Brief explanation.

Ali, the crocodile, lives in the dark water of Putah Creek in the Arboretum just beside the UC Davis campus. To the delight of the ducks there, Ali is a vegetarian. Ali earns income from being employed by UC Davis as a life guard at Putah Creek. His task is to rescue students who fall into the water from time to time. He is especially busy around prelim exams when more students than usual jump into water out of despair. When being rescued by Ali, usually their mood lights up quickly in anticipation of a cool selfie with a crocodile that can be shared on Facebook. By the time they t lapse upon realizing that the water damaged their cell phone beyond repair, the authorities have arrived to help (with their cell phones). Anyway, let's not digress further. While we certainly appreciate Ali's work, our academic interest is focused on his consumption behavior. Being a vegetarian, his main diet consists of almonds. They have the inconvenient feature of getting stuck between his 72 teeth. So he is also a rather heavy consumer of toothpicks. Finally there are his frequent gifts he purchases for Mathilda. Mathilda! She is the duck of the Arboretum who waddles most elegantly with her petite legs by delightfully moving well-shaped hips. He is really in love with her, at a platonic level of course so that nobody gets physically hurt. Adobe Reader X micro We write .. 20 for the amounts of his consumption of almonds, toothpicks, and gifts, respectively. We assume for simplicity that these goods are infinitesimally divisible. Letr (1). We assume that his utility function is given by ura. f.) with 0,0 (0,1) and a +0 0. Finally, we denote by P.PP, the prices of almonds, toothpicks, and gifts, respectively, and p=(PPP). economics New fold (3) a. Use the Kahn-Tucker approach to derive step-by-step the Walrasian demand function rip, w). Verify also second-order conditions b. Verify that the demand function is homogenous of degree zero and satisfies Wal New folder 38 c. To be honest, we do not really know whether Alt has the Cobb-Douglas utility function stated above. Would Ali want to differently substitute a marginal amount of almonds for some toothpicks when having a differentiable utility function from the one above and optimally demanding positive amounts of all good Explain

Question 2 a] Roger lives a simple life: For breakfast, he eats eggs with coffee, and for dinner he eats hot dogs with beer. In between he watches Fox News and earns his money with maintaining a couple of thousand twitter bots. Since he likes everything to be in order and simple, he puts his income into two pots: One with money for breakfast and one with money for dinner. Eggs and coffee are paid only from the breakfast pot; hot dogs and beer only from the dinner pot. That is, p131+p232 :5 ms P3333 +P4$4 E we with p1,pg,p3,p4,w3,wy 33: D, where subscripts 1, 2,3, 4, B, and D refer to eggs, coffee, hot dogs, beer, breakfast, and dinner, respectively. As usual, 33,- is the price of one unit of commodity i, 3:,- is the quantity consumed of commodity :i, and tag and ip is the amount of money in his breakfast or dinner pot, respectively. His utility function is given by afrl,a\"g,rg,:r4} = (r?m+rm)a with e, c, ft, 5,411 33: . aa} Given HIE and ip, derive stepbystep Roger's Walrssian demand functions for eggs, coffee, hot dogs, and beer. 1Verify also secondorder conditions. ab} While watching Fox News, Roger heard about the government shifting money earmarked for ghting drugs to the construction of the border wall. He sud denly thought whether it would be better for him to move one dollar from his breakfast pot to the dinner pot. Find a condition on the primitives {i.e., par ac} Suppose that the primitives are such that it is better for Roger to move a dollar from his breakfast pot to his dinner pot. Suppose further that both e + c :3 1 and h + b :3 1. 1Would it be better for Roger to skip breakfast altogether and just spend all the monej,r on dinner? I] Verify for the case of CobbDouglas utility functions on Hi that the Slutslqvr sub stitution matrix is negative semidenite and symmetric. \f