\begin{tabular}{ll}
\hline Plan A & Plan B \\
\hline Consumption up to 1,000 oranges is taxed at [tex]$5 \%$[/tex]. & Consumption up to 2,000 oranges is taxed at [tex]$25 \%$[/tex]. \\
Consumption higher than 1,000 oranges is taxed at [tex]$20 \%$[/tex]. & Consumption higher than 2,000 oranges is taxed at [tex]$15 \%$[/tex]. \\
\hline
\end{tabular}

Derive the marginal and average tax rates under each tax plan at the consumption levels of 500 oranges, 1,500 oranges, and 2,500 oranges, respectively. Fill in the following table with your results.

\begin{tabular}{|c|c|c|c|c|}
\hline Consumption Level & Marginal Tax Rate (Plan A) & Average Tax Rate (Plan A) & Marginal Tax Rate (Plan B) & Average Tax Rate (Plan B) \\
\hline 500 oranges & [tex]$5 \%$[/tex] & [tex]$\nabla$[/tex] & [tex]$25 \%$[/tex] & [tex]$\nabla$[/tex] \\
\hline 1,500 oranges & [tex]$20 \%$[/tex] & [tex]$\nabla$[/tex] & [tex]$25 \%$[/tex] & [tex]$\nabla$[/tex] \\
\hline 2,500 oranges & [tex]$20 \%$[/tex] & [tex]$\nabla$[/tex] & [tex]$15 \%$[/tex] & [tex]$\nabla$[/tex] \\
\hline
\end{tabular}



Answer :

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.