Your advice is sought on evaluating two policy proposals, each of which combines the effects of an income-support plan with an income-tax program. Let x denote earned income before any taxes or government transfers and let y denote income after taking all taxes and government transfers into account.

Plan A An individual who earns no income (x = 0) receives a tax-free government support of $6,000 annually. No income support is received by anyone with positive earned income (x > 0). Those individuals who earn income in excess of $6,000 are required to pay income tax at the rate of 20% on each dollar earned in excess of $6,000.

Plan B Everyone receives a basic income of $6,000 from the government. Each person then pays income tax at the rate of 40% for every dollar of earned income (that is, not including the basic income of $6,000).

(a) Compute income after taxes and transfers y as a function of earned income x for each of the two plans, and graph both functions on the same diagram.

(b) Which tax system is more favorable from the taxpayer's point of view? How does your answer depend on the individual's level of earned income?