Lesley is a single mother with 2 children. She can earn $10 per hour and can work up to 1,800 hours per year. However, if she does not earn any income at all, she will receive government benefits totaling $18,000 per year. For every $1 of income she earns, her level of government support is reduced by $1. Lesley

Question

BlackTom AI · Accepted Answer

The scenario describes Lesley’s financial setup: hourly wage of 10 dollars, a maximum of 1,800 hours per year, and a government benefit of 18,000 dollars if no income is earned. Importantly, for every additional dollar of income, government benefits decrease by the same amount (a one-for-one offset).

First, I’ll compute the total resources available to Lesley when she earns h dollars in a year. Her earnings from work are income = 10 × h hours, i.e., income = 10h. Government benefits decline with income, so benefits = 18,000 − 10h, assuming this does not go below zero. Since she can work up to 1,800 hours, the maximum income is 10 × 1,800 = 18,000, which would reduce benefits to zero.

Now, total resources (income plus government benefits) can be expressed as: total = income + benefits = 10h + (18,000 − 10h) = 18,000, as long as 10h ≤ 18,000. In other words, for any permissible amount of work up to the cap, the sum of her earnings and the government support remains constant at 18,000. There is no financial gain from working more hours within the allowed range, because any additional earnings are exactly offset by a reduction in benefits.

Option 1: 'has a monetary incentive to work and will maximize her income if she works for 300 hours' — This is incorrect because the total resources do not increase with more work within the 0–1,800 hour range; the 300-hour scenario would still yield the same total 18,000 as any other admissible hour count.

Option 2: 'has a monetary incentive to work and will maximize her income if she works for 600 hours' — Same flaw as above: the one-for-one offset means nothing special happens at 600 hours; the total remains 18,000.

Option 3: 'has no monetary incentive to work, though she may still choose to work' — This aligns with the calculation: additional work does not raise total resources due to the offsetting benefit reduction. The decision to work could be influenced by non-ministerial factors such as non-monetary preferences or constraints, even though there is no monetary gain.

Option 4: 'has a monetary incentive to work and will maximize her income if she works for 900 hours' — Again, the total does not increase with hours worked, so there is no monetary incentive to target 900 hours specifically. The offset eliminates any such gain.

In summary, the key idea is the one-for-one trade-off between earnings and benefits, which keeps total resources constant across all allowed working hours, making any hour-specific incentive unsupported by the math. The only viable interpretation is that there is no monetary incentive to increase work hours, even though working may still occur for non-monetary reasons.

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希望你的学习变得更简单

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