# ndp - E CON 714 M ACROECONOMIC T HEORY II TA T IM L EE A...

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Unformatted text preview: E CON 714: M ACROECONOMIC T HEORY II TA: T IM L EE A PRIL 30, 2010 Search Theoretic Approach to Money If Nt is a Poisson process with rate Î», 1. P( Nt = 0) = exp(âˆ’Î»t), 2. limtâ†’0 P( Nt =1) t =Î» 3. limtâ†’0 P( Nt >1) t = 0. As in class, assume - continuum 1 of agents - interest rate r - arrival rate Î± - probability x of liking what the other guy produces - M âˆˆ [0, 1] people hold money Two value functions, one each of whether or not you have money. Hereâ€™s a heuristic argument of how we get V1 : dt 0 eâˆ’rs V1 ds = 1 âˆ’ eâˆ’rdt V1 = (1 âˆ’ eâˆ’Î±dt ) x (1 âˆ’ M)Ï€ (u + V0 âˆ’ V1 ) r increase comes from the meeting instantaneous increase in V1 Next divide by dt take the limit as dt â†’ 0, 1 âˆ’ eâˆ’rdt V1 = lim rdt dtâ†’0 (1 âˆ’ eâˆ’Î±dt ) x (1 âˆ’ M)Ï€ (u + V0 âˆ’ V1 ) lim dt dtâ†’0 1. 2. 3. 1 Log-linearization New Keynesian Phillips Curve 2 ...
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ndp - E CON 714 M ACROECONOMIC T HEORY II TA T IM L EE A...

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