Do on X = Rx is represented by U ( x 1 ) ~ z ) = ( a x , + b n , ) i) Are goods normal ? a , by o f to Normal: demand is increasing in wealth on / dw to . ( is ) Are the goods substitutes or complement? Is the law of demand satisfied ? iv If n ( pim ) continuous in p & m?A preference relation _ on X is continuous if whenever a > b (namely, it is not true that b _ a), there are balls (neighborhoods in the relevant topology) B. and By around a and b, respectively, such that for all r E Ba and y E Bb, r > y. (See fig. 2.1.) Utility | 17 Definition C2: A preference relation _ on X is continuous if the graph of _ (i.e., the set {(z, y)|x _ y} C X x X) is closed (with the product topology); that is, if { (an, bn)} is a sequence of pairs of elements in X satisfying an _ bri for all n and an - a and by - b, then a ~ b. (See fig. 2.1.)