[Uses the Indifference Curve Approach \(]\) The appendix to this chapter states that when a consumer is buying the optimal combination of two goods \(x\) and \(y,\) then \(M R S_{y, x}=P_{x} / P_{y^{*}}\) Draw a graph, with an indifference curve and a budget line, and with the quantity of \(y\) on the vertical axis, to illustrate the case where the consumer is buying a combination on his budget line for which \(M R S_{x x}>P_{x} / P_{y}\).

Imagine you're in a candy shop, choosing between lollipops and chocolates. You love both, but if you have to give up a lollipop for more chocolates, how many would you be willing to trade? This trade-off is what economists call the Marginal Rate of Substitution (MRS). MRS quantifies your willingness to give up one good to obtain an additional unit of another while keeping the same level of happiness. Mathematically, it's obtained by taking the absolute value of the slope of an indifference curve at any given point.

Indifference curves represent combinations of two goods that give you the same satisfaction. Because most people would rather make smaller trade-offs than larger ones, these curves usually have a downward slope and are convex to the origin. Now, if your willingness to swap lollipops for chocolates (MRS) doesn't match the 'market's willingness' to make the trade (the price ratio of the goods, or Px/Py), you're not at your sweet spot for trading. You'd continue to trade until what you're willing to give up aligns with the 'cost of trade' in the market, finding that balance where one extra chocolate is worth losing just the right number of lollipops, giving you the subjectively best combination of both.

Think of the budget constraint as your financial sandbox. It's the boundary of your purchasing capabilities - how many lollipops and chocolates you can indulge in without spending more cash than you have in your pocket. In the indifference curve analysis, a budget constraint is depicted as a straight line on a graph where one axis represents the quantity of good x (say, lollipops) and the other represents good y (chocolates). The slope of this line is determined by the relative prices of these goods (Px/Py) and your total budget.

Every point on this line represents a feasible bundle of lollipops and chocolates you can buy without going over budget. If you try to go above this line, you're looking at candies you can't afford—dream sweet dreams, but you can't have them. Staying under the line means you're not maximizing the joy from your allocated sweet resources. The whole idea is to get the most bang for your buck, or in this case, the most pleasure from your sweets, without breaking the bank.

The optimal consumption bundle is like hitting the jackpot on a slot machine, except with goods instead of coins. It's the exact mix of lollipops and chocolates that maximizes your happiness given your budget. On a graph, this sweet spot is where an indifference curve just touches the budget constraint line - a point of tangency. Here, the MRS (your personal trade-off rate) equals the price ratio (the market trade-off rate).

This equilibrium of sorts means two things: first, that you're getting the maximum satisfaction possible with your current budget (because you're on the highest reachable indifference curve), and second, that your trade pattern perfectly aligns with market prices. You're not willing to trade any more or any fewer lollipops for chocolates. The optimal consumption bundle ensures not a single penny of your sweets budget is wasted; it's an efficient and satisfying allocation of your resources that aligns with your preferences and constraints.