Explain the consumer's equilibrium by using indifference curve approach.

Consumer's equilibrium under the indifference curve approach is the point at which a consumer, spending a fixed income at given prices, reaches the highest possible indifference curve and so obtains maximum satisfaction.

1. Two tools involved: the analysis combines the indifference map (the consumer's preferences) with the budget line (what the consumer can afford), given by Px·X + Py·Y = B.
2. Goal of the consumer: a rational consumer wants to reach the highest attainable indifference curve, since higher curves mean greater satisfaction.
3. Equilibrium point: equilibrium occurs where the budget line is tangent to the highest indifference curve it can touch, at point E.
4. Necessary (first-order) condition: at the tangency the slope of the indifference curve equals the slope of the budget line, i.e. MRSxy = Px / Py = MUx / MUy.
5. Sufficient (second-order) condition: the indifference curve must be convex to the origin at E, meaning the MRS is diminishing there.
6. Why not points where the line crosses an IC: at points such as C and D the budget line merely cuts a lower indifference curve, so the consumer can still move to a higher curve and do better — these are not equilibrium.
7. Interior point wastes income: a point like G inside the budget line is affordable but leaves income unspent, so it is not the best the consumer can do.
8. Exterior point is unaffordable: a point like F beyond the budget line lies on a higher IC but cannot be bought with the given income.
9. Meaning of the tangency: only at E does the rate at which the consumer is willing to substitute the goods (MRS) equal the rate at which the market lets them substitute (price ratio), so no further gain is possible.
10. Result: at E the consumer allocates the whole income between X and Y in the combination that yields maximum satisfaction, which is the equilibrium.

Thus, the consumer is in equilibrium at the tangency of the budget line and the highest reachable indifference curve, where MRSxy = Px/Py and the indifference curve is convex — the point of maximum satisfaction.