Question

Given a utility function that represents preference over bundles which consists of two goods,

Can we draw indifference map (collection of indifference curves)? How about the reverse? (Given the indifference map, can we derive utility function?)

Answer 1

Yes, it is possible to draw indifference map if the utility function of two goods is given. All that is to be done to draw indifference curve for utility function is to decrease plot all the points (x,y) such that U(x,y) equals a constant. This will help draw the indifference curve for that particular utility function. Thus indifference map can also be drawn.

But the reverse is not possible. Utility function cannot be derived if indifference map is given. The reason for this is that for every value of (x,y), there will be a different indifference curve but the utility function will be the same. So it won't be possible to derive utility function making use of indifference curve or from an indifference map.