Question 4 Anna consumes food and exercising in a gym while Bob only likes food. Preferences are a: + 6 log (y) where a: is food and y is is exercise. (9 = 6 for Anna and 6 = 0 for Bob. Food costs 1 per meal (unit) and gym exercise costs 2 per unit. Bob and Anna both have incomes of 10. (a) How much does Anna spend at the gym? [5 marks] (b) Does it make sense to say that Anna is better off than Bob? [5 marks] (c) A new gym opens in town and, following an extensive advertising campaign, Bob is attracted to joining and buys 2 units of gym time. What is Bob's decision utility expressed in terms of the parameter 9? [5 marks] (d) Bob discovers that his experience utility is actually based only on :c. What is the welfare loss associated with the new gym opening? [5 marks] (e) Discuss the pros and cons of taxing time at the gym in this case. What would the optimal tax depend upon? Are there better policies than taxation to deal with Bob's gullibility? [5 marks]