This interactive exercise builds intuition for the consumer's optimization problem. By dragging your consumption bundle across the graph, you can feel how utility changes as you move along or away from the budget constraint. The key insight is that the highest achievable indifference curve is the one that just touches (is tangent to) the budget line — any curve above it is unaffordable, and any curve below it leaves money on the table.
Notice what happens when you land exactly on the budget line: your spending equals your income, and small movements along the line trade \(X\) for \(Y\) at the market rate \(P_x/P_y\). At the optimum, this market trade-off exactly matches your personal willingness to substitute, the \(\mathrm{MRS}\). If your indifference curve were steeper than the budget line at your chosen point, you could increase utility by buying more \(X\) and less \(Y\); if flatter, the reverse. Only at the tangency point are both forces balanced.
Try changing the sliders to see how the optimal bundle shifts. A higher \(\alpha\) tilts spending toward \(X\); a higher \(P_x\) pivots the budget line inward along the \(X\)-axis, forcing you to buy less of it. The "Show Optimal" button reveals the answer so you can check your intuition and see how close you got.
🎯 How to Play
Click and drag anywhere on the graph to choose your consumption bundle \((X, Y)\). Try to find the point that gives you the highest utility while staying within your budget!