Question

For each of the following scenarios, begin by assuming that all demand factors are set to their original values and Big Winner is charging $300 per room per night.

If average household income increases by 20%, from $50,000 to $60,000 per year, the quantity of rooms demanded at the Big Winner (falls OR rises) from (..........) rooms per night to (.........) rooms per night. Therefore, the income elasticity of demand is ( positive OR negative ) , meaning that hotel rooms at the Big Winner are ( an inferior good OR an normal good)  

If the price of an airline ticket from SFO to LAS were to increase by 10%, from $200 to $220 roundtrip, while all other demand factors remain at their initial values, the quantity of rooms demanded at the Big Winner (falls OR rises)   from (..........) rooms per night to (.........) rooms per night. Because the cross-price elasticity of demand is ( positive OR negative ) , hotel rooms at the Big Winner and airline trips between SFO and LAS are ( substitutes OR complement ).

Big Winner is debating decreasing the price of its rooms to $275 per night. Under the initial demand conditions, you can see that this would cause its total revenue to ( decrease OR increase ) Decreasing the price will always have this effect on revenue when Big Winner is operating on the ( elastic OR inelastic ).

Answer 1

There is a direct relationship between income and demand. As income increases the quantity demanded increases and vice versa.

If the average household income increases by \(20 \%\), the quantity of rooms demanded rises from 200 rooms per night to 250 rooms per night.

Calculate the income elasticity of demand:

Income Elasticity of demand \(=\frac{\% \text { change in quantity demanded or purchased }}{\% \text { change in income }}\)

$$ \begin{aligned} E_{d} &=\frac{\frac{Q_{2}-Q_{1}}{Q_{1}}}{\frac{I_{2}-I_{1}}{I_{1}}} \\ &=\frac{250-200}{200} \times \frac{50,000}{60,000-50,000} \\ &=\frac{50}{200} \times \frac{50,000}{10,000} \\ &=0.25 \times 5 \\ &=1.25 \end{aligned} $$

Therefore, the income elasticity of demand is positive; hence the hotel rooms at the Big winner are normal goods.

There is an indirect relationship between price and demand. As price increases the quantity demanded decreases and vice versa.

If the price of an airline ticket increases by \(10 \%\) the quantity of rooms demanded falls from \(\mathbf{2 0 0}\) rooms per night to \(\mathbf{1 5 0}\) rooms per night.

Cross price elasticity \(=\frac{\% \text { change in quantity demanded }}{\% \text { change in price }}\)

$$ \begin{aligned} &=\frac{\frac{150-200}{200} \times 100}{10} \\ &=\frac{-25}{10} \\ &=-2.5 \end{aligned} $$

The cross-price elasticity of demand is negative; therefore, hotel rooms at the Big winner and airline trips are complements as they are used jointly.

If the price of the rooms is decreasing this would cause the total revenue to increase and the demand is elastic.