Andreas spends his daily income of I on chocolate bars (Good 1) and others (Good 2, composite commodity, taken as numeraire). The price of a chocolate bar is p and the price of good 2 is normalized to one, that is, p indicates the relative price of a candy bar. Andrea's preferences are represented by u(x1, X2) = 2vx1 + x2. (a) Illustrate if Andrea's preferences satisfy the axiom of convexity. (b) Suppose that Andreas' income is sufficiently high so I > 1/p1. Using the La- grangian multiplier method, compute his demand function and indirect utility func- tion. What happens if his income is lower than 1/p1? Explain your answer.(c) Using the dual principle, compute Andreas' compensated (Hicksisn) demand func- tion for chocolate bars. Comparing with your answer {b}, is there any difference between his two demand functions for chocolate bars? If not, illustrate its implica- tions. (d) The original price of a bar was p = 0.5 and Andreas' income was I = 5. But the Norwegian tax administration revised its tax system, and decided to levy an excise tax t = 106% on chocolate bars, thereby increasing the price to p' = 1. Decompose the change in x; due to this tax into the substitution and income effects. Also, choose either compensating or equivalent variations to measure Andreas' welfare change. Justify your choice. Suppose that Andreas couldn't alter his consumption habits for several years so he got addicted to chocolate. Specically, his preferences change to u(x1,x2) = wax1 -- r +x2, where r ) 0 represents his addiction level. Notice that 'fxl r is undened for in