marginal rate of substitution
/ MRS /
Suppose you are choosing between coffee and tea, and someone asks: to stay exactly as happy, how much tea would you accept in exchange for giving up one cup of coffee? Your honest answer is the marginal rate of substitution. It is the rate at which you are personally willing to swap one good for another without feeling any better or worse off.
On a graph, the MRS is the steepness, the slope, of an indifference curve at a point, taken as a positive number. If at your current basket you would trade away one coffee for two teas and feel unchanged, your MRS of coffee for tea is 2. A neat fact ties it to utility: the MRS equals the ratio of the two goods marginal utilities, MU of coffee divided by MU of tea. The MRS usually shrinks as you move along the curve, because as coffee grows scarce in your basket each remaining cup feels precious, so you will give up fewer and fewer teas for it. That falling willingness to substitute is why indifference curves bow inward.
The MRS earns its keep at the moment of choice. A consumer reaches the best affordable bundle when the MRS equals the price ratio of the two goods, that is, when the rate you are willing to trade them matches the rate the market makes you trade them. If your MRS is bigger than the price ratio, the market is offering a swap better than you need, so you should buy more of the cheaper-feeling good; you keep adjusting until the two rates line up. That equality is consumer equilibrium seen through the lens of substitution.
At your current snacks, you would happily give up 1 chocolate bar for 3 gummies and feel no different, so your MRS is 3. If the shop lets you trade 1 chocolate for 4 gummies, that is better than you needed, so you swap and buy more gummies.
MRS is how much of one good you would swap for another, satisfaction unchanged.
MRS is a subjective willingness to trade, while the price ratio is the market's terms. The optimum is where the two are equal; they are not the same thing, and confusing them muddles the whole choice diagram.