Economics.

\fd. You would expect that the more almonds Ali eats, the more they get stuck in his teeth and the more toothpicks he purchases. In light of such considerations, does it make sense to assume Mi has the utility function above? e. Suppose the university would slightly raise Ali's income. {Assuming at most small changes of income is a very realistic assumption at UC Davis} lDan we learn from the Lagrange approach by how much his utility would change? PsgeSof f. Derive Ali's indirect utility function [denote it by 111331.?\" Simplify. g. Can we also answer part e using Ali's indirect utility function? Briefly explain. h. Verify that Ali satises Roy's identity with respect to almonds. i. When Professor Schipper interviews Ali about how exactly he arrives at his optimal consumption bundle, Ali expresses ignorance about maximizing utility subject to his budget constraint. Instead, he seems to minimize his expenditure on consump- tion such that he reaches a certain level of utility. A. smart undergraduate student walks by and claims that this is clear evidence against the assumption of utility maximization in economics. Since Professor Schipper hates lCobbDouglas utility functions and boring calculations1 he sends the student to you so that you can show him hD-W expenditure minimization works. Figain1 use the KuhnTucker approach to derive the Hicksian demand function. j. Derive the expenditure function. Show that the expenditure function is homoge- neous of degree 1 in prices1 strictly increasing in fr. as well as nondecreasing and concave in the price of each good. 11. Professor Schipper cannot compute the Hiclrsian demand using KuhnTucker with out a coffee. Unfortunately, Ali has no coffee to olfer. Yet, he could offer Professor Schipper his expenditure function. Is there a way to quickly calculate the Hicksian demand from the expenditure function without coffee? 5. 1'Iu'rerify the {own price} Slutslry equation for the example of almonds. In. Which term in the {own price]I Slutslcy equation refers to the substitution elfect? As mentioned previously, we don't really know whether Ali has a Cobb-Douglas utility function. Suppose Ali has a continuous utility Function representing locally nonsatiated preferences and that his Hicksian demand function is indeed a function {rather than a correspondence}. Would a change in prices still have qualitatively the same effect on Hicksian demand as when he has the above Cobb-Douglas utility function? If yes, provide a short proof. If not, argue why not. n. Because of the drought, the price of almonds changes from 192 to pi. UC Davis is committed to keep Ali as well olf as before the price change. The newly hired Senior 1|In'rice Provost for lCrocodile Welfare turns to Professor Schipper for advice on the exact amount to be deducted from the budget of the university and paid to Ali as compensation for the price change. Unfortunately, Professor Schipper is so immersed in exciting new research that he is extremely slow in answering his email. Lucltily1 the Senior Vice Provost for Crocodile Welfare spends most of his time in the hammocks on the quad, where he meets you studying for the prelims. Help him calculate the amount