Splitting the Lunch Budget

Split a 40-won lunch budget between gimbap and tteokbokki, then find the best combo.

The 💰 money you can spend is fixed. What you spend on the two foods cannot pass the budget. The best combo is where the last won buys the same happiness on either food. The second formula below states that condition.

For example, you have 4,000 won: a 🍞 bread costs 1,000 and a 🥛 milk costs 2,000. One of each fits the budget exactly. If the last 100 won on bread felt better, buy less milk and one more bread.

p1x1+p2x2=mp_1 x_1 + p_2 x_2 = m
MU1p1=MU2p2\frac{MU_1}{p_1} = \frac{MU_2}{p_2}

Part of these learning paths

Examples & Exercises

Lunch budget m=40m = 40, food 1 costs p1=4p_1 = 4, food 2 costs p2=8p_2 = 8.

The budget equation is the one below — liking both, how should the budget be split?

p1x1+p2x2=mp_1 x_1 + p_2 x_2 = m
Budget 4040, food 1 price 44 (food 2 fixed at 88).
Show proof

  1. Going all-in on one food unbalances the happiness of the last won. Balance comes when the last won buys the same happiness either way.

  2. That point splits the budget exactly in half: 2020 worth of food 1 (55 items) and 2020 worth of food 2 (2.52.5 items). That is why the two readout lines show the same number.

Food 1's price halves from 44 to 22.

How many of each food get bought now?

Budget 4040, food 1 price 22 — half-price sale.
Show proof

  1. Surprisingly, food 2 stays at 2.52.5 items. The split-in-half rule holds regardless of prices.

  2. Food 1: 2020 worth at 22 each is 1010 items — you buy more of the cheaper food, but the other food's share is untouched. That is the signature of this preference.

1. Intro to Microeconomics