Compute marginal Utilities of X for the total Utility function, U = 5XY – Y2


To compute the marginal utility of \( X \) for the given utility function:

\[
U = 5XY - Y^2
\]

The marginal utility of \( X \), denoted as \( MU_X \), is the partial derivative of the utility function \( U \) with respect to \( X \).

### Step-by-Step Computation:

1. The utility function is \( U = 5XY - Y^2 \).
2. To find the marginal utility of \( X \), take the partial derivative of \( U \) with respect to \( X \):

\[
MU_X = \frac{\partial U}{\partial X}
\]

\[
MU_X = \frac{\partial}{\partial X} (5XY - Y^2)
\]

Since \( Y^2 \) is independent of \( X \), its derivative with respect to \( X \) is 0. We only differentiate \( 5XY \) with respect to \( X \):

\[
MU_X = 5Y
\]

### Final Answer:
The marginal utility of \( X \) is:

\[
MU_X = 5Y
\]

Would you like more details on how to compute partial derivatives, or do you have any questions?

Here are 5 related questions:
1. How do you compute the marginal utility of \( Y \) for the same utility function?
2. How does the marginal utility change if \( Y \) is held constant and \( X \) changes?
3. What is the economic interpretation of marginal utility?
4. Can you explain the concept of diminishing marginal utility in the context of this function?
5. How would you compute total utility given specific values of \( X \) and \( Y \)?

**Tip**: Always differentiate carefully when finding marginal utilities, as one variable is held constant while differentiating with respect to the other.

Compute marginal Utilities of X for the total Utility function, U = 5XY – Y^2

Discover how to compute the marginal utility of X for the utility function U = 5XY – Y^2 using partial derivatives. This problem covers key calculus concepts, focusing on the marginal utility formula MU_X = ∂U/∂X. Suitable for undergraduate students studying economics or mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation