a graph depicting the solution to the union's optimization problem, taking care to label axes and key points