Question 1: Compensating and equivalent variation A consumer has demand functions for goods 1 and 2 given by: m2 1+3 2 31(P11P2;m) = %; 332(P11P2Em) = m + 2P1 3102 2p2 He initially has an income of 132, and faces prices 331 = 4 and p2 = 4. (a) How much of good 1 does he buy? (Call this :31.) The price of good 1 now increases to 131 = 8. p2 is unchanged at 4. (b) Assuming that he still has the same income, how much good 1 will he buy now? (Call this :51.) (c) Find the income m\" which he would need after the price increase to buy the same bundle of goods as he did before (i.e. the same bundle of goods as in part (a)). (d) Find the amount of good 1 he would actually buy if he had income m\" and faced the new prices (191 = 81 P2 = 4)' (e) Use your answers to the previous parts to decompose the change from 2:1 to 2:; into an income and a substitution effect. Explain the one small approximation you need to make, because the construction here is not exactly identical to that in the lecture or the text. (f) What is the size of each effect