Economics

PREFERENCE AND UTILITY Problem Set 2 1. Assume a utility function U = U (K. '1'). where K and Y are the commodities consumed by the consumer. Derive the MRS. Interpret your answer. 2. Find the MRSsv {'I' for X} of the following utility functions i) U=3X+.51' ii} U=lnX+lnY iii}U=~.iX+}' 3. Given our. u.(.t'.r}= rare and uzrxx} ontogeny. Show that U: (X9!) is a monotonic transformation of {III}? .1") and it preserves the underlined preference ranking. 4. Suppose that you love drinking coffee and eating Pizza but you strongly dislike consuming them together. that means the more you consume one. the less you want for the other. Try to draw this preference relation assuming that a} You are required to consume both goods at a sitting b} You are required to consume one now and take the other one home to consume later. 5. lGiven a typical consumer's objective utility function U = X \"1'\" . Pt. and P; are the prices of goods 31- and Y respectively. M is the individuals total income. I. Set up the consumer's utility maximization problem and derive the rst order condition. (Hint: MRSEPxJ'Py}. II. Derive the optimal levels of good X and Y. Ill. Derive the indirect utility function W. Solve the dual problem to derive the expenditure rnction. ti. |[Iiiven the Cobb-Douglas utility function U = lming and the Dptimsi levels chi and Y a HM II \" = 311d 1; = ' 'V e e 1. Find the indirect utility function given that o:+ {3 =1 ll. Derive the expenditure function form the indirect utility function