In this version of the game you control the quantities of each good directly using sliders, rather than clicking on the graph. This makes it easier to see how the budget constraint binds: as you increase \(X\), spending rises by \(P_x\) per unit, eating into the income available for \(Y\). The budget bar gives you real-time feedback on whether your chosen bundle is affordable. Bundles above the budget line turn the indifference curve red to signal infeasibility.
The key economic insight is that maximizing utility requires spending all your income (exhausting the budget) and allocating it so that the marginal utility per dollar is equalized across goods. With Cobb-Douglas preferences, this leads to a beautifully simple rule: the consumer spends a fraction \(\alpha\) of income on \(X\) and \((1-\alpha)\) on \(Y\), regardless of prices. Prices only determine how many units each dollar buys, not the expenditure share.
Try pushing one slider to an extreme and watch what happens to utility — even if you can afford a lot of one good, utility suffers because Cobb-Douglas preferences exhibit diminishing marginal returns. The sweet spot is always an interior solution where both goods are consumed in proportion to the preference parameter \(\alpha\).
🎯 How to Play
Use the \(X\) and \(Y\) sliders to choose your consumption bundle. Try to find the combination that gives you the highest utility while keeping total spending within your budget!