# Microconomic Theory - Utility and Preference

**Algebra**Level 2

In a one-person-2-item-one budget world, a consumer has a an indifference curve, U, where U= XY = 24, X is quantity of good X and Y is quantity of good Y. (X and Y are positive integers)

The consumer's total income, I, is $24.

The price of good X, Px= $3

The price of good Y, Py= $2

Question: At the consumer's optimum point, what is the marginal rate of substitution between good X and good Y or MRS xy ? ( The MRS xy is just a fancy name for the slope of the indifference curve) :-)

There are several ways to approach this: Graphically, algebraically, or using the Lagrange multiplier.

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