For part (c), why does the program yield a wage rate of $6 per hour up to 100 hours of work per month?

Assume that an individual can earn $12 per hour if they work. Draw the budget constraints that show the monthly consumption-leisure trade-off under the following three transfer programs. In each graph, assume that a person can work at most 24 hours per day for 30 days per month, totaling 720 hours. Thus, the axis intercepts, in the absence of any program, are 720×$12 = $8,640 in consumption and 720 hours of leisure.

c) The government guarantees $900 per month in income and reduces that benefit by $1 for every $2 in labor income, until the benefit reaches $300 per month. After that point, the government does not reduce the benefit further. This program yields a wage rate of $6 per hour up to 100 hours of work per month. The reduction ends after $600 is deducted, which occurs at 100 hours per month (100×6 = $600). Wages are 100×$12 = $1,200, plus benefits of $300, for a total consumption of $1,500 and 720 - 100 = 620 hours of leisure. At greater than 100 hours, the new budget line parallels the baseline $12 per hour line but is $300 higher. Thus, the new y-intercept is $8,640 + $300 = $8,940.

Under transfer program c, the government guarantees $900 per month in income, reducing the benefit by $1 for every $2 in labor income until it reaches $300 per month. This results in a wage rate of $6 per hour up to 100 hours of work per month.

Explanation:

Program c outlines a transfer program where the government ensures a minimum income of $900 per month, decreasing the benefit by $1 for every $2 in labor income until it reaches $300. To understand the impact on the wage rate, we can analyze the budget constraints.

For the first 100 hours of work per month at $6 per hour, the reduction in benefits is $1 for every $2 earned, leading to a total reduction of $600. At 100 hours, the individual earns $600 from work and receives $300 in benefits, resulting in a total consumption of $900.

Beyond 100 hours, the reduction in benefits stops, and the wage rate becomes the baseline of $12 per hour. However, the budget line is $300 higher due to the fixed benefits. The new y-intercept is $8,640 + $300 = $8,940, reflecting the increased consumption level with the fixed benefits.

In summary, the program creates a wage rate of $6 per hour up to 100 hours, after which the individual earns the full $12 per hour, plus fixed benefits, affecting the consumption-leisure trade-off.

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