1. In the Republic of Morpheus, workers need 14 hours of rest per day to stay in good health. All workers have the same preferences and receive $10 as non labour income. Assume that the wage is $4 per hour and that, at that wage, each worker maximises his utility by working 6 hours per day. a. Draw the budget constraint of a representative worker, an indifference curve and the utility maximising point. (Make sure you label the chart) The government would like to increase the labour supply and tries two alternative policies: (i) increase the wage to $5 an hour, (ii) increase the wage to $7 an hour but only for every hour after the 6th. b. Illustrate the effect of policies (i) and (ii) on the worker's budget constraint. Use two separate graphs. c. Can labour supply actually decrease under policy (i)? Why? Why not? d. Can labour supply actually decrease under policy (ii)? Why? Why not? 2. Consider a country with a tax system where the marginal rate of income tax is 0% on incomes below Ea and 25% on income above a. Suppose a new high marginal tax rate of 50% is introduced for incomes above Eb, where b>a. Let the nominal wage be W=1. There are T=L-R hours available that can be allocated between work and leisure. Preferences over consumption and leisure satisfy all the assumptions. a. Illustrate the effect of the introduction of the high marginal tax rate on the budget constraint. b. Does economic theory predict whether the new high marginal tax rate increases or decreases labour supply for those who earn more than Eb? c. In April 2010 the labour government raised the top tax rate in the UK to 50% for taxable income exceeding 150,000, largely to raise revenue. Yet far less revenue was earned than forecasted (the top rate was later lowered to 45% in April 2013). How can the low tax revenue be explained? Our model focuses on labour supply as the key decision variable what other behavioural responses may follow from the introduction of a new top tax rate