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hi there! i need help with the slutsky equation. in the picture below it asks how much do we have to adjust income to keep (x1,x2) just affordable? what do they mean by this? is this the vertical distance between the orginal budget line and the pivoted?
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Whenever the price of a good change two effects happen, one being that the rate at which one can exchange one good for another change, and second is that the total purchasing power of one’s income changes. The first one is called, the substitution effect and the second one is called the income effect. To study the substitution effect, we let the relative prices to change and adjust money income so as to hold purchasing power constant.

Meaning of the statement that the income has been adjusted to keep the original bundle (X1,X2) just affordable means that, the income has been adjusted to ensure that the purchasing power of the consumer is constant. However, being just affordable means that while the consumer can still afford the original bundle, the bundle no longer is optimal as the pivoted budget line intersects the original indifference curve.

Diagrammatically, this is reflected by the budget line pivoting around the original choice. Keeping purchasing power constant is not the vertical distance between the original and pivoted budget lines.

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