(Refer to 3.9 Appendix: Using Calculus.) Suppose utilin equals In (Cu) + 3 ln (:2, 1+: ) where In (c) represents the natural logarithm of c. whose derivative equals 1 ft. The parameter ,8 is a positive number. (a) Prove that real money balances are q\" = 1%\"? (b) Derive expressions for the lifetime consumption pattern c? I and ('5', + l . (c) What effect does an increase in have on real money balances and the lifetime consumption pattern? Give an intuitive interpretation of the parameter :3