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.

a) The formula for income elasticity of demand (YED) is: $YED = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{Y_2 - Y_1}{(Y_1 + Y_2)/2}}$ Where $Q_1$ and $Q_2$ are old and new quantities demanded, and $Y_1$ and $Y_2$ are old and new incomes.

• (i) Engineer: Step 1: Calculate the percentage change in quantity demanded and income. Y_1 = \3,000$,$Y_2 = $5,000$$Q_1 = 15 \text{ kg}$,$Q_2 = 10 \text{ kg}$ $\%\Delta Q_d = \frac{10 - 15}{(15 + 10)/2} = \frac{-5}{12.5} = -0.4$ $\%\Delta Y = \frac{5,000 - 3,000}{(3,000 + 5,000)/2} = \frac{2,000}{4,000} = 0.5$ Step 2: Calculate the income elasticity of demand. $YED_{Engineer} = \frac{-0.4}{0.5} = \text{-0.8}$

• (ii) Nurse: Step 1: Calculate the percentage change in quantity demanded and income. Y_1 = \2,500$,$Y_2 = $4,000$$Q_1 = 8 \text{ kg}$,$Q_2 = 12 \text{ kg}$ $\%\Delta Q_d = \frac{12 - 8}{(8 + 12)/2} = \frac{4}{10} = 0.4$ $\%\Delta Y = \frac{4,000 - 2,500}{(2,500 + 4,000)/2} = \frac{1,500}{3,250} = \frac{6}{13} \approx 0.4615$ Step 2: Calculate the income elasticity of demand. YED_{Nurse} = \frac{0.4}{6/13} = \frac{0.4 \times 13}{6} = \frac{5.2}{6} = \frac{13{15} \approx 0.87}

b)

• (i) Engineer: Since the income elasticity of demand is negative ($-0.8$), wheat is an inferior good to the Engineer.
• (ii) Nurse: Since the income elasticity of demand is positive ($0.87$) and less than 1, wheat is a normal good (specifically, a necessity) to the Nurse.

c)

• (i) Engineer: Wheat is an inferior good to the Engineer because as the Engineer's income increased, the quantity of wheat demanded decreased. Consumers typically reduce their consumption of inferior goods when their income rises, opting for higher-quality alternatives.
• (ii) Nurse: Wheat is a normal good to the Nurse because as the Nurse's income increased, the quantity of wheat demanded also increased. Consumers typically increase their consumption of normal goods as their income rises.

d)

• (i) Engineer: Step 1: Calculate the average tax rate for old and new incomes. 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:$$5,000 \times 0.10 = $500$. Average tax rate:$\frac{$500}{$5,000} \times 100% = 10%$. Step 2: Identify the system of taxation. As the Engineer's income increased from$$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.

• (ii) Nurse: Step 1: Calculate the average tax rate for old and new incomes. 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:$$4,000 \times 0.10 = $400$. Average tax rate:$\frac{$400}{$4,000} \times 100% = 10%$. Step 2: Identify the system of taxation. As the Nurse's income increased from$$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.

That's 2 down. 3 left today — send the next one.