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Prove this instatement in economics: Ernst Engel, a German economist, discovered that, statistically, as income increases...

Prove this instatement in economics:

Ernst Engel, a German economist, discovered that, statistically, as income increases in a society, the proportion spent on food falls. This is called the Engel’s Law. Show in theory, if food is a necessity good, the Engel’s Law always holds.

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It can be mentioned that if food is a necessity good then what happens is that at a particular level of income you get to consume food according to your need and if the income increases, still the amount of necessity e goods that is fold would more or less remain the same because a person would have the same appetite as earlier even if the income increases as a result of which the money spent on other goods increase and this tells us that even if the income increases you get to spend more on luxury goods rather than necessity is because even if the income is less you would definitely spend on necessities and in this regard according to Engels Law if food is a necessity then you would spend less proportionately with increase in the income

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