Question

The demand function for a given product is D(p) = 600 – p. What is the elasticity at the price p = 100?

Answer 1

The elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this case, the elasticity at p = 100 is 500, indicating that the demand is elastic at this price.

Step-by-step explanation:

The elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this case, the demand function is given as D(p) = 600 - p, where p represents the price. To find the elasticity at p = 100, we need to find the percentage change in quantity when the price changes from p = 100 to p = 99 and from p = 100 to p = 101.

Using the demand function, we can find the quantity demanded at p = 100 as follows: D(100) = 600 - 100 = 500. Now, to find the percentage change in quantity when price changes from p = 100 to p = 99, we calculate: ((D(99) - D(100)) / D(100)) * 100 = ((600 - 99) - (600 - 100)) / (600 - 100) * 100 = 1 / 500 * 100 = 0.2%.

To find the percentage change in quantity when price changes from p = 100 to p = 101, we calculate: ((D(101) - D(100)) / D(100)) * 100 = ((600 - 101) - (600 - 100)) / (600 - 100) * 100 = -1 / 500 * 100 = -0.2%.

Now, we can calculate the elasticity as the absolute value of the percentage change in quantity divided by the percentage change in price: (|0.2%| / 0.2% ) * (100 / 1) = 1 * 500 = 500.

The elasticity at p = 100 is 500. Since the absolute value of elasticity is greater than 1, we can conclude that the demand is elastic at this price.

Answer 2

The elasticity of demand measures how responsive the quantity demanded is to changes in price. For the given demand function, the elasticity is calculated as the percentage change in quantity divided by the percentage change in price. At a price of p = 100, the elasticity of demand is -18.18.

Step-by-step explanation:

The elasticity of demand measures how responsive the quantity demanded of a product is to changes in its price. It is calculated as the percentage change in quantity divided by the percentage change in price. In this case, the demand function is D(p) = 600 - p, where p is the price.

To calculate the elasticity at a specific price, you need to find the percentage change in quantity. Here, the price is p = 100, so the quantity demanded is D(100) = 600 - 100 = 500.

Next, calculate the percentage change in quantity:

% change in quantity = (new quantity - old quantity) / ((new quantity + old quantity) / 2) x 100

% change in quantity = (500 - 600) / ((500 + 600) / 2) x 100

% change in quantity = -18.18%

Finally, divide the percentage change in quantity by the percentage change in price:

Elasticity = (% change in quantity) / (% change in price)

Elasticity = -18.18% / 1% = -18.18

Therefore, at a price of p = 100, the elasticity of demand is -18.18.