1. Consider a consumer with income M and utility function u(x1; x2) =x1^0.5+ x2^0.5(so there are two goods).
(i) Set up the consumerís decision problem and Önd the demand function(given any price vector p = (p1; p2), p1; p2 > 0).
(ii) What will the consumer demand if M = 100 and p1 = p2 = 1 ?
(iii) Are x1, respectively x2: (a) normal or inferior goods ? (b) goods witha normal price effect or Giffen goods ?


2. Jill consumes 10 units of coke and 5 units of beer at income level M,as her income rises she consumes less of coke which means coke is an inferior good at that level of income. Show that coke must have been a normal good at some level of income.


3. Suppose John has preferences over lotteries given by the VNM function u =p x^1/2.Which lottery does he prefer between (4;9; 0.5; 0.5) and (1; 16; 0.5; 0.5)or is he indi§erent? Now suppose John's preferences have changed and he isrisk neutral now. Which lottery would he prefer? Explain why you do not need to know the form of the risk neutral personís utility function to answer this question.