Final answer:
The claim that an ordinary demand curve contains only income effects is false; it includes both substitution and income effects, while a compensated demand curve removes income effects entirely. The income elasticity of another good when one is an inferior good could be either positive or negative.
Step-by-step explanation:
The statement provided is False. An ordinary demand curve contains both the substitution and income effects, whereas a compensated demand curve, also known as a Hicksian demand curve, holds utility constant and contains only substitution effects. When a price changes, the substitution effect captures the change in consumption because relative prices have changed, while the income effect represents the change in consumption because the consumer's purchasing power has changed. The compensated demand curve removes the income effect to examine only the consumer's response to a change in relative price, assuming they are compensated to keep utility constant.
If one of the goods a consumer buys has a negative income elasticity of demand, meaning it is an inferior good, the amount consumed increases as income decreases. For the other good that the consumer buys, the income elasticity of demand could be positive, meaning it's a normal good, or it could also be negative, as consumers might allocate their resources differently among various inferior goods. However, typically, if one good is inferior, we might expect that the other is a normal good, though it's not a strict rule.