# Marginal Rate of Substitution and Maximizing the Utility

An agent has a daily budget of $240 and her daily utility function is the consumption of two goods, X and Y:

U(X, Y) = X Y

If the price for good X (Px) is $8 and that for good Y (Py) is $10, what is the best combination of X and Y for the agent's daily consumption?

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#### Solution Preview

The agent's budget function is:

Px * X + Py * Y = Budget

or 8X + 10Y = 240 (1)

The marginal utility of X and Y are

MUx = dU/dX = Y

MUy = ...

#### Solution Summary

The solution provides detailed explanation about the calculation of the marginal rate of substitution and the shows how to maximize the utility given the budget constraint.

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