To determine how the annual tax revenues of Germany and France compare to each other, we need to calculate the annual tax revenue for each country based on the given data and then compare the results.
### Step-by-Step Solution:
1. Identify the input data:
- France:
- Workforce: [tex]\(31,491,232\)[/tex]
- Average Salary: [tex]\(€29,766\)[/tex]
- Income Tax Rate: [tex]\(69.3\%\)[/tex] or [tex]\(0.693\)[/tex]
- Germany:
- Workforce: [tex]\(38,844,017\)[/tex]
- Average Salary: [tex]\(€32,104\)[/tex]
- Income Tax Rate: [tex]\(45.2\%\)[/tex] or [tex]\(0.452\)[/tex]
2. Calculate the annual tax revenue for each country:
- France:
[tex]\[
\text{Annual Tax Revenue}_{\text{France}} = \text{Workforce}_{\text{France}} \times \text{Average Salary}_{\text{France}} \times \text{Tax Rate}_{\text{France}}
\][/tex]
[tex]\[
\text{Annual Tax Revenue}_{\text{France}} = 31,491,232 \times 29,766 \times 0.693 \approx €649,596,032,116.42
\][/tex]
- Germany:
[tex]\[
\text{Annual Tax Revenue}_{\text{Germany}} = \text{Workforce}_{\text{Germany}} \times \text{Average Salary}_{\text{Germany}} \times \text{Tax Rate}_{\text{Germany}}
\][/tex]
[tex]\[
\text{Annual Tax Revenue}_{\text{Germany}} = 38,844,017 \times 32,104 \times 0.452 \approx €563,665,841,439.14
\][/tex]
3. Calculate the difference in tax revenue between France and Germany:
[tex]\[
\text{Difference} = \text{Annual Tax Revenue}_{\text{France}} - \text{Annual Tax Revenue}_{\text{Germany}}
\][/tex]
[tex]\[
\text{Difference} = €649,596,032,116.42 - €563,665,841,439.14 \approx €85,930,190,677.28
\][/tex]
4. Compare the difference to the provided options:
a. The French government gathers [tex]\(€85,930,190,677\)[/tex] more than the German government.
b. The French government gathers [tex]\(€543,141,128,984\)[/tex] more than the German government.
c. The German government gathers [tex]\(€309,680,310,056\)[/tex] more than the French government.
d. The German government gathers [tex]\(€223,750,119,378\)[/tex] more than the French government.
The difference calculated is approximately [tex]\(€85,930,190,677.28\)[/tex].
Therefore, the best answer from the choices provided is:
a. The French government gathers [tex]\(€85,930,190,677\)[/tex] more than the German government.
