Amy the architect and Bill the builder both have the same preferences, given by: U = (C – 180) (L – 50) 2 If Amy works, she receives a wage w a = £10 per hour worked. Bill meanwhile is paid w b = £5 per hour worked. Amy and Bill both have a total of 100 hours per week, and neither of them has any non - labour income.

a) How do Amy and Bill decide how many hours to work? Set up their optimization problem and find the number of hours that they each choose to work.

b) Show Amy and Bill’s optimal choices in a single diagram (it does not have to be exactly to scale). Explain intuitively the reasons behind the different choice of hours made by Amy and Bill; make sure you mention the mechanisms at work behind the differences.

c) Now suppose the government wants to raise money to fund some investment programs. They decide that the best way to do this is to tax the income of high - wage earners. Any worker earning over £8 an hour is taxed at a rate of 20% of their income. How does this affect the labour supply decisions of Amy and Bill? How much revenue is the government able to collect under this taxation scheme?