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What is the marginal rate of substitution for the utility function U=2X+3Y ?

What is the marginal rate of substitution for the utility function U=2X+3Y ?

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Answer #1

Marginal rate of substitution is the rate at which the consumer is willing to give up one good in order to obtain one more unit of the other good. It is also the slope of the indifference curve.

Marginal rate of substitution = marginal utility of good X / Marginal utility of good Y

Marginal Utility of good X can be calculated by differentiating the utility function with respect X keeping Y constant. So, marginal utility of good X = 2

Marginal Utility of good Y can be calculated by differentiating the utility function with respect Y keeping X constant. So, marginal utility of good Y = 3

So, marginal rate of substitution = marginal utility of good X / Marginal utility of good Y

= 2/3 is the answer.

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