Econ Lab · Consumer choice
Budget constraints
You walk into a cafe with a fixed amount to spend, and two things to spend it on: coffee and tea. Every dollar that goes to coffee is a dollar that cannot go to tea. So before you ever pick a favourite, your money has already drawn a line through the bundles you can have and the ones you cannot.
Move the sliders and watch the line. That single line is the whole of what you can afford.
The budget line is everything you can just afford. Tea costs one cup of tea, so income reads straight in cups of tea. Right now income is cups, a coffee costs cups, and the slope is that same price ratio, the real cost of one coffee in tea given up. All tea gets you cups, all coffee gets you cups.
Two different moves to try. Change income and the line slides without tilting, a parallel shift, because the price ratio holds. Change the price of coffee and the line pivots around the fixed tea intercept, tilting to a new slope, because the trade-off between the goods has changed.
Slide income to move the line out and in. Slide the coffee price to pivot it around the tea corner.
Income measured in tea
We set the price of tea to one and let everything be counted in cups of tea. That choice is called a numeraire, and it just means we pick one good as the ruler. Now income is not an abstract dollar figure, it is simply how many cups of tea you could buy if you bought nothing else.
Spend it all on tea and you reach the top corner at m cups. Spend it all on coffee and you reach the side corner. The line joins the two.
The slope is a price tag
Here is the part worth keeping. The steepness of the line is the price of coffee in cups of tea. If coffee costs two, then buying one more coffee means giving up two cups of tea, so the line drops two for every step right.
That give-up rate is the real cost of coffee. The dollar price is only a label, the slope is what the choice actually costs you in the other good.
A price rise pivots, more income slides
Push the coffee price up. The tea corner does not move, because your income still buys the same amount of tea. But the coffee corner pulls in, since each coffee now costs more tea. The line pivots around the top and gets steeper.
Now push income up instead. Both corners move out together and the line slides outward, keeping the same slope. Nothing about relative prices changed, so the steepness is untouched. You can simply afford more of everything.
What you just did
You found the edge of what money allows before any taste entered the picture. The next step is to lay preferences on top and ask which affordable bundle a person actually wants. But the budget line comes first, because it sets the field of play. A price change tilts that field, an income change widens it.