competitive equilibrium

8. Halloween is an old American tradition. Kids go out dressed in costume and neighbors give them candy when they come to the door. Spike and Cinderella are brother and sister. After a long night collecting candy, they sit down as examine what they have. Spike finds that he has 40 candy bars and 20 packs of gum. His sister finds she has 30 candy bars and 40 packs of gum. Spike likes candy bars exactly twice as much as gum and would always be willing to trade two packs of gum for one candy bar. Cinderella, on the other hand, likes gum exactly twice as much as candy bars and would always be willing to trade two candy bars for one pack of gum. 

a. Illustrate this situation in an Edgeworth box. Let Spike’s origin be in the lower left, and Cinderella’s be in the upper right hand corner. Put candy bars on the horizontal axis and gum on the vertical. 

b. Now draw in indifference curves for the two agents that reflect the description given above. Indicate the endowment point, and the contract curve. Illustrate a competitive equilibrium. Is there more than one competitive equilibrium? 

#10. Ken McSubstitute and Ron O’Complement were flying to a fast food festival in Fiji when an unexpected storm forced their plane to ditch in the middle of the Pacific. Miraculously, they are washed up on a desert island. Ken finds that he has only 5 slightly wet hamburgers and 15 orders of fries in his pockets. Ron discovers he has 15 hamburgers and 5 orders of fries. Ken only cares about how much he gets to eat. His utility function is: Us(H,F) = H+F. On the other hand, Ron believes that it is uncivilized to eat hamburgers without french fries or french fries without hamburgers. His utility function is: Uc(H,F) = min(H,F). 

a. In an Edgeworth box, show the endowment point, the Pareto Opimal Allocations, and the competitive equilibrium 

b. Is the competitive equilibrium Pareto Optimal? 

   Related Questions in Mathematics

  • Q : Profit-loss based problems A leather

    A leather wholesaler supplies leather to shoe companies. The manufacturing quantity requirements of leather differ depending upon the amount of leather ordered by the shoe companies to him. Due to the volatility in orders, he is unable to precisely predict what will b

  • Q : Law of iterated expectations for

     Prove the law of iterated expectations for continuous random variables.

    2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution that satisfies the bounds exactly for k ≥1, show that it satisfies the bounds exactly, and draw its PDF. T

  • Q : Ordinary Differential Equation or ODE

    What is an Ordinary Differential Equation (ODE)?

  • Q : Numerical Analysis Hi, I was wondering

    Hi, I was wondering if there is anyone who can perform numerical analysis and write a code when required. Thanks

  • Q : Problem on mass balance law Using the

    Using the mass balance law approach, write down a set of word equations to model the transport of lead concentration.

    A) Draw a compartmental model to represent  the diffusion of lead through the lungs and the bloodstream.

  • Q : Statistics math Detailed explanation of

    Detailed explanation of requirements for Part C-1 The assignment states the following requirement for Part 1, which is due at the end of Week 4: “Choose a topic from your field of study. Keep in mind you will need to collect at least [sic] 3- points of data for this project. Construct the sheet y

  • Q : Problem on reduced row-echelon The

    The augmented matrix from a system of linear equations has the following reduced row-echelon form.

    280_row echelon method.jpg

  • Q : Econ For every value of real GDP,

    For every value of real GDP, actual investment equals

  • Q : How to calculate area of pyramid

    Calculate area of pyramid, prove equation?

  • Q : State Fermat algorithm The basic Fermat

    The basic Fermat algorithm is as follows:

    Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers

    c2 - n; (c+1)2 - n; (c+2)2 - n.....

    until a perfect square is found. If th