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 : Define Well-formed formulas or Wffs

    Wffs (Well-formed formulas): These are defined inductively by the following clauses:
      
    (i) If  P  is an n-ary predicate and  t1, …, tn are terms, then P(t1, …, t

  • Q : Explain the work and model proposed by

    Explain the work and model proposed by Richardson.

  • Q : Mean and standard deviation of the data

    Below is the amount of rainfall (in cm) every month for the last 3 years in a particular location:

    130 172 142

    150 144 117

    165 182 104

    120 190 99

    170 205 110

    80 196 127

    120 175

  • Q : Elasticity of Demand For the demand

    For the demand function D(p)=410-0.2p(^2), find the maximum revenue.

  • Q : Research Areas in Medical Mathematical

    Some Research Areas in Medical Mathematical Modelling:

    1. Modeling and numerical simulations of the nanometric aerosols in the lower portion of the bronchial tree.

    2. Multiscale mathematical modeling of

  • Q : Define Big-O notation Big-O notation :

    Big-O notation: If f(n) and g(n) are functions of a natural number n, we write

    f(n) is O(g(n))

    and we say f is big-O of g if there is a constant C (independent of n) such that f

  • 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 : Who firstly discovered mathematical

    Who firstly discovered mathematical theory for random walks, that rediscovered later by Einstein?

  • Q : Global And Regional Economic Development

    The Pharmatec Group, a supplier of pharmaceutical equipment, systems and services, has its head office in London and primary production facilities in the US. The company also has a successful subsidiary in South Africa, which was established in 1990. Pharmatec South A

  • Q : Relationships Between Data Introduction

    Relationships Between Data - Introduction to Linear Regression Simple Regression Notes

    If you need guidance in terms of using Excel to run regressions, check pages 1 - 10 of the Excel - Linear Regression Tutorial posted to th