Math Solutions

(All Steps) Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=Y+X^2 Derive the function for the marginal rate of substitution

Question: Suppose a consumer's preferences can be represented by the utility function:

\[U\left( X,Y \right)=Y+{{X}^{2}}\]
  1. Derive the function for the marginal rate of substitution holding utility constant:
    \[{{\left. \frac{\Delta Y}{\Delta X} \right|}_{{\bar{U}}}}\]
  2. Does the marginal rate of substitution fall as you go down the indifference curve? Explain.

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