i L_ .,, Assume Moana has preferences represented by utility function U (331, 332) = (3:1)1/3 (362)2/3 . Good 1 is coconuts (331) while good 2 is bananas (332). Suppose she has an income level of m : 120 dollars. In addition, the price of good 1 is p1 = 2 and the price of good 2 is p2 = 1. (a) What is the MRS at consumption bundle (15, 90)? What about (20,80)? (b) Interpret what Moana's MRS represent at (15,90) and (20, 80), respectively. (c) What is the optimal consumption? [50 points] Suppose there is a per-unit tax (or sales tax) of t = 2 imposed on coconuts. Assume Moana is the only person (or a representative consumer) in this economy. (d) What is the optimal consumption? (e) Graph the optimal consumption bundles before and after the tax. (f) In part (e), we see a tax-induced \"price effect,\" which can be decomposed to \"substitution\" and \"income\" effects. Add to your answer in (e), the necessary graphs to demonstrate these effects separately. (g) How does the demand for coconuts change due to substitution effect? [10 points] Heihei tells Moana that if coconuts is an inferior good, then the law of demand does not hold. (h) Is this true? Justify your answer using a graph