Introduction:
In economics, inferior goods refer to those products for which demand decreases as consumer income increases. This is in contrast to normal goods, for which demand increases as income rises. Turnips, a root vegetable commonly used in cooking, can be considered an example of an inferior good. To determine the income elasticity of demand for turnips, we need to understand whether it falls between 0 and 1, is positive but could be greater than or less than or equal to 1, is negative, or is definitely greater than 1.

Income Elasticity of Demand:
Income elasticity of demand measures the responsiveness of demand for a product to changes in consumer income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.

Inferior Goods:
Inferior goods are those for which demand decreases as consumer income rises. This can be attributed to several factors, such as an increase in consumer preferences for higher-quality substitutes or a shift towards more luxury goods as income increases. Turnips, being an inferior good, are typically associated with lower-income households who may switch to other vegetables or food options when their income rises.

Income Elasticity Range:
The income elasticity of demand for inferior goods falls within a specific range. Let's explore the possibilities:

- Between 0 and 1: If the income elasticity of demand for turnips is between 0 and 1, it indicates that turnips are a necessity for some consumers, but their demand is not highly responsive to changes in income. In this case, as income increases, the demand for turnips may decrease, but not significantly.

- Positive but could be greater than or less than or equal to 1: A positive income elasticity suggests that turnips are indeed an inferior good, as their demand decreases with increasing income. The exact value of the elasticity could be greater than 1, indicating a relatively higher responsiveness, or less than or equal to 1, indicating a moderate responsiveness.

- Negative: A negative income elasticity of demand would imply that turnips are not inferior goods but rather normal goods. However, this contradicts the definition and understanding of turnips as inferior goods.

- Definitely greater than 1: A value of income elasticity greater than 1 would imply that turnips are not inferior goods but rather luxury goods. This is highly unlikely, considering the nature and perception of turnips as a lower-cost vegetable option.

Conclusion:
Based on the definition and characteristics of inferior goods, it can be concluded that the income elasticity of demand for turnips is positive but could be greater than or less than or equal to 1. As consumer income increases, the demand for turnips is expected to decrease, although the exact responsiveness may vary.