2. Assume that demand for three goods has been evaluated at the follow ing three price vectors: 201 = (1.12)]? = (2. 1.2);103 = (2.2.1); With income m = 12 in all cases. Consider two different data sets specifying 11:1 E 53(p1. 12). 11:2 E $(p2. 12). and $3 E $(p3.12). (a) Suppose that :51 = (4. 2. 2). $2 = (2.4. 2). and 3:3 = (2. 2.4). Show that there are no cycles in the affordability matrix. What does this imply for existence of a utility function rationalizing these choices? (b) Suppose instead that 3:1 : (2.3.2). 3:2 : (2.2.3). and 11:3 : (3.2.2). Show that there is a cycle in the affordability matrix. What does this imply for existence of a utility function rational izing these choices