Assume that demand for three goods has been evaluated at the follow- ing three price vectors: p= (1,2,2); p = (2, 1,2); p = (2,2,1); with income m= 12 in all cases. Consider two different data sets specifying r r(p, 12), x = x(p, 12), and z = x(p, 12). E (a) Suppose that x = (4,2, 2), r = (2, 4,2), and (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 r= (2,3,2), (2,2,3), and 2 (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?