$Q = 100 - 5P$
What will be the point price elasticity of demand at price ₹ 10 ?
Calculating Point Price Elasticity of Demand
The question asks for the point price elasticity of demand at a specific price point using the given demand function.
Demand Function and Elasticity Formula
The demand function is given as: $Q = 100 - 5P$
The formula for point price elasticity of demand ($E_{pd}$) is:
$E_{pd} = \frac{dQ}{dP} \times \frac{P}{Q}$Step 1: Find the derivative of Quantity (Q) with respect to Price (P)
First, we find the derivative $\frac{dQ}{dP}$ from the demand function:
$ \frac{dQ}{dP} = \frac{d}{dP}(100 - 5P) = -5 $The derivative represents the rate of change of quantity demanded with respect to price.
Step 2: Calculate Quantity (Q) at the given Price (P)
The given price is $P = ₹ 10$. Substitute this into the demand function to find the corresponding quantity $Q$:
$ Q = 100 - 5(10) $ $ Q = 100 - 50 $ $ Q = 50 $Step 3: Calculate the Point Price Elasticity of Demand
Now, substitute the values of $\frac{dQ}{dP}$, $P$, and $Q$ into the elasticity formula:
$ E_{pd} = \left( -5 \right) \times \left( \frac{10}{50} \right) $ $ E_{pd} = -5 \times \frac{1}{5} $ $ E_{pd} = -1 $The point price elasticity of demand is -1. Economists often refer to elasticity in absolute terms. The absolute value is $|E_{pd}| = |-1| = 1$. This indicates unit elasticity at the price of ₹10.
Important Questions from Demand analysis
- If the gross elasticity of demand is negative, the two products in consideration are __________ products.
- For a linear demand curve, which of the following is true ?
In the above diagram, if curve IC represents income - consumption curve, then it means that :
- A consumer spends ₹ 240 when the price of the commodity is ₹ 15 and ₹ 300 when the price rises to ₹ 20. The elasticity of demand is :
Which one of the following demands states consumers are adequately buying all the products put into the marketplace?
