Econ Lab · Consumer theory
Consumer choice
You have a fixed amount to spend and a choice between coffee and tea. Every way of splitting the money between cups of each is a point on a single line, your budget. The question is which point on that line you like best.
Change the price of coffee, your income, or how much you care about coffee, and watch the best choice move.
The best affordable bundle is where the budget line just touches the highest indifference curve it can reach. At that single tangent point, the rate you are willing to swap tea for coffee equals the rate the market makes you swap them, the price ratio.
With taste the split leans toward tea, about cups of tea to of coffee. Raise income and both rise together in the same proportion, the budget line shifts straight out and the tangency slides along it without changing the mix.
Move the sliders for the price of coffee, income, and taste. The optimum re-solves and the curve through it redraws.
Two lines, two meanings
The straight line is the budget. It marks what you can just afford, and its steepness is the price ratio, how many cups of tea you give up for one more cup of coffee. The bowed curve is an indifference curve, a set of coffee-and-tea bundles you like exactly the same. Curves further out are better, because more of both is more to enjoy.
The best bundle is a tangency
You want the furthest-out curve you can still afford. Slide along the budget and you cross curve after curve, reaching better ones, until you hit the single curve the budget only touches. Push past it and you fall back to worse curves. That touching point, the tangency, is the best you can do.
In words, the rate you are personally willing to trade tea for coffee has lined up with the rate the market charges. When those two rates disagree there is still a better swap to make, so you are only done when they match.
Why demand curves slope down
Now drop the price of coffee. The budget line swings outward along the coffee axis, the tangency slides toward more coffee, and you choose to buy more of it. Do that at every price and you have just traced out the demand curve for coffee from scratch. The downward slope you took for granted in the earlier modules was hiding this choice all along.
What you just did
You solved the consumer's problem, the foundation of intermediate microeconomics. Demand, in the end, is not an assumption. It falls out of people spending limited budgets on the bundles they most prefer, one tangency at a time.