Question 1: (100 marks) Emma has a job with a wage of w per hour. She can freely choose how many hours she works per day. This job is her only source of income. She spends all her income on consumption. Her preferences are defined over consumption and hours of free time. Emma maximises her utility. She can allocate 12 hours per day to either free time or working, as she needs the other 12 hours per day for sleeping, meals, etc. a. (168 words) Explain the trade-off between consumption and free time that Emma faces and the condition that characterises her optimal choice of consumption and free time. Use a relevant diagram to illustrate Emma's budget constraint and preferences and to support your arguments. (24 marks) b) (252 words) As the company Emma works for suffers from an economic downturn, Emma's union and her employer agree to reduce the wage per hour. How does this decrease in wage affect Emma's optimal choice of consumption and free time? Decompose the overall effect of the wage decline into a substitution effect and an income effect. Use a relevant diagram to support your reasoning. (36 marks) c) (280 words) Now assume that the wage per hour was initially w = 18 and is, after the wage cut, w = 16. Emma's utility function is given by Ut, c) = t(24 - t) + C, where t and denote hours of free time per day and consumption level per day, respectively. Calculate her optimal consumption levels and hours of free time initially (Le with w = 18) and after the wage decrease (i.e. with w = 16). Compare your results and relate them to your analysis in part b). (Recall that she can allocate 12 hours per day to either free time or working.) (40 marks)