Kiyotaki-Wright Experiment Todd R. Kaplan

Kiyotaki Wright Model What is money? –medium of exchange –unit of account, –store of value Why is money useful? –Double coincidence of wants.

Experiment: (2) (3) (1) Desired good (produced good) Good123 Cost149

Patterns of Trade. (what is money here?) (2) (3) (1) Desired good (produced good) Good123 Cost

Another pattern possible? (2) (3) (1) Desired good (produced good) Good123 Cost145

Discounting Does discounting effect things? Can “everyone accepts everything” be an equilibrium? Can “no one accepts anything” be an equilibrium?

Advanced (if time permits) Does it make sense for a type 1 to speculate and trade a 2 for a 3? Call V2 the value for a type 1 to hold 2 and V3 for the value of holding good 3. Assume that type 2 will always trade a 3 for a 2 and a 1 for a 2, but never a 1 for a 3 (higher cost). If NO type 1’s trade for a 2 for a 3, then the probability of type 2 holding 3 is p given by –p= p*(1/2)+(1-p)*1/2  p=1/2. (assuming matching prob of ½).

Proportions (2) (3) (1) (2)(3) Half of 2(1)’s meet 3’s and stay the same. Half of 2(1)’s meet 1’s and become 2(3)s. Half of 2(3)’s meet 3’s and becomes 2(1)s. Half of 2(3)’s meet 1’s and stay 2(3)s. If there are 90 2(3)s and 10 2(1)s, next period there will be how many 2(3)s? 45+5=50.

Dynamic program We can now use dynamic programming Bellman’s equation to see if 1 would have incentive to deviate and trade for (3) V2=-4+B(1/2*1/2*V3+1/2*1/2*(V2+20)+1/2*V2) V3=-5+B(1/2*(20+V2)+1/2*V3) Solving yields V2=(23B-16)/(4+B(B-5)), V3=(-20+(47-20B)B)/(4+B(B-5)) If B=.8, then V2=3.75, V3=7.5.

More dynamic If instead 1 stuck with only hold 2, his value would be V2=-4+B(1/2*1/2*(V2+20)+3/4*V2) V2=(-4+B*20/4)/(1-B) If B=.8, then V2=0.