Aristotle earns 5 dollars per hour.He has 110 hours per week available for either labor or leisure.In the old days he paid no taxes and received nothing from the government.Now he gets a $200 payment per week from the government but he must pay half of his labor income in taxes.(His before-tax wages are the same as they were before, and he has no other source of income than wages and payments from the government.)He notices that with the government payment and his taxes, he can exactly afford the combination of leisure and consumption goods that he used to choose.How many hours per week did he work in the old days?
A)100
B)20
C)45
D)60
E)None of the above.

Question

Quizplus · Accepted Answer

In the old days, Aristotle's income was solely from his labor, with no taxes. Let's denote the number of hours he worked as $H$, and his wage per hour as $W = \$5$. Thus, his total income was $5H$.In the new system, he receives a government payment of \$200, but pays half of his labor income in taxes. Therefore, his net income from labor is now $\frac{1}{2} \times 5H = 2.5H$. Adding the government payment, his total income becomes $2.5H + 200$.Given that he can afford exactly the same combination of leisure and consumption goods as before, his income must remain the same in both scenarios. Therefore, we set the two expressions for income equal to each other:$$5H = 2.5H + 200$$Solving for $H$, we get:$$5H - 2.5H = 200$$$$2.5H = 200$$$$H = \frac{200}{2.5} = 80$$Since 80 is not one of the provided options, the correct answer is E) None of the above.

Aristotle Earns 5 Dollars Per Hour