Table 2 below shows the incomes of an Engineer and a Nurse and their demand schedule for wheat in a month. Use the information to answer the questions that follow.

$Y_1 = \$3,000$, $Y_2 = \$5,000$  
$Q_1 = 15 \text{ kg}$, $Q_2 = 10 \text{ kg}$
$$
\%\Delta Q_d = \frac{10 - 15}{(15 + 10)/2} = \frac{-5}{12.5} = -0.4
$$
$$
\%\Delta Y = \frac{5,000 - 3,000}{(3,000 + 5,000)/2} = \frac{2,000}{4,000} = 0.5
$$

$$
YED_{\text{Engineer}} = \frac{-0.4}{0.5} = \boxed{\text{-0.8}}
$$

$Y_1 = \$2,500$, $Y_2 = \$4,000$  
$Q_1 = 8 \text{ kg}$, $Q_2 = 12 \text{ kg}$
$$
\%\Delta Q_d = \frac{12 - 8}{(8 + 12)/2} = \frac{4}{10} = 0.4
$$
$$
\%\Delta Y = \frac{4,000 - 2,500}{(2,500 + 4,000)/2} = \frac{1,500}{3,250} = \frac{6}{13} \approx 0.4615
$$

$$
YED_{\text{Nurse}} = \frac{0.4}{6/13} = \frac{0.4 \times 13}{6} = \frac{5.2}{6} = \boxed{\frac{13}{15} \approx \text{0.87}}
$$

Old income: $\$3,000$, tax rate $15\%$. Tax paid: $\$3,000 \times 0.15 = \$450$. Average tax rate: $\frac{\$450}{\$3,000} \times 100\% = 15\%$.  
New income: $\$5,000$, tax rate $10\%$. Tax paid: $\$5,000 \times 0.10 = \$500$. Average tax rate: $\frac{\$500}{\$5,000} \times 100\% = 10\%$.

As the Engineer's income increased from $\$3,000$ to $\$5,000$, the average tax rate decreased from $15\%$ to $10\%$. This indicates a **regressive tax system**.  
Reason: In a regressive tax system, the average tax rate decreases as income increases.

Old income: $\$2,500$, tax rate $8\%$. Tax paid: $\$2,500 \times 0.08 = \$200$. Average tax rate: $\frac{\$200}{\$2,500} \times 100\% = 8\%$.  
New income: $\$4,000$, tax rate $10\%$. Tax paid: $\$4,000 \times 0.10 = \$400$. Average tax rate: $\frac{\$400}{\$4,000} \times 100\% = 10\%$.

As the Nurse's income increased from $\$2,500$ to $\$4,000$, the average tax rate increased from $8\%$ to $10\%$. This indicates a **progressive tax system**.  
Reason: In a progressive tax system, the average tax rate increases as income increases.