PracticeQuestion4 econ 326.pdf

PracticeQuestion4 econ 326.pdf - Econ 326 Practice Question...

Info icon This preview shows pages 1–3. Sign up to view the full content.

Econ 326 Practice Question 4 (Chapter 9) Heejeong Kim 1. Which of the following quadratic functions are strictly convex? (a) y ( x ) = 9 x 2 - 4 x + 8 (b) u ( x ) = 9 - 2 x 2 (c) y ( x ) = - 3 x 2 + 39 (d) v ( x ) = 8 - 5 x + x 2 2. Consider f ( x ) = 3 x 2 3 - 5 x for x > 0. Find the first-order condition and solve. Show that your solution is a global maximizer. Is the function globally increasing or decreasing? 3. Consider f ( x ) = x 3 3 - 2 x 2 + 3 x + 7 for x 0. Find the solution to the first-order condition and determine if the solution is a local maximizer or minimizer. Where is the global maximum or global minimum? 4. Consider the function f ( x ) = x a - x b for x > 0 where 0 < a < 1 and b > 1. Solve the first-order condition and show that this is a global maximizer. 5. A firm has the following total-cost and demand functions C = 1 3 Q 3 - 7 Q 2 + 111 Q + 50 Q = 100 - P (a) Write out the total-revenue function R in terms of Q .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

(b) Formulate the total-profit function π in terms of Q . (c) Find the profit-maximizing level of output Q * .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern