Demand, Supply and Elasticity: Question 5

Worked solution

Part (a): Income elasticity of demand for oak dining tables

Percentage change in average household income, using the original income of $40,000 as the base: $\%\Delta \text{income} = \frac{46{,}000-40{,}000}{40{,}000}\times100 = +15\%$

Percentage change in quantity demanded of oak dining tables, using the original quantity of 500 as the base: $\%\Delta Q_d = \frac{620-500}{500}\times100 = +24\%$

$YED = \frac{\%\Delta Q_d}{\%\Delta \text{income}} = \frac{24}{15} = +1.6$

The sign of YED is positive, so oak dining tables are a normal good: quantity demanded rises as income rises. The size of YED is $1.6$, which is greater than 1, so demand is income elastic, oak dining tables behave as a luxury good, with sales rising proportionately faster than income.

Part (b): Cross elasticity of demand between tables and chairs

Percentage change in the price of oak dining tables, using the original price of $800 as the base: $\%\Delta P_{\text{tables}} = \frac{680-800}{800}\times100 = -15\%$

Percentage change in quantity demanded of oak dining chairs, using the original quantity of 1,800 as the base: $\%\Delta Q_{d,\text{chairs}} = \frac{2{,}070-1{,}800}{1{,}800}\times100 = +15\%$

$XED = \frac{\%\Delta Q_{d,\text{chairs}}}{\%\Delta P_{\text{tables}}} = \frac{15}{-15} = -1.0$

The sign of XED is negative: as the price of tables fell, the quantity of chairs demanded rose, the two move in opposite directions. A negative cross elasticity means oak dining tables and oak dining chairs are complements, consistent with the idea that customers often buy a matching table and chairs together.

Part (c): Implications for the retailer’s business decisions

(i) Income elasticity of demand. Because demand for oak dining tables is income elastic ($YED=+1.6$), sales are highly sensitive to the state of the economy: they should rise disproportionately fast during an economic upswing (as seen here), but they could equally fall sharply if household incomes fall in a downturn. This is an important warning for the retailer: it should be cautious about permanently expanding production capacity or hiring extra artisans purely on the basis of a temporary boom in incomes, since demand for this luxury item could weaken quickly if economic conditions turn. The retailer might instead focus marketing efforts on higher-income households, whose spending on such a luxury good is less likely to be as strongly affected by a downturn.

(ii) Cross elasticity of demand. Because oak dining tables and oak dining chairs are strong complements ($XED=-1.0$), a change in the price of one product has a sizeable knock-on effect on demand for the other. This means the retailer’s pricing decisions on tables should not be made in isolation: cutting the price of tables (even at a lower margin per table) could significantly boost sales, and profit, on chairs sold alongside them. The retailer could exploit this by offering a bundled discount on a table-and-chairs set, using the table as a way to draw in customers who then also buy the complementary chairs.

Final answers

• (a) $YED = +1.6$. Oak dining tables are a normal, income-elastic (luxury) good
• (b) $XED = -1.0$. Oak dining tables and oak dining chairs are complements
• (c) (i) Sales of this luxury good are highly sensitive to the economic cycle, so capacity expansion should not be based on a temporary income boom; (ii) tables and chairs should be priced and marketed together (e.g. a bundled discount), since a price cut on tables strongly boosts demand for chairs