A midwestern state aids its institutions of higher education by giving a credit against its income tax equal to $50$ percent of any gift to such institutions $($subject to a limit of $$50$ credit per person$).$ Two residents of that state, Mr$.$ Blue $($in the $10$ percent federal tax bracket$)$ and Ms$.$ Jones $($in the $35$ percent federal tax bracket$),$ each contribute $$100$ to an eligible state university. A: How much will the state tax liabilities of each change as a result of thier gifts? B: State income tax payments and contributions to charitable organizations $($such as unifederal tax liability. How much will federal tax liability change for Mr$.$ Blue and Ms$.$ Jones as a result of their contributions? C: Considering changes in both federal and state tax liabilities, what is the net after$-$tax cost of Mr$.$ Blue$$s and Ms$.$ Jones$$s gifts? $($Hint: Subtract the changes in state and federal liabilities from $$100.)$ D: Suppose the state program changed from a credit to a deduction. If the state tax rate was a flat $3$ percent, how much would state liability for Mr$.$ Blue and Ms$.$ Jones change? E: From the previous computations, which approach $($credit or deduction$)$ do you suppose universities in the state would favor?