4. Juana has utility function u(71. $2) = 21 + Ina2. The price of good 1 is p1 > 0, the price of good 2 is p2 > 0. and Juana's income is I. Assume that I > pi. (a) Calculate Juan's demand functions a; and z; by solving her utility max- imization problem (b) Are good 1 and good 2 inferior or normal goods? (c) Calculate the price elasticity of Juana's demand for good 1. (d) Suppose the price of good 2 goes up, in a graph, explain why the total effect of the price change on good 1 equals to the substitution effect