340

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -~- +

Let us denote the voN NEUMANN non-normalized prices
(i.e. the long-run equilibrium non-normalized prices corresponding
 to the voN NEUMANN rate of interest) by p,°, p1°, … b,°,
4:° ..., 4°. Equation (5) may be linearized in the neighbourhood
 of the voN NEUMANN prices in the following way.
We get from (7) and (0)

(10)

_ 1 —d,
Agy,= App, — Tir À Pryt+1

where Aq, ,=q;,-q’, and Ap, =p, ,-p,’. Expanding the
left-hand side of (5) in a TAYLOR series and neglecting higherpower
 terms, we have by virtue of (19)

20)

_— n _ n I —
Pix — 2 An Pau — (1+ 7 ) >. {riz by) Pi, +

7 [1 —a — —
—_— by) ; — a, o =0
+2 AE | Pied Pot

where pi =Ap. pC. We also have from (18)

(ZI)

et n —
Po HS Li Pis -

Substituting for Por from this and writing (20) in matrix form,
we get

(22)

M—a—(1+P)best—c] p,+ b(I—d)e-!p,,, =0

9] Morishima - pag. 12