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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.

u(x,y)=xαy1αu(x, y) = x^{\alpha} y^{1-\alpha}

Smooth, strictly convex preferences. Interior tangency: MRS = p_x/p_y.

02468100246810good xgood 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.

Utility & Indifference — Economics Labs · hbar.university