Answer to Question #237222 in Macroeconomics for Calista

Question

Distinguish between income elasticity of demand and cross price elasticity of demand. Include in answer a provision of their formula.

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Answer 1

Difference between Income Elasticity of demand and Cross Price Elasticity of Demand.

Elasticity is defined as the reaction of the demand for a certain product after a given alteration in the price of an item.

Elasticity in the income of demand refers to the relative modification in demand of one good or either a service which occurs in reaction to a modification of the income of a consumer while Cross price elasticity of demand refers to the relative modification in demand of one good or service due to alteration in the price of another good or service.

Income elasticity of demand can be used to determine the difference between goods. For example, it can be used to differentiate a normal good from an inferior good. Normal goods have a positive elasticity, their demand increases with an increase in consumers’ income like organic food. On the other hand, an inferior good has a negative elasticity, their demand falls with an increase in consumers’ income like clothes out of fashion while Cross price elasticity determines the relationship between two goods, it shows whether the two are substitutes or complements. Substitutes are goods that can be used in place of the other. They compete. An example includes coffee and tea. Complementary goods are goods which are used together and at the same time like a car and fuel.

Income elasticity can be calculated as the percentage alteration of demanded quantity of a certain product over the percentage modification of the income of the consumer while Cross price elasticity can be determined by the change in percentage of the price of demanded quantity of product X over the percentage alteration in the price of a quantity Y

FORMULAS

Income Elasticity of Demand is calculated as follows;

$=\frac {\text{Percentage Change in Quantity demanded} }{ \text{Percentage Change in consumer income} }$

Cross Price Elasticity of demand is calculated as shown below;

Cross Elasticity Demand Formula

$\begin{aligned} &E_{xy} = \frac {\text{Percentage Change in Quantity of X} }{ \text{Percentage Change in Price of Y} } \\ &\phantom{ E_{xy} } = \frac { \frac { \displaystyle \Delta Q_x }{ \displaystyle Q_x } }{ \frac { \displaystyle \Delta P_y }{ \displaystyle P_y } } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ Q_x } \times \frac {P_y }{ \Delta P_y } \\ &\phantom{ E_{xy} } = \frac {\Delta Q_x }{ \Delta P_y } \times \frac {P_y }{ Q_x } \\ &\textbf{where:} \\ &Q_x = \text{Quantity of good X} \\ &P_y = \text{Price of good Y} \\ &\Delta = \text{Change} \\ \end{aligned}$