8. Tutorial Question 4- Consider a consumer whose preferences over consumption bundles of nonnegative amounts of each of three distinct commodities can be represented by a modified Stone- Geary utility function of the forme U(q1, 92, 93) = (q1 - V1)"'1(q2 - V2)"'2(93 - 13)1-1-dz if (91, 92, 93) EQ -00 if (91, 92, 93) # Qwhere ql is the quantity of commodity one, qz is tine quantity of conunodity two, {33 is the quantity of commodity three, and-'l IS' = {where} E Hit: ca 2" at q: '3- ;vsra 3* ms Note that q1, q2, and qa are choice variables, while 141, yz, ya, {1:1 and {12 are xed preference parameters. Typically, we would assmne that 1'1 3 ,-*' 3 Marshallian demands are also known as Walrasian demands, ordinary demands, and uncompensated demands. 1'2 ;a [Lyra ;a [LE] a: r11 =: 1,3 :2 o:2 s: 1 , and :11 + a:2 at: 1 . You should make these typical assumptions when answering this question:l Suppose that this consumer is a price taker in all markets, faces a price vector (pl, 192, 393) E 1121+, and is endowed with a monetary income of y 3': plyl + 3321!, + para ;;a D. You may assume that the budget constraint binds and any required constraint qualication conditions and secondorder conditions for a maximum are satised by any solution to this consumer's budget-constrained utility maximisation problem.\"l 1 What is this consumer's budgetconstrained utility mm problem?\"l 2 What is the W function for this consumer's budgetconstrained utility clam Problem?\" 3 What are the rstorder conditions for this consumer's budgetconstrained utility womwnisatlmiee problem?\" 4 Find the Marshallian demand functions [or correspondences] for this consumer. 4 Be sure to show all of your workings\"l 5 What is the point income elasticity of demand for each of the three conunodities? 5/