# utility functions of perfect complements

if preferences are described and in this case the preferences are perfect complements, we want to find an utility function that describes the preferences so we can draw an indifference curve. the utility function is u(x1,x2) = min(x1,x2) this makes sense for goods that are consumed on a one-to-one basis. what about other proportions? for example consumer always uses 2 teaspoons of sugar with each cup of tea? if x1 is the number of cups of tea and x2 the number of teaspoons, it says the function would be min(x1,1/2x2) how come?

• How come? How come not...? Do you see any problems with the function $\min(x_1,x_2/2)$? What other function would you propose? Commented Oct 31, 2023 at 21:18
• Yo @tessa! I commented a pseudo answer under your other question. I recommend challenging the teacher's statements. Try to find a counterexample, either using math or computer programs, whichever you are better at. Commented Oct 31, 2023 at 21:20
• @Giskard i would have proposed the function min(x1,2x2) because x1= 1 cup of tea and x2 = 2 teaspoons of sugar. but i looked at it for a bit longer and realized that that function wouldn't be of any help. if i have 4 cups of tea and 3 spoons of sugar, i'd only be able to fill 1.5 cups of tea -> so i divide 3/2. i don't understand it as far as being able to explain why in a statement but i think i'll be able to put up an utility function given preferences that are perfect complements. again thank you very much for your help and your tips Commented Nov 1, 2023 at 0:48