Assume that a taxpayer can choose when he is to receive $$10,000$ of fully taxable income. If the taxpayer receives the income at the end of Year $1,$ he will receive exactly $$10,000.$ If he delays receipt of the income until the end of Year $2,$ the amount will grow to $$11,000.$ If the taxpayer takes the money at the end of Year $1,$ he can invest the proceeds and earn a pre$-$tax return of $10$ percent over the next year.

a$.$ If the taxpayer faces a marginal tax rate of $31$ percent in both Year $1$ and Year $2,$ when should he elect to receive the income?

b$.$ At what pre$-$ tax rate of return, will the taxpayer be indifferent to taking the money in Year $1$ and Year $2?$

c$.$ If the taxpayer$$s marginal tax rate increases to $35$ percent in Year $2,$ when should he elect to receive the income?

d$.$ What would the tax rate need to be in Year $2$ to make the taxpayer indifferent?