Question 2: Deriving the Labor Demand Curve (3 pts) In this question I ask you to derive the aggregate labor demand curve. To do so, note that aggregate profits 7, taking wages w and interest rates r as given, are: 7 = AKall-a - w . L-r . K a) Maximize profit with respect to labor (i.e. find where 91 = 0). Solve for w. This is the aggre- gate labor demand curve. b) Is the labor demand curve downward sloping? Mathematically, why? c) Holding A and L constant, what happens to wages when K increases? Do workers prefer more or less capital in this situation