Utility & Indifference
Tangency between the budget line and the highest attainable indifference curve
Two goods, one budget. Cobb-Douglas gives a smooth tangency; Leontief pins the optimum at a kink; perfect substitutes usually land at a corner. Shift prices and income and watch the optimal bundle relocate.
Smooth, strictly convex preferences. Interior tangency: MRS = p_x/p_y.
optimal x*
5.000
optimal y*
5.000
u(x*, y*)
5.000
Tangency, corner, or kink — the optimum sits where the highest attainable indifference curve meets the budget line. Drag to push income; shift prices to rotate the constraint.