Reason Why all Giffen Goods are Inferior whereas not all Inferior Goods are Giffen.
Inferior goods are the goods whose demand falls as income of the consumer increases. On the other hand 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 of a good does not hold in giffen good cases.
When the price of a good changes the effect on the quantity demanded would be accumulative result of aforementioned effects. Substitution effect says, a person would substitute consumption in favor of good which has become cheaper. Therefore, 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.
An inferior good is the one whose income effect is positive and hence 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. For a good to be a giffen good, the positive income effect should outweigh negative substitution effect to actually violate law of demand. Hence that is the reason we refer to all giffen goods as inferior good but not all inferior goods are giffen.
Tejvan Pettinger ;<https://www.economicshelp.org/blog/1189/economics/giffen-good/ > October 10, 2019.
why not with diagrams