Final answer:
The question explores the equivalence of a $1 per-unit tax on good x with a lump sum tax in a context where a consumer has a linear utility function and an income of $100. Changes in income and taxes alter the consumer's budget constraint and utility-maximizing choices. Without specific consumption quantities, calculation of the lump sum tax amount cannot be exact.
Step-by-step explanation:
Understanding the Impact of Taxes and Income Changes on Consumer Choices
The question pertains to a common economic scenario where a consumer is subjected to a per-unit tax on a good. To understand the impact of this tax on a consumer's choice and income, consider the utility function u(x,y) = x + y, with a total income of $100. If there is a $1 per-unit tax on good x, the lump sum tax equivalent is sought — the amount that would raise the same revenue as the per-unit tax.
Let's examine how changes in income and taxes affect consumer choices through theoretical and practical examples. In the provided scenarios, adjustments in income levels notably shift the budget constraint and influence utility-maximizing decisions. For instance, Kimberly, with a budget constraint between concert tickets and overnight retreats, alters her choices as her income level changes.
An increase in income expands the budget constraint outward, indicating more choices for the consumer that leads to a higher utility level. A lump sum tax would similarly reduce Kimberly's disposable income and shift her budget constraint inward. The key to determining how much income the lump sum tax must raise is knowing the amount consumed of good x; this will inform us of the revenue generated by the per-unit tax, which must equal the lump sum tax for revenue-neutrality.
Ultimately, without knowledge of the consumption quantities or the elasticity of demand for good x, we cannot calculate the exact lump sum amount. It depends on how the imposed taxes change the consumer's purchasing behavior — exemplified in the shift of her budget constraint and the choices she makes given her utility function.