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 the formula:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

First, let's find the initial quantity demanded when p1 = 10, p2 = 5, and I = 1000.

Q1 = 26 - 35p1 + 2p2 + 0.01I
Q1 = 26 - 35(10) + 2(5) + 0.01(1000)
Q1 = 26 - 350 + 10 + 10
Q1 = -304

Now, let's find the final quantity demanded when p1 increases by 1%.

Q1' = 26 - 35(p1 + 0.01) + 2p2 + 0.01I
Q1' = 26 - 35(10.01) + 2(5) + 0.01(1000)
Q1' = 26 - 350.35 + 10 + 10
Q1' = -304.35

Now, let's find the percentage change in quantity demanded.

% Change in Quantity Demanded = (Q1' - Q1) / Q1 * 100
% Change in Quantity Demanded = (-304.35 - (-304)) / (-304) * 100
% Change in Quantity Demanded = 0.35 / (-304) * 100
% Change in Quantity Demanded ≈ -0.115%

Now, let's find the percentage change in price.

% Change in Price = (p1' - p1) / p1 * 100
% Change in Price = (10.01 - 10) / 10 * 100
% Change in Price = 0.01 / 10 * 100
% Change in Price = 0.1%

Now, let's calculate the price elasticity of demand.

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
Elasticity = (-0.115%) / (0.1%)
Elasticity = -0.115

Since the price elasticity of demand is negative, demand for good 1 is elastic. This means that a small increase in price will lead to a relatively larger decrease in quantity demanded.