Visualize utility functions and indifference curves. Explore marginal utility, budget constraints, and optimal bundles in 2D.
A two-good utility function U(x, y) defines two families of curves on the plane, and this tool draws both at once: indifference curves U(x, y) = c and the budget line p_x x + p_y y = m set by the prices and income you enter. The marked optimum is the highest indifference curve the budget line reaches, with marginal utilities reported at any point you click. The usual surprise: the textbook tangency MRS = p_x/p_y only holds for smooth, convex preferences with an interior solution - corner optima and non-convex utility break it, and the tool shows where.
A concrete input and expected output from the current implementation.
Input
U = x^0.5 * y^0.5 with p_x = 2, p_y = 1, m = 100
Expected output
Budget line y = 100 - 2x. Optimal bundle (25, 50) at utility 35.36, on the indifference curve x*y = 1250. There MU_x = 0.71 and MU_y = 0.35, so MRS = 2 = p_x/p_y. The budget is exhausted: 2*25 + 50 = 100.
For Cobb-Douglas U = x^a * y^b the tangency MRS = (a*y)/(b*x) = p_x/p_y together with the budget gives x* = a*m/((a+b)*p_x) = 0.5*100/2 = 25 and y* = b*m/((a+b)*p_y) = 0.5*100/1 = 50.
Each indifference curve is the set of (x, y) pairs where U(x, y) equals a fixed level c, and the tool draws several of these levels together. Curves with larger c lie in the preferred region, and curves of a single function never cross. Spacing carries information: where adjacent curves pack tightly, utility changes rapidly across that region, and wide gaps mark a slower rise.
The budget line joins the intercepts m/p_x and m/p_y with slope -p_x/p_y; every point on it spends all of the income m. The tool marks the point on the line that lies on the highest reachable indifference curve. When that point is interior it satisfies the tangency condition MRS = MU_x/MU_y = p_x/p_y; otherwise the optimum is a corner on an axis.
No, that is a real corner solution. An interior tangency is the answer only when the touch lies on the budget line and preferences are convex. With linear utility (perfect substitutes) or a non-convex function such as U = x^2 + y^2, the maximum sits on an axis and the tangent point is either off the budget line or the worst affordable point.
Only an ordering. Utility is ordinal: 35.36 is preferred to 30, and that is the whole content of the number. Any strictly increasing transformation of the function produces identical indifference curves and the same optimal bundle, so the displayed level is not a meaningful unit of satisfaction.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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