For parts (a)-(c) of this question, suppose that the core dimension indices are computed as discussed in class, but that the HDI is arithmetically averaged i.e. H D1 = g (ILE + 15 + 1y). (a) Derive the marginal contribution to HDI of (i) one additional year of life expectancy, and (ii) one additional dollar of per capita income. Carefully show all algebraic steps in your answers. [1 mark] (b) Derive the algebraic formula for the implicit valuation of longevity. Carefully show all algebraic steps, and explain the intuition behind your formula. [1 mark] (c) Show algebraically that the implicit valuation of longevity is increasing in per capita income at a constant rate. [1 mark]