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Let's solve the problem step by step.

The demand function is given as:

\[
q = 100 - 5p
\]

### Part (a): Find \( \varepsilon \) when \( p = 15 \).

The price elasticity of demand, \( \varepsilon \), is given by:

\[
\varepsilon = \left( \frac{dq}{dp} \right) \cdot \frac{p}{q}
\]

First, we need to calculate \( \frac{dq}{dp} \), the derivative of the demand function with respect to price \( p \):

\[
\frac{dq}{dp} = -5
\]

Now, substitute \( p = 15 \) into the demand function to find \( q \):

\[
q = 100 - 5(15) = 100 - 75 = 25
\]

Now, using the formula for elasticity:

\[
\varepsilon = (-5) \cdot \frac{15}{25}
\]

Simplify:

\[
\varepsilon = -5 \cdot 0.6 = -3
\]

So, \( \varepsilon = -3 \).

### Part (b): Is the demand elastic, inelastic, or unit elastic?

The rule for elasticity is:
- If \( |\varepsilon| > 1 \), demand is **elastic**.
- If \( |\varepsilon| = 1 \), demand is **unit elastic**.
- If \( |\varepsilon| < 1 \), demand is **inelastic**.

Since \( |\varepsilon| = 3 \), which is greater than 1, the demand is **elastic**.

---

Would you like more details on any part? Here are some related questions you might want to explore:

1. What does it mean when demand is elastic?
2. How would the elasticity change if \( p \) were increased or decreased?
3. What factors can affect the elasticity of demand for a commodity?
4. How does elasticity affect pricing decisions for businesses?
5. Can a product ever shift from being elastic to inelastic? If so, how?

**Tip:** Price elasticity gives insight into how sensitive consumers are to price changes, and can influence decisions on whether to raise or lower prices.

For a particular commodity, the demand function is q = 100 - 5p. a. Find ε when p = 15. b. Is demand elastic, inelastic, or unit elastic?

Learn how to calculate the price elasticity of demand for a commodity with the demand function q = 100 - 5p when p = 15. This problem uses the formula ε = (dq/dp) * (p/q) and provides a step-by-step solution for understanding whether the demand is elastic, inelastic, or unit elastic. Suitable for Grade 12 or college students.

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