20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 upsxy

Info icon This preview shows pages 10–17. Sign up to view the full content.

View Full Document Right Arrow Icon
20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 U(PS)=X+Y U=X^1/2Y^1/2
Image of page 10

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

View Full Document Right Arrow Icon
Solve the Rational Consumer’s Problem. Method 1 (for Cobb Douglas Utility). Use the equilibrium condition: With ( , ) X U X Y MU X ( , ) Y U X Y MU Y
Image of page 11
Solve the Rational Consumer’s Problem. Method 2 (for Cobb Douglas Utility). From the budget constraint, isolate one of the good as the function of income, prices and the other good. Substitute the expression of Y into the utility function U(X,Y). Maximize the utility function which is now a function of only one of the good (good X in this case). The F.O.C yields the solution for good X. Substitute the value of good X onto the budget constraint to get the solution for good Y. X Y Y P M Y X P P
Image of page 12

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

View Full Document Right Arrow Icon
Solve the Rational Consumer’s Problem. Advanced Mathematical Method. Lagrangean Multipliers (for Cobb Douglas Utility).. Set and And let (1)/(2) Similar equilibrium condition as the graphical method. Solve for the quantity of two goods given prices and income level.
Image of page 13
Solve the Rational Consumer’s Problem.
Image of page 14

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

View Full Document Right Arrow Icon
Solve the Rational Consumer’s Problem. Example: Dan spends all his 100 weekly income on two goods, X and Y. His utility function is given by: If Px = $4/unit and Py = $10/unit, how much of each good should he buys. 1 1 2 2 ( , ) U X Y X Y 1 1 2 2 ( , ) U X Y X Y
Image of page 15
Solve the Rational Consumer’s Problem. For other types of utility functions: Perfect Substitute Linear Utility Function The slope of the Utility Function, MRS, is a constant. It is either equal, greater, or less than the slope of the budget line (good Y is on the vertical axis).
Image of page 16

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

View Full Document Right Arrow Icon
Image of page 17
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