Price Elasticity of Demand at P=3 and P=5

Definition of Price Elasticity of Demand
Price elasticity of demand is a measure that shows how sensitive the quantity demanded of a good is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Formula for Price Elasticity of Demand
The formula for price elasticity of demand is:

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

Calculation of Price Elasticity of Demand at P=3
At p=3, the demand function is:

Q = 75 - 5(3) = 60

Now, let's assume that the price changes from p=3 to p=2.5. The percentage change in price is:

% Change in Price = [(2.5 - 3) / 3] x 100% = -16.67%

The corresponding change in quantity demanded is:

Q1 = 75 - 5(2.5) = 62.5

% Change in Quantity Demanded = [(62.5 - 60) / 60] x 100% = 4.17%

Therefore, the price elasticity of demand at p=3 is:

Price Elasticity of Demand = 4.17% / -16.67% = -0.25

Calculation of Price Elasticity of Demand at P=5
At p=5, the demand function is:

Q = 75 - 5(5) = 50

Now, let's assume that the price changes from p=5 to p=6. The percentage change in price is:

% Change in Price = [(6 - 5) / 5] x 100% = 20%

The corresponding change in quantity demanded is:

Q2 = 75 - 5(6) = 45

% Change in Quantity Demanded = [(45 - 50) / 50] x 100% = -10%

Therefore, the price elasticity of demand at p=5 is:

Price Elasticity of Demand = -10% / 20% = -0.5

Explanation of Results
Both price elasticity of demand calculations are negative, which indicates that the demand for the good is price inelastic. This means that a change in price will result in a relatively small change in the quantity demanded.

The price elasticity of demand at p=5 is higher than the price elasticity of demand at p=3. This suggests that the demand for the good is more elastic at higher prices than at lower prices.