Sir Rober Giffen has given this paradox. According to him, in the early 19th Century in Ireland, the people were poor and there were two food items available, potatoes and meat. Potatoes were cheaper in price than meat. Earlier, people behaved just like the Law of Demand since potatoes were cheap and higher became the demand for them. Meat being costly meant its demand decreased considerably in the market. In this way, the Law of Demand played a crucial role for this transaction.
After a few weeks, the potatoes became even cheaper in price which further increased their demand which meant, people started to save their money significantly. These savings were then utilized to purchase some meat which earlier was not possible. In this manner, people started to contradict the Law of Demand in terms of purchasing potatoes and meat.
The above behavior of the population meant that, over a period of time, even though there was a decrease in price for potatoes, there was contraction/fall in its demand and simultaneously it occurred that, there was an expansion in demand for meat and that’s how this situation became a paradox.