1. **Problem Statement:** We are given a 5% decrease in the price of chocolate sauce, which causes a 10% increase in the quantity demanded of chocolate sauce and a 15% increase in the quantity demanded of ice cream. We need to calculate: a. The price elasticity of demand for chocolate sauce. b. The cross elasticity of demand for ice cream with respect to the price of chocolate sauce and determine if they are substitutes or complements. 2. **Formulas and Important Rules:** - Price elasticity of demand (PED) is calculated as: $$\text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}$$ - Cross elasticity of demand (XED) is calculated as: $$\text{XED} = \frac{\% \text{ change in quantity demanded of good B}}{\% \text{ change in price of good A}}$$ - Interpretation of XED: - If XED > 0, goods are substitutes. - If XED < 0, goods are complements. 3. **Calculations:** a. Price elasticity of demand for chocolate sauce: $$\text{PED} = \frac{10\%}{-5\%} = \frac{10}{-5} = -2$$ The negative sign indicates the usual inverse relationship between price and quantity demanded. b. Cross elasticity of demand for ice cream with respect to the price of chocolate sauce: $$\text{XED} = \frac{15\%}{-5\%} = \frac{15}{-5} = -3$$ Since XED is negative, ice cream and chocolate sauce are complements. 4. **Final Answers:** - Price elasticity of demand for chocolate sauce is $-2$. - Cross elasticity of demand for ice cream with respect to the price of chocolate sauce is $-3$, indicating they are complements.