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 λ, 1. P( Nt = 0) = exp(−λt), 2. limt→0 P( Nt =1) t =λ 3. limt→0 P( Nt >1) t = 0. As in class, assume - continuum 1 of agents - interest rate r - arrival rate α - probability x of liking what the other guy produces - M ∈ [0, 1] people hold money Two value functions, one each of whether or not you have money. Here’s a heuristic argument of how we get V1 : dt 0 e−rs V1 ds = 1 − e−rdt V1 = (1 − e−αdt ) x (1 − M)π (u + V0 − V1 ) r increase comes from the meeting instantaneous increase in V1 Next divide by dt take the limit as dt → 0, 1 − e−rdt V1 = lim rdt dt→0 (1 − e−αdt ) x (1 − M)π (u + V0 − V1 ) lim dt dt→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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