You are to analyse two alternative tax systems: (1) a 7.15% proportional tax on personal income (which includes both labour income and non-labour income); (2) a 7.7% sales tax.

Using the consumption-leisure model, solve for the consumer equilibrium under each scenario assuming that the utility function is = ^{a 1-a} , the wage is $20, non-labour income is $50 and = 0.5. Individuals face a time endowment of 16 hours per day.

With a proportional tax on personal income, the budget constraint takes the following form:

= [(16 ) + ](1 ) , = 0.0715. With a sales tax, the price of consumption increases by 7.7%. Since we assumed that the price without the tax is set to 1, the sales tax will increase the price to $1 (1 + 0.077). Hence, the budget constraint with the sales tax is (1 + 0.077) = (16 ) + .

Report hours worked, consumption and utility in equilibrium for scenario (1) and then scenario (2). Plot the equilibrium on a graph with consumption on the vertical axis and leisure on the horizontal axis. Your graph should have a budget constraint and an indifference curve going through the optimal bundle.