The decision to save is often a "residual" decision. To model it consider a world with K goods and denote "saving" as the K'th good. The consumer has in mind a continuous and strictly concave function v (not necessarily increasing!) defined over R-1 where v (x1,..., TK-1) is the value he attaches to the combination of the first K-1 goods. The consumer also has in mind an aspiration level v*. Given a price vector p = (P1,..., PK-1) and wealth level w he maximizes the function v over {(x1,..., XK-1) px w and v (x1,..., XK-1) v*}. If he is left with some wealth he spends it on the K'th good (savings). a. Show that this behavior can be (fully) rationalized by a preference relation over all vectors (X1, ..., XK) R