You find the tangent to the curve at the point of interest and then find the slope of the tangent.
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indifference curve analysis is not much in use because it only tells us that demand curve has a negative slope except when they don't ....
indifferent curves are convex to their origin, they do not intersect, and have a negative slope
The MRS measures how much of a good you are willing to give up in exchange for one more unit of the other good, keeping utility constant. The MRS diminishes along a convex indifference curve in that as you move down along the indifference curve, you are willing to give up less and less of the one good in exchange for the other. The MRS is also the slope of the indifference curve, which increases (becomes less negative) as you move down along the indifference curve. The MRS is constant along a linear indifference curve, since in this case the slope does not change. The consumer is always willing to trade the same number of units of one good in exchange for the other.
Indifference curve is a curve that shows consumption bundles that give the consumer the same level of satisfaction. Indifference map, on the other hand Indifference curve is a graph of two or more indifference curves.
Consumer equilibrium is the point where consumer attains highest level of satisfaction. There are two conditions of equilibrium under ordinal approach 1- Necessary Condition: 'Budget line is tangent to the highest possible indifference curve.' 2- Sufficient Condition: 'At equilibrium, Indifference curve must be convex to the origin' Thus, at equilibrium , Px/Py (absolute slope of Budget line) = dy/dx (absolute slope of Indifference Curve) (In simple words, it'd determination of consumer's equilibrium with the help of Indifference curve.)