Suppose that the demand function for widgets is  . The (own) price elasticity of demand for widgets when their price is    per widget is

To find the own price elasticity of demand for widgets, we need the demand function itself and the specific price at which we are calculating the elasticity. However, since the actual demand function and the specific price are not provided in your question, I can give you the general steps to calculate the price elasticity of demand.

1. Break Down the Problem

• Identify the demand function, which is typically expressed as $Q_d = f(P)$, where $Q_d$ is the quantity demanded and $P$ is the price.
• Determine the point at which the elasticity should be calculated (the specific price).

2. Relevant Concepts

• The price elasticity of demand (PED) is defined as: $\text{PED} = \frac{\partial Q_d}{\partial P} \times \frac{P}{Q_d}$ where:
  • $\frac{\partial Q_d}{\partial P}$ is the slope of the demand curve (the change in quantity demanded with respect to a change in price).
  • $P$ is the price at which we are calculating elasticity.
  • $Q_d$ is the quantity demanded at that price.

3. Analysis and Detail

• Substitute the specific values into the formula after calculating the derivative of the demand function.
• It's crucial to find the specific quantity demanded $Q_d$ when $P$ is at the given price.

4. Verify and Summarize

• After getting the elasticity value, interpret it:
  • If $|\text{PED}| > 1$, demand is elastic.
  • If $|\text{PED}| < 1$, demand is inelastic.
  • If $|\text{PED}| = 1$, demand is unitary elastic.

Final Answer

Once you provide the demand function and price, I can help you calculate the own price elasticity of demand at that specific point.