Question

which of the following is true?
a. income elasticity is positive for normal goods where the quantity demanded rises as income rises.
b. income elasticity is negative for inferior goods where the quantity demanded falls as income rises.
c. income elasticity is negative for inferior goods where the quantity demanded rises as income falls.
d. income elasticity is positive for normal goods where the quantity demanded falls as income falls.
e. all of the above.

if the income elasticity of demand for hot dogs is (-0.75), hot dogs are (\boxed{\text{an inferior}}) good and if the income elasticity of demand for lobster is (2.00), lobster is (\boxed{\text{a normal}}) good.

Explanation:

Part 1: Multiple - Choice Question (Income Elasticity)

1. Recall the concept of income elasticity of demand:

• For normal goods, income elasticity of demand (\(E_I\)) is positive (\(E_I>0\)) because as income rises, the quantity demanded of normal goods rises, and as income falls, the quantity demanded of normal goods falls.
• For inferior goods, income elasticity of demand (\(E_I\)) is negative (\(E_I < 0\)) because as income rises, the quantity demanded of inferior goods falls, and as income falls, the quantity demanded of inferior goods rises.

1. Analyze each option:

• Option A: Says income elasticity is positive for normal goods where quantity demanded rises as income rises. This is correct for normal goods.
• Option B: Says income elasticity is negative for inferior goods where quantity demanded falls as income rises. This is correct for inferior goods (since for inferior goods, when income rises, quantity demanded falls, and \(E_I=\frac{\%\Delta Q}{\%\Delta I}\), so if \(\%\Delta Q\) is negative and \(\%\Delta I\) is positive, \(E_I\) is negative).
• Option C: Says income elasticity is negative for inferior goods where quantity demanded rises as income falls. If income falls (\(\%\Delta I\) is negative) and quantity demanded of inferior goods rises (\(\%\Delta Q\) is positive), then \(E_I=\frac{\%\Delta Q}{\%\Delta I}=\frac{positive}{negative}=negative\), which is correct for inferior goods.
• Option D: Says income elasticity is positive for normal goods where quantity demanded falls as income falls. If income falls (\(\%\Delta I\) is negative) and quantity demanded of normal goods falls (\(\%\Delta Q\) is negative), then \(E_I=\frac{\%\Delta Q}{\%\Delta I}=\frac{negative}{negative}=positive\), which is correct for normal goods.
• Since options A, B, C, and D are all correct, Option E (All of the above) is the right choice.

The income elasticity of demand for hot dogs is - 0.75. Since the income elasticity of demand is negative (\(-0.75<0\)), according to the definition of inferior goods (income elasticity of demand is negative), hot dogs are inferior goods.

The income elasticity of demand for lobster is 2.00. Since the income elasticity of demand is positive (\(2.00 > 0\)), according to the definition of normal goods (income elasticity of demand is positive), lobster is a normal good.

Answer:

E. All of the above.

Part 2: Hot - Dog Good Type (Income Elasticity = - 0.75)