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Appendix

The partial derivatives of the first dynamic equation of the system (equation 9) are given by;

Γ0=1/1i>0Γ1=1ya0R+1(YCA+RYCB)b1b01iR><0Γ2=1yYCA(YCA+YCB)R1(YCA+RYCB)b01iR>0Γ3=MA/P11i<0Γ4=MB/P21i>0

where,

a0=D1RR(YCAYCCBYCBYCCA)+(YCA)2YCB[D1yB(1D1yA)]+YCAD1yC(YCA+YCB)><0b0b1==(YCA+RYCB)D1R+(1D1yA)(YCA)2+D1YBYCAYCB>0(1D1yA)YCAYCCBD1yBRYCBYCCAD1YCA><0

The partial derivatives for the second dynamic equation (equation 12) are;

ϕ0 = 0

ϕ1 = α < 0

ϕ3 = 0

ϕ4 = 0

For the competitive solution:

φ2=σ{LC(YLC)2YCARσ[YCCB(1σ)σRYCCA]}b2+LC(YLC)2{RYCCAYCCBb0+YCAb1[YCCB(1σ)σRYCCA]}

where,

b2=(YCCB+RYCCA)(LCYACR1σYLL1)

ϕ2 < 0 for σ > 1/2

ϕ2 = 0 for σ1/2

ϕ2 > 0 for σ < 1/2

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*

The author would like to thank Richard E. Baldwin, Graciana del Castillo, Ronald Findlay, Mohsin S. Khan, Peter Montiel, Robert A. Mundell, and Vincent R. Reinhart for useful suggestions. All remaining errors are the responsibility of the author.

Commodity Markets and the International Transmission of Fiscal Shocks
Author: International Monetary Fund