Question 1: Optimal consumption and taxes (8 marks)

You just turned 27 (January 1st) and have total financial assets of$15,000. Your current is salary$70,000 which you expect to grow at a real rate of 1.5% per year until you retire. You are paid on an annual basis with wages being received at the end of each year. Assume that you will retire when you turn 67 and that you will die on your 90th birthday. Your current subsistent consumption is $20,000 per year. You prefer to live it up while you are young and can enjoy your consumption. That is, you want your discretionary consumption to decline by 1.25% per year in real terms for the rest of your life. Assume that you incur relatively high costs commuting to and from work, i.e. you expect your subsistent consumption to decline once you retire. In specific, assume that your subsistent consumption remains constant (in real terms) during your working years then declines by 10% once you retire. To be perfectly clear, your subsistent consumption in your 67th year will be10% less than your subsistent consumption the prior year and grow at a real rate of zero thereafter. Assume that the real valuation rate is 4% per year. Lastly, assume that you pay taxes according to the following (hypothetical) tax system:

Taxable Income Levels	Average Tax Rate
$0 to $19,999.99	0%
$20,000 to $69,999.99	21%
$70,000 to $100,000	25%
>$100,000	29%

You should also assume that:

i) you are not taxed on investment income (i.e., you only need to account for taxes on wage income and)

ii) this tax system offers no tax credits or deductions and has no surtax.