All Inferior goods are Giffen goods.
Inferior goods are the goods whose demand decreases upon income increase of the consumer. Whereas, giffen goods are the goods whose demand falls as the price of goods falls and increases as the price of the good increases. This means the law of demand is violated in the case of giffen goods.
Substitution effect- a person would substitute or opt for consumption in favor of goods which have become cheaper. As a result, substitution effect is always negative.
Income effect describes the change in purchasing power of a consumer due to price change and it can be positive or negative.
In the case of a giffen good, the positive income effect should outweigh negative substitution effect to violate law of demand.
For an inferior good, income effect is positive. Increase in purchasing power caused by fall in price would reduce the consumption of that good but the law of demand still holds due to the substitution effect outweighing income effect.
This is the reason why we refer to all giffen goods as inferior but not inferior goods are giffen.
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