1) Consider a consumer with the Cobb-Douglas utility function U(q1,q2) = \\I C[1'12 , where q1 and q2 are the quanties of goods 1 and 2 consumed, respectively. This consumer has an income denoted by Y which is devoted to goods 1 and 2. The prices of goods 1 and 2 are denoted p 1 and p2. a. What is this consumer's MRS as functions of :11 and :12? b. Write out the Lagrangian for the consumer's utility maximization problem. c. Using the Lagrangian method, derive the consumer's demand equations for both goods as functions of the variables p1, p2, and Y