Problem 2 Maria's utility function is U(x, y) = 4x]/2 +y, with the price of nuts, Pr, equal to $1 and the price of berries, Py, equal to $5. Furthermore, assume Maria's initial income to be $145. [10 marks overall] (2.a) Determine how many units of nuts and berries she would optimally choose to consume to maximise her utility subject to her budget constraint. Call the initial optimal consumption bundle as bundle A. [2 marks] (2.b) If the price of the nuts increased to become $2, and everything else re- mained unchanged, what would the total effect on her consumption of nuts be, compared to when the price of nuts was at $1? Call the new consumption bundle following an increase in the price of nuts as bundle C. [2 marks] (2.c) Decompose this total effect into a substitution and an income effect. Denote as B the intermediate decomposition bundle. [2 marks] (2.d) Provide a graphical illustration of these effects, together with a represen- tation of the various bundles A, B and C. [2 marks] (2.e) Provide a quantification of the welfare changes that this increase in the price of nuts induced for Maria, either in terms of her consumer surplus, or compensating variation or equivalent variation. Comment on your results. [2 marks]