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Question 1 [25 marks] A man has 24 hours everyday to spend and faces a wage rate of to pounds per hour. By choosing to work for t hours, he earns an income of wt pounds which will be used for consuming two goods, denoted by 1 and 2. He gets utility from leisure {the time not spent for work) and from consumption of the goods, and his utility function takes the form of similar, where :3, is the consumption of good i = 1, 2, and I is the amount of leisure enjoyed. Let p1 = .82 be the price of good 1, p2 = 3 the price of good 2, and w = .814 the wage rate. (a) Derive his optimal consumption-leisure choice and indirect utility function. [18 marks] (b) Prove that his Marshallian demand function is homogeneous of degree zero in pl, 102, and m. [7 marks]