You can spend your income on apples and oranges. Apples currently cost $0.25 and oranges cost $0.50. When your income is $40, you buy 10 apples and 8 oranges. When your income increases to $80, you buy 12 apples and 6 oranges

1. What type of good are apples (inferior, necessity, luxury)?

We need to calculate the income elasticity of apples. Let:

\[\frac{\%\Delta a}{\%\Delta m} = \displaystyle \cfrac{\left(\frac{a_2-a_1}{a_1}\right)}{\left(\frac{m_2-m_1}{m_1}\right)} = \cfrac{\left(\frac{12-10}{10}\right)}{\left(\frac{80-40}{40}\right)}=\cfrac{\left(\frac{2}{10}\right)}{\left(\frac{40}{40}\right)} = \frac{0.20}{1} = 0.20\]

Apples are a (normal) necessity. For every 1% increase (decrease) in income \((m)\), you will buy 0.20% more (fewer) apples \((a)\).

2. What type of good are oranges (inferior, necessity, or luxury)?

We need to calculate the income elasticity of oranges. Let:

\[\frac{\%\Delta o}{\%\Delta m} = \displaystyle \cfrac{\left(\frac{o_2-o_1}{o_1}\right)}{\left(\frac{m_2-m_1}{m_1}\right)} = \cfrac{\left(\frac{6-8}{8}\right)}{\left(\frac{80-40}{40}\right)}=\cfrac{\left(\frac{-2}{8}\right)}{\left(\frac{40}{40}\right)} = \frac{-0.25}{1} = -0.25\]

Oranges are inferior goods. For every 1% increase 9decrease) in income \((m)\), you will buy 0.25% fewer (more) oranges \((o)\).

You can can have cereal and milk for breakfast. When milk is $2/gallon, you consume 5 bowls of cereal per week. When milk increases to $4/gallon, you consume 4 bowls of cereal per week.

3. What is the relationship between these two goods?

These goods are complements, because there is an inverse relationship between the consumption of one good and the price of the other.

4. What is the cross-price elasticity?

We need to calculate the cross-price elasticity of these two goods. Let:

\[\frac{\%\Delta c}{\%\Delta p_m} = \displaystyle \cfrac{\left(\frac{c_2-c_1}{c_1}\right)}{\left(\frac{p_{m2}-p_{m1}}{p_{m1}}\right)} = \cfrac{\left(\frac{4-5}{5}\right)}{\left(\frac{4-2}{2}\right)}=\cfrac{\left(\frac{-1}{5}\right)}{\left(\frac{2}{2}\right)} = \frac{-0.20}{1} = -0.20\]

For every 1% increase (decrease) in the price of milk \((p_m)\), you buy 0.20% fewer (more) boxes of cereal \((c)\).