Consider a perfectly competitive firm with production set YC RN, where RN is the set of N-dimensional vectors. (a) Give a precise definition of a production vector y e Y. (b) Let p and p' e RN be strictly positive price vectors. Suppose when the price vector is p the firm's profit maximizing production vector is y e Y, and when the price vector p', the firm's profit maximizing production vector is y' = Y. Prove that (y' - y)-(p' - p) 20. (c) What does (b) imply about the shape of supply curves and factor demand curves? Prove your answer. Consider a perfectly competitive firm with production set YC RN, where RN is the set of N-dimensional vectors. (a) Give a precise definition of a production vector y e Y. (b) Let p and p' e RN be strictly positive price vectors. Suppose when the price vector is p the firm's profit maximizing production vector is y e Y, and when the price vector p', the firm's profit maximizing production vector is y' = Y. Prove that (y' - y)-(p' - p) 20. (c) What does (b) imply about the shape of supply curves and factor demand curves? Prove your