The mythical country of Januvia imposes a tax based on the number of titanium coins each taxpayer owns at the end of each year per the following schedule:

$ \begin{array}{cc}
\hline \text { Number of titanium coins } & \text { Tax } \
\hline 0 -200 & \$ 500+\$ 5 \text { per titanium coin } \ 201-500 & \$ 1,000+\$ 6 \text { per titanium coin } \ 500 & \$ 4,000+\$ 7 \text { per titanium coin }\
\hline
\end{array} $
Marvin,a resident of Januvia,owns 300 titanium coins at the end of the current year.
I.Marvin's titanium coins tax is $2,800.
II.Marvin's marginal tax rate is $6.
III.Marvin's average tax rate is $9.33.
IV.Marvin's average tax rate is $6.

Question

The mythical country of Januvia imposes a tax based on the number of titanium coins each taxpayer owns at the end of each year per the following schedule:

$ \begin{array}{cc}
\hline  \text { Number of titanium coins } & \text { Tax } \
\hline 0  -200 & \$ 500+\$ 5 \text { per titanium coin } \ 201-500 & \$ 1,000+\$ 6 \text { per titanium coin } \ >500 & \$ 4,000+\$ 7 \text { per titanium coin }\
\hline 
\end{array} $
Marvin,a resident of Januvia,owns 300 titanium coins at the end of the current year.
I.Marvin's titanium coins tax is $2,800.
II.Marvin's marginal tax rate is $6.
III.Marvin's average tax rate is $9.33.
IV.Marvin's average tax rate is $6.

Quizplus · Accepted Answer

Using the given table, Marvin’s tax would be
$$\$1,000+\$6(300-200)=\$2,800$$
Thus, Statement I is correct.
Marvin’s marginal tax rate is the additional tax he pays on an additional dollar of income.
From the given table, we see that for someone with between 201 and 500 titanium coins, the marginal tax rate is $6 per coin. Marvin, with 300 coins, falls in this category, so Statement II is correct.
Marvin’s average tax rate is the total tax he pays divided by his total income.
Since Marvin has 300 coins, his total tax payable is $\$1,000+\$6(300-200)=\$2,800$.
His total income is $500+300(5)=\$2,000$.
Therefore, his average tax rate is $\frac{\$2,800}{\$2,000}\approx\$9.33$.
Thus, Statement III is correct, but Statement IV is incorrect.

The Mythical Country of Januvia Imposes a Tax Based on the Number