Question 2 [20 marks] This question refers to a hypothetical social drinker -called Carlota- who goes to a pub every evening. It is assumed that she is willing to select her weekly consumption of two products beer (X) and wine (1) so as to maximize her satisfaction. Carlota has not been able to describe her utility function U = U(x, y) with a specific formula, but after carefully introspection, she has been able to draw three indifference curves (shown in Figure 1) on which to base her choice of x (number of glasses of beer per week) and y (number of glasses of wine per week). 50 100 150 15 12.5 10 150 100 2.5 X 10 15 20 Figure 1 Carlota needs to sort out what happens with her satisfaction in two different situations. Situation 1 Last week Carlota spent $100. 00 on social drinking in a North Wollongong pub where she paid $4. 00 for each glass of beer and $8. 00 for each glass of wine. Situation 2 This Monday, Carlota found another pub in the North Beach where one glass of beer cost $2.00 and one glass of wine $4. 00. She is planning to take advantage of this finding and reduce her spending on social drinking to just $50. 00 per week, even though this could reduce her maximum level of satisfaction. YYYY MMM DD Page 8 of 9 UNIVERSITY OF WOLLONGONG AUSTRALIA Part A [10 marks] What is the solution to her optimization problem in Situation 1? [2 marks] Explain carefully using mathematics. [8 marks] Part B [10 marks] What is the maximum level of satisfaction she would reach in Situation 2? [2 marks] Explain carefully using mathematics. [8 marks] Please note: Precision in your answers is required to receive full marks