help with these multiple choice questions. the chosen answered aren't necessarily correct.

You are trying to design a tax system that will simultaneously achieve both of the following goals: 1) a person with no income would pay no taxes, and 2) a high-income person would pay a higher fraction of income in taxes than a low-income person. Which of the following statements is correct? a. A lump-sum tax would achieve the second goal but not the first. O b. A regressive tax would achieve the second goal but not the first. c. A progressive tax could achieve both goals. O d. A proportional tax could achieve the second goal but not the first.The deadweight loss of an income tax is determined by the an: a. amount of total tax revenue to the government. I\"? b. marginal tax rate. IA ,' c. average tax rate. 0 d. ability-to-pay principle