intermediate microeconomics convexity and indifference curves
A set of points is convex if any two points can be joined by a straight line that is contained completely within the set.
The assumption of a diminishing MRS is equivalent to the assumption that all combinations of x and y which are preferred to x* and y* form a convex set.
If the indifference curve is convex, then the combination (x1 + x2)/2, (y1+ y 2 )/2 will be preferred to either (x1,y1) or (x2,y2)
This implies that “well-balanced” bundles are preferred to bundles that are heavily weighted toward one commodity.
The assumption of a diminishing MRS is equivalent to the assumption that all combinations of x and y which are preferred to x* and y* form a convex set.
If the indifference curve is convex, then the combination (x1 + x2)/2, (y1+ y 2 )/2 will be preferred to either (x1,y1) or (x2,y2)
This implies that “well-balanced” bundles are preferred to bundles that are heavily weighted toward one commodity.
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