Consider a consumer whose preferences over consumption bundles of non- negative amounts of each of three distinct commodities can be represented by a modified Stone-Geary utility function of the form (91 - 71) " (92 - 72) 02 (93 - 73) 1-01-02 if (91, 92, 93) E Q, U (91, 92, 93) = - 00 if (91, 92, 93) $ Q, where qi is the quantity of commodity one, q2 is the quantity of commodity two, q3 is the quantity of commodity three, and Q = {(91, 92, 93) ER; : 91 > 71, 92 > 72, 93 > 73) . Note that q1, 92, and q3 are choice variables, while 71, 72, 73, a1 and a2 are fixed preference parameters. Typically, we would assume that 71 2 0, Marshallian demands are also known as Walrasian demands, ordinary demands, and uncompensated demands. 72 2 0, 73 2 0, 0 Pill + P272 + P373 2 0. You may assume that the budget constraint binds and any required constraint qualification conditions and second-order conditions for a maximum are satisfied by any solution to this consumer's budget-constrained utility maximisation problem. 1. What is this consumer's budget-constrained utility maximisation prob- lem? 2. What is the Lagrangean function for this consumer's budget-constrained utility maximisation problem? 3. What are the first-order conditions for this consumer's budget-constrained utility maximisation problem? 4. Find the Marshallian demand functions (or correspondences) for this consumer. Be sure to show all of your working. 5. What is the point income elasticity of demand for each of the three commodities?5