A partner of a business receiving the income described below files federal income taxes as a single taxpayer, perform the following:

a$.$ Calculate the tax liability, after$-$tax earnings, marginal tax rates, and average tax rates for the following levels of partnership earnings before taxes: $$12,200$; $$71,700$; $$299,600$; $$410,300$; $$1$million; $$1\mathrm{.}5$million; and $$2$ million.

b$.$ Plot the marginal tax rates$($measured on the y$-$axis$)$ against the pretax income levels$($measured on the x$-$axis$).$ Explain the relationship between these variables.