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Sagot :
To derive the marginal and average tax rates under each tax plan at the given consumption levels, we can analyze each plan step-by-step for the consumption values of 500, 1,500, and 2,500 oranges.
### Plan A
- Marginal Tax Rate: This is the rate applied to the last unit of consumption.
- Average Tax Rate: This is the total tax paid divided by the total consumption, expressed as a percentage.
Consumption Level: 500 oranges
- Marginal Tax Rate: Since 500 oranges are within the first 1,000 oranges, the marginal tax rate is [tex]\( 5\% \)[/tex].
- Average Tax Rate: The total tax paid on 500 oranges is [tex]\( 500 \times 0.05 = 25 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{25}{500} \times 100 = 5\% \)[/tex].
Consumption Level: 1,500 oranges
- Marginal Tax Rate: The first 1,000 oranges are taxed at [tex]\( 5\% \)[/tex] and the remaining 500 oranges are taxed at [tex]\( 20\% \)[/tex]. Therefore, the marginal tax rate for the last unit falls in the [tex]\( 20\% \)[/tex] bracket.
- Average Tax Rate: The tax for the first 1,000 oranges is [tex]\( 1000 \times 0.05 = 50 \)[/tex] oranges. The tax for the next 500 oranges is [tex]\( 500 \times 0.20 = 100 \)[/tex] oranges. The total tax paid is [tex]\( 50 + 100 = 150 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{150}{1500} \times 100 = 10\% \)[/tex].
Consumption Level: 2,500 oranges
- Marginal Tax Rate: The first 1,000 oranges are taxed at [tex]\( 5\% \)[/tex] and the remaining 1,500 oranges are taxed at [tex]\( 20\% \)[/tex]. The marginal tax rate for the last unit consumed (in the 1,500 additional oranges) is [tex]\( 20\% \)[/tex].
- Average Tax Rate: The tax for the first 1,000 oranges is [tex]\( 1000 \times 0.05 = 50 \)[/tex] oranges. The tax for the next 1,500 oranges is [tex]\( 1500 \times 0.20 = 300 \)[/tex] oranges. The total tax paid is [tex]\( 50 + 300 = 350 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{350}{2500} \times 100 = 14\% \)[/tex].
### Plan B
Consumption Level: 500 oranges
- Marginal Tax Rate: Since 500 oranges are within the first 2,000 oranges, the marginal tax rate is [tex]\( 25\% \)[/tex].
- Average Tax Rate: The total tax paid on 500 oranges is [tex]\( 500 \times 0.25 = 125 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{125}{500} \times 100 = 25\% \)[/tex].
Consumption Level: 1,500 oranges
- Marginal Tax Rate: Since 1,500 oranges are within the first 2,000 oranges, the marginal tax rate is [tex]\( 25\% \)[/tex].
- Average Tax Rate: The total tax paid on 1,500 oranges is [tex]\( 1500 \times 0.25 = 375 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{375}{1500} \times 100 = 25\% \)[/tex].
Consumption Level: 2,500 oranges
- Marginal Tax Rate: The first 2,000 oranges are taxed at [tex]\( 25\% \)[/tex], and the remaining 500 oranges are taxed at [tex]\( 15\% \)[/tex]. The marginal tax rate for the last unit consumed (in the 500 additional oranges) is [tex]\( 15\% \)[/tex].
- Average Tax Rate: The tax for the first 2,000 oranges is [tex]\( 2000 \times 0.25 = 500 \)[/tex] oranges. The tax for the next 500 oranges is [tex]\( 500 \times 0.15 = 75 \)[/tex] oranges. The total tax paid is [tex]\( 500 + 75 = 575 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{575}{2500} \times 100 = 23\% \)[/tex].
### Table Summary
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Consumption Level} & \textbf{Plan A Marginal Tax Rate} & \textbf{Plan A Average Tax Rate} & \textbf{Plan B Marginal Tax Rate} & \textbf{Plan B Average Tax Rate} \\
\hline
500 oranges & 5\% & 5\% & 25\% & 25\% \\
\hline
1,500 oranges & 20\% & 10\% & 25\% & 25\% \\
\hline
2,500 oranges & 20\% & 14\% & 15\% & 23\% \\
\hline
\end{tabular}
This completes the detailed step-by-step derivation of the marginal and average tax rates for each tax plan at the given consumption levels.
### Plan A
- Marginal Tax Rate: This is the rate applied to the last unit of consumption.
- Average Tax Rate: This is the total tax paid divided by the total consumption, expressed as a percentage.
Consumption Level: 500 oranges
- Marginal Tax Rate: Since 500 oranges are within the first 1,000 oranges, the marginal tax rate is [tex]\( 5\% \)[/tex].
- Average Tax Rate: The total tax paid on 500 oranges is [tex]\( 500 \times 0.05 = 25 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{25}{500} \times 100 = 5\% \)[/tex].
Consumption Level: 1,500 oranges
- Marginal Tax Rate: The first 1,000 oranges are taxed at [tex]\( 5\% \)[/tex] and the remaining 500 oranges are taxed at [tex]\( 20\% \)[/tex]. Therefore, the marginal tax rate for the last unit falls in the [tex]\( 20\% \)[/tex] bracket.
- Average Tax Rate: The tax for the first 1,000 oranges is [tex]\( 1000 \times 0.05 = 50 \)[/tex] oranges. The tax for the next 500 oranges is [tex]\( 500 \times 0.20 = 100 \)[/tex] oranges. The total tax paid is [tex]\( 50 + 100 = 150 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{150}{1500} \times 100 = 10\% \)[/tex].
Consumption Level: 2,500 oranges
- Marginal Tax Rate: The first 1,000 oranges are taxed at [tex]\( 5\% \)[/tex] and the remaining 1,500 oranges are taxed at [tex]\( 20\% \)[/tex]. The marginal tax rate for the last unit consumed (in the 1,500 additional oranges) is [tex]\( 20\% \)[/tex].
- Average Tax Rate: The tax for the first 1,000 oranges is [tex]\( 1000 \times 0.05 = 50 \)[/tex] oranges. The tax for the next 1,500 oranges is [tex]\( 1500 \times 0.20 = 300 \)[/tex] oranges. The total tax paid is [tex]\( 50 + 300 = 350 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{350}{2500} \times 100 = 14\% \)[/tex].
### Plan B
Consumption Level: 500 oranges
- Marginal Tax Rate: Since 500 oranges are within the first 2,000 oranges, the marginal tax rate is [tex]\( 25\% \)[/tex].
- Average Tax Rate: The total tax paid on 500 oranges is [tex]\( 500 \times 0.25 = 125 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{125}{500} \times 100 = 25\% \)[/tex].
Consumption Level: 1,500 oranges
- Marginal Tax Rate: Since 1,500 oranges are within the first 2,000 oranges, the marginal tax rate is [tex]\( 25\% \)[/tex].
- Average Tax Rate: The total tax paid on 1,500 oranges is [tex]\( 1500 \times 0.25 = 375 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{375}{1500} \times 100 = 25\% \)[/tex].
Consumption Level: 2,500 oranges
- Marginal Tax Rate: The first 2,000 oranges are taxed at [tex]\( 25\% \)[/tex], and the remaining 500 oranges are taxed at [tex]\( 15\% \)[/tex]. The marginal tax rate for the last unit consumed (in the 500 additional oranges) is [tex]\( 15\% \)[/tex].
- Average Tax Rate: The tax for the first 2,000 oranges is [tex]\( 2000 \times 0.25 = 500 \)[/tex] oranges. The tax for the next 500 oranges is [tex]\( 500 \times 0.15 = 75 \)[/tex] oranges. The total tax paid is [tex]\( 500 + 75 = 575 \)[/tex] oranges. Thus, the average tax rate is [tex]\( \frac{575}{2500} \times 100 = 23\% \)[/tex].
### Table Summary
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Consumption Level} & \textbf{Plan A Marginal Tax Rate} & \textbf{Plan A Average Tax Rate} & \textbf{Plan B Marginal Tax Rate} & \textbf{Plan B Average Tax Rate} \\
\hline
500 oranges & 5\% & 5\% & 25\% & 25\% \\
\hline
1,500 oranges & 20\% & 10\% & 25\% & 25\% \\
\hline
2,500 oranges & 20\% & 14\% & 15\% & 23\% \\
\hline
\end{tabular}
This completes the detailed step-by-step derivation of the marginal and average tax rates for each tax plan at the given consumption levels.
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