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

Question

a. Calculate the price elasticity of demand when
𝑝1 = 10, 𝑝2 = 5, 𝐼 = 1000. Is demand for good 1 elastic or inelastic?
Explain.

Answer 1

To calculate the price elasticity of demand, we need to use the following formula:

E = (%ΔQ / %ΔP)

Where E is the price elasticity of demand, %ΔQ is the percentage change in quantity demanded, and %ΔP is the percentage change in price.

In this case, we are 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. We are asked to calculate the price elasticity of demand when 𝑝1 = 10, 𝑝2 = 5, 𝐼 = 1000 for good 1.

To calculate the percentage change in quantity demanded, we need to find the difference between the original quantity demanded and the new quantity demanded, and then divide it by the original quantity demanded:

%ΔQ = (Qnew - Qoriginal) / Qoriginal

To calculate the percentage change in price, we need to find the difference between the new price and the original price, and then divide it by the original price:

%ΔP = (Pnew - Poriginal) / Poriginal

Now let's calculate %ΔQ and %ΔP:

%ΔQ = (Qnew - Qoriginal) / Qoriginal
%ΔQ = ((26 - 35 * 10 + 2 * 5 + 0.01 * 1000) - (26 - 35 * 10 + 2 * 5 + 0.01 * 1000)) / (26 - 35 * 10 + 2 * 5 + 0.01 * 1000)
%ΔQ = 0 / (26 - 35 * 10 + 2 * 5 + 0.01 * 1000)
%ΔQ = 0

%ΔP = (Pnew - Poriginal) / Poriginal
%ΔP = ((10 - 10) / 10)
%ΔP = 0

Now let's plug in the values into the price elasticity of demand formula:

E = (%ΔQ / %ΔP)
E = (0 / 0)

As we can see, the numerator is 0 and the denominator is also 0. This indicates that the price elasticity of demand is undefined. Therefore, we cannot determine whether the demand for good 1 is elastic or inelastic based on the given information.