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The question asks which of the following statements about a linear demand curve are correct:

1. **Statement I**: "The price elasticity of demand always changes along the line."
   - This statement is **correct**. For a linear demand curve, price elasticity varies along the curve. It is elastic at higher prices and inelastic at lower prices because the percentage change in quantity demanded varies at different price levels.

2. **Statement II**: "Every linear demand curve has a price elastic portion and a price inelastic portion."
   - This statement is also **correct**. A linear demand curve indeed has both elastic and inelastic regions. At the upper portion of the demand curve (high prices, low quantities), demand tends to be elastic, while at the lower portion (low prices, high quantities), demand tends to be inelastic.

3. **Statement III**: "A downward sloping demand curve is price inelastic when it is steep enough."
   - This statement is **also correct**. A steep demand curve indicates that quantity demanded is relatively unresponsive to changes in price, which corresponds to price inelasticity.

### Correct answer:
**e. More than one of the above statements are correct.**  
Both Statements I and II are definitely correct, and III can be considered correct when referring to a steep demand curve.

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### Related questions:
1. How do we calculate the price elasticity of demand?
2. What factors influence the elasticity of demand in different markets?
3. Can the entire demand curve ever be price inelastic?
4. How does a steep versus a flat demand curve affect market pricing strategies?
5. What role does elasticity play in consumer behavior?

#### Tip:
Remember that in a perfectly elastic demand curve, a small change in price leads to an infinite change in quantity demanded, while in a perfectly inelastic curve, the quantity demanded does not change regardless of the price.

Consider a linear demand curve. Which of the following statements are correct?
I. The price elasticity of demand always changes along the line.
II. Every linear demand curve has a price elastic portion and a price inelastic portion.
III. A downward sloping demand curve is price inelastic when it is steep enough.

Explore how elasticity changes along a linear demand curve and learn about the distinction between elastic and inelastic portions. This problem covers key economic concepts related to demand curves and elasticity theory, suitable for undergraduate economics students.

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