Answer :
Sure, let’s break this down step by step.
### b. After-Tax Salary Increase
Question: If Vanessa pays a marginal tax rate of 20 percent and receives a [tex]$5,000 salary increase, how much will she have after paying taxes? Solution: 1. Initial Salary Increase: $[/tex]5,000
2. Tax Rate: 20%
3. Tax Amount: [tex]$5,000 * 0.20 = $[/tex]1,000
4. After-Tax Salary Increase: [tex]$5,000 - $[/tex]1,000 = [tex]$4,000 Vanessa will have $[/tex]4,000 after paying taxes.
### c. Employer-Provided Health Insurance
Question: If HeadBook spends [tex]$5,000 on health insurance for Vanessa instead of giving her a raise, how much more can be spent on health insurance compared to if Vanessa bought it herself with her after-tax salary increase? Solution: 1. Employer's Spending on Health Insurance: $[/tex]5,000
2. Vanessa's After-Tax Salary Increase: [tex]$4,000 The difference is calculated as: 3. Difference: $[/tex]5,000 - [tex]$4,000 = $[/tex]1,000
The employer can spend [tex]$1,000 more on Vanessa's health insurance than she could if she had to purchase it herself after receiving the raise. ### d. Preferences and Profit Motive Question: 1. Would Vanessa prefer the raise or the employer-provided insurance? 2. Would HeadBook have any profit motive for denying Vanessa her preference? Solution: 1. Vanessa's Preference: - If Vanessa opts for the raise, she effectively has $[/tex]4,000 after tax to spend.
- If the employer provides health insurance, she receives health insurance valued at [tex]$5,000. Vanessa would prefer the raise because the difference in spending ($[/tex]1,000) is less beneficial to her than the straight cash value of the raise.
Vanessa's Preference: Raise
2. Employer's Profit Motive:
- HeadBook spends an additional [tex]$1,000 on health insurance if they provide it directly rather than giving Vanessa the raise. Therefore, HeadBook does not have a profit motive for denying Vanessa her preference. Employer's Profit Motive: No ### e. Tax Law Change and Spending on Health Insurance Question: Suppose the government changes the tax law so that individuals can now deduct the cost of health insurance from their personal incomes. If Vanessa gets the $[/tex]5,000 raise and spends all of it on health insurance, will her tax liability change? How much will she be able to spend on health insurance?
Solution:
1. Initial Tax Liability on [tex]$5,000 Raise: - Tax Amount: $[/tex]1,000 (as calculated previously)
2. New Tax Liability:
- With the new law, health insurance is deductible. So the tax Vanessa pays now considers the deduction.
- Initial taxable amount: [tex]$5,000 - Taxable amount after spending on health insurance: $[/tex]5,000 (salary) - [tex]$5,000 (deduction) = $[/tex]0
- Tax Owed: 20% of [tex]$0 = $[/tex]0
3. Change in Tax Liability:
- Initial Tax Liability: [tex]$1,000 - New Tax Liability: $[/tex]0
- The change in tax liability is [tex]$1,000, but we need to consider the effect of deduction: - Additional amount deducted (tax-saving mechanism): $[/tex]5,000 * 0.20 = [tex]$1,000 - Net effect of tax change: $[/tex]1,000 - [tex]$4,000*0.20 tax on the $[/tex]4,000, post-deduction salary raise =[tex]$200 (Tax liability decreases by $[/tex]200 )
Final Conclusion: Vanessa's spending on health insurance:
- Before Deduction: [tex]$4,000 - After Deduction Implementation: Net tax liability derived which slightly impact ($[/tex]200 saving), final conclusion, aligns with calculative spending on deduct tax
Therefore, Vanessa can effectively still spend [tex]$4,000. However, slightest correction, Vanessa can spend: $[/tex]4,200 (due to new tax-deduction)
### b. After-Tax Salary Increase
Question: If Vanessa pays a marginal tax rate of 20 percent and receives a [tex]$5,000 salary increase, how much will she have after paying taxes? Solution: 1. Initial Salary Increase: $[/tex]5,000
2. Tax Rate: 20%
3. Tax Amount: [tex]$5,000 * 0.20 = $[/tex]1,000
4. After-Tax Salary Increase: [tex]$5,000 - $[/tex]1,000 = [tex]$4,000 Vanessa will have $[/tex]4,000 after paying taxes.
### c. Employer-Provided Health Insurance
Question: If HeadBook spends [tex]$5,000 on health insurance for Vanessa instead of giving her a raise, how much more can be spent on health insurance compared to if Vanessa bought it herself with her after-tax salary increase? Solution: 1. Employer's Spending on Health Insurance: $[/tex]5,000
2. Vanessa's After-Tax Salary Increase: [tex]$4,000 The difference is calculated as: 3. Difference: $[/tex]5,000 - [tex]$4,000 = $[/tex]1,000
The employer can spend [tex]$1,000 more on Vanessa's health insurance than she could if she had to purchase it herself after receiving the raise. ### d. Preferences and Profit Motive Question: 1. Would Vanessa prefer the raise or the employer-provided insurance? 2. Would HeadBook have any profit motive for denying Vanessa her preference? Solution: 1. Vanessa's Preference: - If Vanessa opts for the raise, she effectively has $[/tex]4,000 after tax to spend.
- If the employer provides health insurance, she receives health insurance valued at [tex]$5,000. Vanessa would prefer the raise because the difference in spending ($[/tex]1,000) is less beneficial to her than the straight cash value of the raise.
Vanessa's Preference: Raise
2. Employer's Profit Motive:
- HeadBook spends an additional [tex]$1,000 on health insurance if they provide it directly rather than giving Vanessa the raise. Therefore, HeadBook does not have a profit motive for denying Vanessa her preference. Employer's Profit Motive: No ### e. Tax Law Change and Spending on Health Insurance Question: Suppose the government changes the tax law so that individuals can now deduct the cost of health insurance from their personal incomes. If Vanessa gets the $[/tex]5,000 raise and spends all of it on health insurance, will her tax liability change? How much will she be able to spend on health insurance?
Solution:
1. Initial Tax Liability on [tex]$5,000 Raise: - Tax Amount: $[/tex]1,000 (as calculated previously)
2. New Tax Liability:
- With the new law, health insurance is deductible. So the tax Vanessa pays now considers the deduction.
- Initial taxable amount: [tex]$5,000 - Taxable amount after spending on health insurance: $[/tex]5,000 (salary) - [tex]$5,000 (deduction) = $[/tex]0
- Tax Owed: 20% of [tex]$0 = $[/tex]0
3. Change in Tax Liability:
- Initial Tax Liability: [tex]$1,000 - New Tax Liability: $[/tex]0
- The change in tax liability is [tex]$1,000, but we need to consider the effect of deduction: - Additional amount deducted (tax-saving mechanism): $[/tex]5,000 * 0.20 = [tex]$1,000 - Net effect of tax change: $[/tex]1,000 - [tex]$4,000*0.20 tax on the $[/tex]4,000, post-deduction salary raise =[tex]$200 (Tax liability decreases by $[/tex]200 )
Final Conclusion: Vanessa's spending on health insurance:
- Before Deduction: [tex]$4,000 - After Deduction Implementation: Net tax liability derived which slightly impact ($[/tex]200 saving), final conclusion, aligns with calculative spending on deduct tax
Therefore, Vanessa can effectively still spend [tex]$4,000. However, slightest correction, Vanessa can spend: $[/tex]4,200 (due to new tax-deduction)
