Tom, Dick, and Harry live in the same apartment building in downtown Los Angeles. Tom and Dick work at local auto parts stores, and each of them has an income of y dollars per week. Harry is less fortunate. He used to have a good job at the LAPD, but his penchant for firing large caliber weapons in crowded public places led to his dismissal. He currently has no income. Tom and Dick (who are originally from Texas) firmly believe in a man’s right to draw his gun in the defence of just about anything, and are happy to financially support Harry. Tom gives Harry zT dollars each week, and Dick gives Harry zD dollars each week Tom’s utility UT depends upon the dollar value of his own weekly consumption, cT , and of Harry’s weekly consumption, cH : Likewise, Dick’s utility UD depends upon the dollar value of his own weekly consumption, cD, and of Harry’s weekly consumption: Harry spends all of the money that he receives from Tom and Dick. Tom and Dick spend all of the money that they have left after giving a little to Harry. a) Find the Nash equilibrium values of the transfers zT and zD. b) Imagine that Tom and Dick agree to give the same amount,, to Harry, and that they choose this amount to maximize the sum of their utilities. What is?
Tom, Dick, and Harry live in the same apartment building in downtown Los Angeles. Tom and Dick work at local auto parts stores, and each of them has an income of y dollars per week. Harry is less fortunate. He used to have a good job at the LAPD, but his penchant for firing large caliber weapons in crowded public places led to his dismissal. He currently has no income. Tom and Dick (who are originally from Texas) firmly believe in a man’s right to draw his gun in the defence of just about anything, and are happy to financially support Harry. Tom gives Harry zT dollars each week, and Dick gives Harry zD dollars each week
Tom’s utility UT depends upon the dollar value of his own weekly consumption, cT , and of Harry’s weekly consumption, cH :
Likewise, Dick’s utility UD depends upon the dollar value of his own weekly consumption, cD, and of Harry’s weekly consumption:
Harry spends all of the money that he receives from Tom and Dick. Tom and Dick spend all of the money that they have left after giving a little to Harry.
a) Find the Nash equilibrium values of the transfers zT and zD.
b) Imagine that Tom and Dick agree to give the same amount,
, to Harry, and that they choose this amount to maximize the sum of their utilities. What is
?
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