Is it possible to derive indifference curves given marshallian demand function?

Question

In a two good world, will a marshallian demand function the likes of `D(p,m)` where p is the price of one good and m the income yield a utility function or indifference curve function? If so, how does one go about solving this?

Answer 1

The short answer to your question is no.

Consumer Choice theory, and the optimization problem, requires us to examine 2 facets of the consumer problem:

(1) what bundle of goods are affordable? (these are denoted by the budget constraint, which is derived from the available income and the prices of goods)

(2) what bundle of goods are desirable? (these are denoted by the utility function for a consumer)

A given utility function for 2 goods (X, Y) might be of the form U = X^0.5Y^0.5 (if it is a Cobb Douglas utility function), or U = 2X + 3Y (if it is a perfect substitutes utility function). In both cases, we see utility is only a function of the quantity or X and Y, not the prices or incomes. An indifference curve is simply a map / graph of the combinations of X and Y that satisfy a given level of utility so this is not dependent on income or prices either.