Question

For the utility function $u(x, y) = x^{1/5}y^{1/4}$, (i) Calculate the optimal demand functions $x^$ and $y^$. (ii) From the maximized utility function $u(x^, y^)$, determine whether the associated preferences are risk-averse, risk-seeking, or risk-neutral. (You may find it convenient to write the maximized function in the form $u(x^, y^) =$ $\phi\omega$ to avoid clutter - but it's up to you.) For a bonus point, what do you think is the condition for utility function $u(x, y) = x^a y^b$ to represent risk-averse preferences?

          For the utility function $u(x, y) = x^{1/5}y^{1/4}$,
(i) Calculate the optimal demand functions $x^*$ and $y^*$.
(ii) From the maximized utility function $u(x^*, y^*)$, determine whether the
associated preferences are risk-averse, risk-seeking, or risk-neutral. (You may
find it convenient to write the maximized function in the form $u(x^*, y^*) =$
$\phi\omega$ to avoid clutter - but it's up to you.)
For a bonus point, what do you think is the condition for utility function
$u(x, y) = x^a y^b$ to represent risk-averse preferences?

Show more…

For the utility function u(x, y) = x^1/5y^1/4,
(i) Calculate the optimal demand functions x^* and y^*.
(ii) From the maximized utility function u(x^*, y^*), determine whether the
associated preferences are risk-averse, risk-seeking, or risk-neutral. (You may
find it convenient to write the maximized function in the form u(x^*, y^*) =
ϕω to avoid clutter - but it's up to you.)
For a bonus point, what do you think is the condition for utility function
u(x, y) = x^a y^b to represent risk-averse preferences?

Added by Madison B.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Basques Licit

Step 1

The marginal utility of x is given by the partial derivative of u with respect to x: ∂u/∂x = (1/5) * x^(-4/5) * y^(1/4) The marginal utility of y is given by the partial derivative of u with respect to y: ∂u/∂y = (1/4) * x^(1/5) * y^(-3/4) Show more…

Show all steps

lock

Thanks for your feedback!

For the utility function u(x, y) = x^(1/5) * y^(1/4), calculate the optimal demand functions x* and y*. From the maximized utility function (x*, y*), determine whether the associated preferences are risk-averse, risk-seeking, or risk-neutral. (You may find it convenient to write the maximized function in the form u(y*) = w to avoid clutter - but it's up to you.) For a bonus point, what do you think is the condition for the utility function to represent risk-averse preferences?

Play audio

Feedback

Powered by NumerAI

Basques Licit and 75 other subject Microeconomics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later