The correct answer is: A. $\frac{{{\text{Proportional change in the price of commodity X}}}}{{{\text{Proportional change in the demand of commodity Y}}}}}$
The cross elasticity of demand is a measure of how responsive the demand for one good is to a change in the price of another good. It is calculated as follows:
$$\text{Cross elasticity of demand} = \frac{{\text{Proportional change in the demand of commodity X}}}{{\text{Proportional change in the price of commodity Y}}}$$
A positive cross elasticity of demand indicates that the two goods are substitutes. This means that if the price of commodity X increases, the demand for commodity Y will increase. A negative cross elasticity of demand indicates that the two goods are complements. This means that if the price of commodity X increases, the demand for commodity Y will decrease.
The cross elasticity of demand is a useful tool for businesses to understand how their sales will be affected by changes in the prices of their competitors’ products. It can also be used to understand how changes in consumer preferences will affect the demand for different goods.
Here is a brief explanation of each option:
- Option A is the correct answer. It is the formula for calculating the cross elasticity of demand.
- Option B is incorrect. It is the formula for calculating the income elasticity of demand.
- Option C is incorrect. It is the formula for calculating the price elasticity of demand.
- Option D is incorrect. Only option A is correct.