2. Consider Garfield's utility function u(21, 12) = 12 + 12In1, where 21 is lasagna and x2 is 'everything else.' Suppose his allowance from Jon is m = 30. The prices are p, = 3 and p2 = 1. Illustrate your answers on the same graph (a) Derive his optimal consumption bundle (b) If the price of lasagna has tumbled due to the popularity of the Atkins diet. Now, it only costs p, = 2 to buy a unit of lasagna. What is his new consumption bundle now? (c) Decompose the change in Garfield's consumption of lasagna into substitution and income effects (d) Does Garfield have homothetic preferences for the two goods? Why or why not? 3. A consumer has a utility function u(21, 12) = 2172 and a budget constraint PIT, + p272 = m where p] = 1, p2 = 1 and m = 1 (a) What are the consumer's optimal choices? What is her utility level? (b) Now, suppose the price of good 1 doubled. For any level of income, calculate her optimal choices and utility levels. (c) How much additional income does this consumer have to be given to compensate her for the price decrease