The competitive model assumes that a firm's residual demand curve is perfectly elastic-the firm is a price taker. Although this will rarely be exactly correct, it can be a reasonable approximation in many settings. Firm i's residual demand is given by D, (p) = D(p) - So (p) where D (p) is the quantity demanded at price p and S, (p) is the supply of all of i's competitors at price p. a) Take the derivative of residual demand with respect to price. b) Assume that there are N identical firms, including firm i. The output of an individual firm is q. Convert the derivatives from part (a) into elasticities. c) How does the residual demand elasticity depend on the number of firms, the elasticity of demand, and the elasticity of supply?