To calculate the price elasticity of demand, we can use the following formula:
E = (%ΔQ1 / %Δp1)
Where E is the price elasticity of demand, %ΔQ1 is the percentage change in quantity demanded of good 1, and %Δp1 is the percentage change in the price of good 1.
To calculate the percentage change in quantity demanded (%ΔQ1), we need to know the initial quantity demanded and the new quantity demanded. However, these values are not given in the question. Without this information, we cannot calculate the price elasticity of demand.
Therefore, we cannot determine whether the demand for good 1 is elastic or inelastic based on the given information.
Given 𝑄1 = 26 − 35𝑝1 + 2𝑝2 + 0.01𝐼 , where 𝑝1 is the price of good 1, 𝑝2 is the price of good 2, and 𝐼 is income
a. Calculate the price elasticity of demand when
𝑝1 = 10, 𝑝2 = 5, 𝐼 = 1000. Is demand for good 1 elastic or inelastic?
Explain.
2 answers
Apologies for the confusion caused earlier in my response. It seems there was a misunderstanding regarding the interpretation of the equation and calculation of quantity.
Given the equation 𝑄1 = 26 − 35𝑝1 + 2𝑝2 + 0.01𝐼, we can interpret it as a demand function for good 1, where 𝑝1 represents the price of good 1, 𝑝2 is the price of good 2, and 𝐼 is income.
To calculate the price elasticity of demand, we need to take the derivative of 𝑄1 with respect to 𝑝1 and then multiply it by 𝑝1/Q1 (the ratio of the price of good 1 to the quantity demanded of good 1). This will give us the price elasticity of demand for good 1.
Taking the derivative of 𝑄1 with respect to 𝑝1, we get:
d𝑄1/d𝑝1 = -35
Now, to calculate the price elasticity of demand, 𝐸, we need to multiply d𝑄1/d𝑝1 by 𝑝1/Q1, where 𝑝1 = 10 and 𝑝2 = 5. However, we do not have the values for 𝑞1 (quantity demanded of good 1) and 𝑄1 (initial quantity demanded of good 1) given in the question, so we cannot calculate 𝐸.
Unfortunately, without the necessary information, we cannot determine the price elasticity of demand or whether the demand for good 1 is elastic or inelastic.
Given the equation 𝑄1 = 26 − 35𝑝1 + 2𝑝2 + 0.01𝐼, we can interpret it as a demand function for good 1, where 𝑝1 represents the price of good 1, 𝑝2 is the price of good 2, and 𝐼 is income.
To calculate the price elasticity of demand, we need to take the derivative of 𝑄1 with respect to 𝑝1 and then multiply it by 𝑝1/Q1 (the ratio of the price of good 1 to the quantity demanded of good 1). This will give us the price elasticity of demand for good 1.
Taking the derivative of 𝑄1 with respect to 𝑝1, we get:
d𝑄1/d𝑝1 = -35
Now, to calculate the price elasticity of demand, 𝐸, we need to multiply d𝑄1/d𝑝1 by 𝑝1/Q1, where 𝑝1 = 10 and 𝑝2 = 5. However, we do not have the values for 𝑞1 (quantity demanded of good 1) and 𝑄1 (initial quantity demanded of good 1) given in the question, so we cannot calculate 𝐸.
Unfortunately, without the necessary information, we cannot determine the price elasticity of demand or whether the demand for good 1 is elastic or inelastic.
1 answer