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7. Consider the problem of maximizing the utility function ca numerical answer. ) u(c, s) = f(c) +g(s) subject to the budget constraint pc + sky , where c denotes consumption, s denotes saving, f : R. - R and g : R+ - R are (strictly) increasing, strictly concave functions with g'(0) > f'(y/p), and p and y are positive scalars. (a) How do we know that the budget constraint is binding at any solution (c*, s*) to this decision problem? Explain briefly. (b) Re-state the given problem as compactly as possible in terms of a single choice variable and then state the associated first- and second-order necessary and sufficient conditions for an interior solution. Explain briefly the economic intuition for the first-order condition. (c) Using your part-(b) answer, show that (i) a small increase in p, other things being equal, causes a decrease c* and (ii) a small increase in y, other things being equal, causes an increase in c*. (iii) Would these comparative statics results be the same if g(.) were simultaneously convex and concave instead of strictly concave? Explain briefly. 2