Using the model developed in The Economy Unit 3, Section 3.7, consider Ella who is a consultant in Sydney. Her standard rate of pay is $75 per hour. There is enough work available to her to allow her to choose the number of hours she works each week. Assume that Ella's spending on goods and services cannot exceed her earnings per day. a) Initially when facing w = $75 per hour Ella chooses to work 10 hours per day and have 14 hours of free time per day. Using a fully labelled diagram describe Ella's utility maximizing combination of free time and consumption. (4 marks) b) Due to the financial impact of recent inflation, the firms Ella usually consults for have reduced their spending on consultants. To remain competitive, Ella is forced to drop her standard rate to $50 per hour. Using the same diagram as used in part \"a\" show Ella's new utility maximizing combination of free time and spending on goods and services assuming that her hours of free time each day decrease to 8 hours. (4 marks) c) On your diagram decompose the overall change in hours of free time in response to the wage decrease into the (1) income effect and (ii) substitution effect. You must use words as well as the diagram to explain the decomposition of the overall change. (7 marks)