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(V 8.14) Under current tax law some individuals can save up to $2000 a year in an Individual Retirement Account (I.R.A.), a savings vehicle that has an especially favourable tax treatment. Consider an individual at a specific point in time who has income Y, which he or she wants to spend on consumption C', I.R.A. savings S1, or ordinary savings S2. Suppose that the "reduced form" utility function is taken to be U (C, S1, S2) - SPS,CN. (This a reduced form since the parameters are not truly exogenous taste parameters, but also include the tax treatment of the assets, etc.) The budget constraint of the consumer is given as C + S1 + 52 = Y, and the limit that her or she can contribute to the I.R.A. is denoted by L. (a) Derive the demand functions for Si and S2 for a consumer for whom the limit L is not binding. b) Derive the demand functions for S, and S2 for a consumer for whom the limit L is binding