Question: Consider the following utility functions:

1. \(U(x, y)=y \sqrt{x}\)
2. \(U(x, y)=3 x+y\)
3. \(U(x, y)=\sqrt{x y}\)
4. \(U(x, y)=x y+x\)
5. \(U(x, y)=x^{0.4} y^{0.6}\)

Answer the following for each of the utility functions above:

- Find the expressions for the marginal utility with respect to \(x\) and marginal utility with respect to \(y\).

- Does the utility function have the property of non-satiation?

- Do the consumer's preferences exhibit diminishing marginal utility of \(x\) ? Is the marginal utility of y diminishing?

- Find the expression for \(MRS\). Along the indifference curve, is \(MRS\) diminishing, constant or increasing as we increase \(x\) and decrease \(y\) ?

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