Chapter . Chapter 19a

Step 1

Work It Out
Work It Out
Chapter 19a
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Question

Tamara has 80 hours per week that she can allocate to work or leisure. Her job pays a wage rate of $20 per hour, but Tamara is being taxed on her income in the following way. On the first $400 that Tamara makes, she pays no tax. That is, for the first 20 hours she works, her net wage—what she takes home after taxes—is $20 per hour. On all income above $400, Tamara pays a 75% tax. That is, for all hours above the first 20 hours, her net wage rate is only $5 per hour. Tamara decides to work 30 hours. Her indifference curves have the usual shape.

What is the slope of the budget constraint for Tamara during the first 20 hours of work per week? If she works more than 20 hours per week?

The slope of the budget constraint for the first 20 hours: $xRJpkiMOLgimadJy6ELPzA==

The slope of the budget constraint if she works more than 20 hours: $CC3ymPjDPgXWhdy08F4bTQ==

The opportunity cost of leisure (equal to minus the slope of her budget line,BL1) during the first 20 hours of work is 20: for each hour of leisure, she gives up $20 of income. If Tamara works beyond the first 20 hours, she earns a net $5 per hour. If she works for all remaining 60 hours, in those 60 hours she makes $300. The opportunity cost of leisure (equal to minus the slope of her budget line,BL1) during those 60 hours is 5: for each hour of leisure, she gives up $5 of income. For further review, see section “The Time Allocation Budget Line.”
What is the slope of the budget constraint for Tamara during the first 20 hours of work per week? If she works more than 20 hours per week?
3:28

Step 2

Question

The government changes the tax scheme. Now only the first $100 of income is tax-exempt. That is, for the first 5 hours she works, Tamara’s net wage rate is $20 per hour. But the government reduces the tax rate on all other income to 50%. That is, for all hours above the first 5 hours, Tamara’s net wage rate is now $10. After these changes, Tamara finds herself exactly equally as well off as before. That is, her new optimal choice is on the same indifference curve as her initial optimal choice.

What is the opportunity cost of leisure for Tamara during the first 5 hours of work per week? If she works more than 20 hours per week?

The slope of the budget constraint for the first 20 hours: $xRJpkiMOLgimadJy6ELPzA==

The slope of the budget constraint if she works more than 20 hours: $5ecJn6Q4fRhOaPvdOfnWyg==

The opportunity cost of leisure (equal to minus the slope of her budget line, BL2) during the first 5 hours of work is 20: for each hour of leisure, she gives up $20 of income. For any hours she works beyond the first 5 hours, she earns a net $10 per hour. If she works for all the remaining 75 hours, she makes $750. The opportunity cost of leisure (equal to minus the slope of her budget line, BL2) during those 75 hours is 10: for each hour of leisure, she gives up $10 of income. For further review, see section “The Time Allocation Budget Line.”
What is the opportunity cost of leisure for Tamara during the first 5 hours of work per week? If she works more than 20 hours per week?
2:45

Step 3

Question

The government changes the tax scheme. Now only the first $100 of income is tax-exempt. That is, for the first 5 hours she works, Tamara’s net wage rate is $20 per hour. But the government reduces the tax rate on all other income to 50%. That is, for all hours above the first 5 hours, Tamara’s net wage rate is now $10. After these changes, Tamara finds herself exactly equally as well off as before. That is, her new optimal choice is on the same indifference curve as her initial optimal choice.

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