Derive the Marshallian demand functions

Question

b) Assume that the preferences can be represented by the utility function u = x1x2 and the budget constraint is given as p1x1 + p2x2 = m. Derive the Marshallian demand functions for x1 and x2.

And then d) Derive the indirect utility function associated with the Marshallian demand functions in b.

Is there any easy formulas that I can follow?

Answer 1

Easy formulas? Well its more of a process. Here's what you do:

Find marginal utility of x1 = MUx1

Find marginal utility of x2 = MUx2

Put MUx1/MUx2 which is marginal rate of substitution, MRS

Set MRS = P1/P2

This gives you a formula which you can isolate x1 and x2 to plug into your budget constraint which is that formula: p1x1 + p2x2 = m

Using that budget constraint, then solve for x1 = ..... and x2 =....... Those are your demand functions