Maurice Tutor

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    Argosy University/ Phoniex University/
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    Oct-2001 - Nov-2016

Category > Management Posted 15 Jan 2018 My Price 10.00

Thick-market effects

Thick-market effects and coordination failure. (This follows Diamond, 1982.)33 Consider an island consisting of N people and many palm trees. Each person is in one of two states, not carrying a coconut and looking for palm trees (state P) or carrying a coconut and looking for other people with coconuts (state C ). If a person without a coconut finds a palm tree, he or she can climb the tree and pick a coconut; this has a cost (in utility units) of c. If a person with a coconut meets another person with a coconut, they trade and eat each other’s coconuts; this yields u units of utility for each of them. (People cannot eat coconuts that they have picked themselves.)

A person looking for coconuts finds palm trees at rate b per unit time. A person carrying a coconut finds trading partners at rate aL per unit time, where L is the total number of people carrying coconuts. a and b are exogenous

Individuals’ discount rate is r. Focus on steady states; that is, assume that L is constant

(a) Explain why, if everyone in state P climbs a palm tree whenever he or she finds one, then rVP = b(VC − VP − c), where VP and VC are the values of being in the two states.

(b) Find the analogous expression for VC.

(c) Solve for VC − VP , VC, and VP in terms of r, b, c, u, a, and L.

(d) What is L, still assuming that anyone in state P climbs a palm tree whenever he or she finds one? Assume for simplicity that aN = 2b.

(e) For what values of c is it a steady-state equilibrium for anyone in state P to climb a palm tree whenever he or she finds one? (Continue to assume aN = 2b.)

(f) For what values of c is it a steady-state equilibrium for no one who finds a tree to climb it? Are there values of c for which there is more than one steady-state equilibrium? If there are multiple equilibrium, does one involve higher welfare than the other? Explain intuitively.

Answers

Maurice Tutor
(5)
Status NEW Posted 15 Jan 2018 09:01 PM My Price 10.00

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