Sarah and Mike are single and considering whether to get married. They also have to decide how to employ their 8 working hours a day. They can either record music (l) or stay at home producing household goods (). Thus, their time constraint is as follows: + = 8 They are both very successful singers and their wages in the music industry are identical = = 10. Sarah and Mike get utility out of consuming household goods () and consumption goods (). They can use their salaries to purchase consumption goods at a price of 1. Their utility functions are: = 21 2 + = 16 2 +

(i) Should Sarah and Mike get married? Explain. (4 marks)

(ii) Sarah and Mike decide to get married. They realise that they can hire staff to produce household goods for them. They also enjoy spending time together listening to music (m). They also get older, and their preferences have changed. Their new respective utility functions are: = 4 2 + (1/2) 2 and = 5 2 + (1/2) 2 , where m refers to music albums. They both work full-time and thus their individual incomes are = = 50. Now that they are a couple, they maximise the sum of their utilities subject to their joint household budget constraint. Both the price of the consumption goods and music albums is 1.

(a) Write their maximisation problem, clearly indicating the objective function and choice variables. (4 marks)

(b) Find their optimal levels of private and music consumption (, and m) in this marriage. (5 marks)