Question: A consumer's utility function is given by u(x,y) = 4x^1/3 y^2/3 , what is this consumer's marginal rate of substitution between goods x and y.

A consumer's utility function is given by u(x,y) = 4x^1/3 y^2/3 , what is this consumer's marginal rate of substitution between goods x and y. Suppose you also know that good x costs $2, good y costs $8 and the consumer has an income of $100.

Optimal consumption for x = 16.67

Optimal consumption for y = 8.34

Marginal Rate of Substitution = y/2x

Does this consumer find goods x and y to be substitutes or compliments? Explain with math and words how you know this.

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