2. [30 marks] Kate has 200 days a year to devote to leisure (l) or labour, L. Her daily wage is $1000, her utility is U = lC where C is consumption, and her MRS = C/l. Under the income tax system where Kate lives, the first $60,000 of her income is taxed at 20%. Any income above $60,000 is taxed at 40%.

a. [6 marks] Accurately draw Kates budget line.

b. [10 marks] Find how much labour Kate would supply, and show on a diagram, in the following cases:

i. no tax.

ii. under the tax system described. Calculate the total tax Kate would be paying in this case. It has been argued that lowering the marginal tax rate at high incomes might actually increase individual welfare without reducing total tax revenues.

c. [7 marks] Suppose the government modifies the tax schedule so that all income earned is taxed at 20%. How much will Kate work now? How much tax will she pay? Is utility higher than in part b(ii)? Show on a diagram.

d. [7 marks] Suppose the government instead modifies the tax schedule to a linear tax, where every individual receives a $10,000 lump sum transfer, but also pays a 10% tax on all income earned. How much will Kate work now? How much (net) tax will she pay? Is utility higher than in part b (ii)? Show on a diagram.