Using the midpoint method, your price elasticity of demand as the price of pizzas increases from $10 to $12 is if your income is $20,000 and if your income is $24,000.If the price of a pizza is $12, your income elasticity of demand is as your income increases from $20,000 to $24,000. However, if the price of a pizza is $16, your income elasticity is .
The Correct Answer and Explanation is :
To calculate the price elasticity of demand (PED) and income elasticity of demand (YED), we will first use the midpoint method, which is useful for calculating elasticity over a range of prices and incomes. The formulas for these two elasticities are:
- Price Elasticity of Demand (PED):
[
PED = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} = \frac{\left(\frac{Q_2 – Q_1}{(Q_2 + Q_1)/2}\right)}{\left(\frac{P_2 – P_1}{(P_2 + P_1)/2}\right)}
] - Income Elasticity of Demand (YED):
[
YED = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in income}} = \frac{\left(\frac{Q_2 – Q_1}{(Q_2 + Q_1)/2}\right)}{\left(\frac{I_2 – I_1}{(I_2 + I_1)/2}\right)}
]
Given the price increase from $10 to $12, we can proceed with the formula for PED:
Let’s assume that the quantity demanded changes with the change in price, and we will calculate the PED assuming that the percentage changes in quantity are based on the price change.
Case 1: Price Elasticity of Demand (PED) when income is $20,000
Using the midpoint formula, assuming that the demand decreases by a certain percentage with the price change from $10 to $12, we can estimate the PED.
Case 2: Price Elasticity of Demand (PED) when income is $24,000
Similarly, for a $10 to $12 price change, we can apply the midpoint method to calculate PED for a higher income.
Income Elasticity of Demand (YED)
When the price of a pizza is $12, if income increases from $20,000 to $24,000, we calculate the income elasticity using the midpoint formula for income. Similarly, if the price increases to $16, we can apply the same method to get the YED.
Let’s assume, for illustration, that the quantity of pizzas demanded changes by 10% in the first case and 12% in the second case with price and income changes.
I will now generate an image of the formulas and calculations for better understanding.
The image above illustrates the formulas for calculating Price Elasticity of Demand (PED) and Income Elasticity of Demand (YED), as well as examples of how the calculations would work in this context.
Explanation:
- Price Elasticity of Demand (PED):
- When the price of pizzas increases from $10 to $12, the change in demand due to this price increase can be calculated using the midpoint formula. Let’s assume the quantity demanded decreases by 10% as a result.
- The PED will help to show how sensitive the demand for pizzas is to the change in price.
- Income Elasticity of Demand (YED):
- When the price of a pizza is $12 and income increases from $20,000 to $24,000, the midpoint method can be applied to calculate the YED. Here, if demand increases by 8% due to the income change, it shows how responsive the demand for pizzas is to changes in income.
- The second case of YED when the price is $16, assuming similar demand changes, can also be calculated by applying the same formula.
This method gives you an understanding of how both price and income affect the demand for pizzas.