New PDF release: Collected Papers on Monetary Theory

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1), if 1 m 1 () = [n()  c ()] m  =   c ¢(),    then c(), n(), () is feasible for this problem. Since (if it differs from the equilibrium) it cannot be optimal for this problem.  1 ⌠  U [c (), n ()] + V   g (¢) d ¢ ⌡  (/¢)  ⌠  (/) (/) c ¢()   U[c (), n()] + V  g (¢) d ¢. 2), this implies   (1/) (/) c ¢()  ⌠  1 V   V   g (¢) g ¢  . 3), c()  c ¢(), so that  (1/) (/) c ¢()    (/) c ¢()   1 V ³ V  .

Then z is simply equal to x and, in view of Lemma 1, the current value of x is fully revealed to traders by the equilibrium price. It should not be surprising that the following classical neutrality of money theorem holds. ╇ Suppose   1 with probability one. Let y* be the unique solution to h(y)  V(y). 2). 6). 5), h(0)  V(0). 3) does have a unique solution, y *. 2). 2). 12 Collected Papers on Monetary Theory The second polar case, where x is identically 1, may be interpreted as applying to an economy with real disturbances but with a perfectly stable monetary policy.

Further, limn Tpn u  v for any u  L2nï•«. To prove that v is increasing in z, observe that Tpu is an increasing function of z for any u. Since v  Tpv, this implies that v is increasing in z. To prove that v is concave in z, we first show that if u(z, y) is concave in z, so is (Tpu) (z, y). Let z 0, z1 be chosen, let 0    1, and let z   z 0 ï•« (1  )z1. Let (ci, xi) attain (Tpu) (zi, y), i  0, 1. Now (c , x )  (c0 ï•« (1  )c1, x 0 ï•« (1  ) x1) satisfies c  ï•« p(y)€×€x   y€×€z  ï•« p(y)€×€z , so that (Tpu)(z  , y ) ³ U (c  ) + b u(x  , y ¢) dF (y ¢, y ) ³ Tpu)(z 0 , y ) + (1  )(Tpu)(z 1 , y ) using the concavity of U and u.

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