Back Matter

### Appendix

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

$\begin{array}{ccc}{\mathrm{\Gamma }}_{\mathrm{0}}& \mathrm{=}& \mathrm{-}\mathrm{1}\mathrm{/}{\mathrm{1}}_{\mathrm{i}}\mathrm{>}\mathrm{0}\hfill \\ {\mathrm{\Gamma }}_{\mathrm{1}}& \mathrm{=}& \frac{{\mathrm{1}}_{\mathrm{y}}\mathrm{}{\mathrm{a}}_{\mathrm{0}}\mathrm{}\mathrm{R}\mathrm{+}\mathrm{1}\mathrm{}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{+}{{\mathrm{RY}}_{\mathrm{C}}}^{\mathrm{B}}\mathrm{\right)}\mathrm{}{\mathrm{b}}_{\mathrm{1}}}{{\mathrm{b}}_{\mathrm{0}}\mathrm{}{\mathrm{1}}_{\mathrm{i}}\mathrm{}\mathrm{R}}\mathrm{}\begin{array}{cc}\mathrm{>}& \\ \mathrm{<}& \mathrm{0}\end{array}\hfill \\ {\mathrm{\Gamma }}_{\mathrm{2}}& \mathrm{=}& \mathrm{-}\frac{{\mathrm{1}}_{\mathrm{y}}\mathrm{}{\mathrm{Y}}_{{\mathrm{C}}^{\mathrm{A}}\mathrm{}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{+}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{B}}\mathrm{\right)}\mathrm{}\mathrm{R}\mathrm{-}\mathrm{1}\mathrm{}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{+}{{\mathrm{RY}}_{\mathrm{C}}}^{\mathrm{B}}\mathrm{\right)}}}{{\mathrm{b}}_{\mathrm{0}}\mathrm{}{\mathrm{1}}_{\mathrm{i}}\mathrm{}\mathrm{R}}\mathrm{>}\mathrm{0}\hfill \\ {\mathrm{\Gamma }}_{\mathrm{3}}& \mathrm{=}& {\mathrm{M}}^{\mathrm{A}}\mathrm{/}{\mathrm{P}}_{\mathrm{1}}\mathrm{}{\mathrm{1}}_{\mathrm{i}}\mathrm{<}\mathrm{0}\hfill \\ {\mathrm{\Gamma }}_{\mathrm{4}}& \mathrm{=}& {\mathrm{M}}^{\mathrm{B}}\mathrm{/}{\mathrm{P}}_{\mathrm{2}}\mathrm{}{\mathrm{1}}_{\mathrm{i}}\mathrm{>}\mathrm{0}\hfill \end{array}$

where,

$\begin{array}{ccccc}{\mathrm{a}}_{\mathrm{0}}& \mathrm{=}& {{\mathrm{D}}_{\mathrm{1}}}^{\mathrm{R}}\mathrm{R}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{C}}{{\mathrm{A}}_{\mathrm{Y}}}_{\mathrm{CC}}\mathrm{B}\mathrm{-}{\mathrm{Y}}_{\mathrm{C}}{\mathrm{B}}_{{\mathrm{Y}}_{\mathrm{CC}}}\mathrm{A}\mathrm{\right)}\mathrm{+}{\mathrm{\left(}{\mathrm{Y}}_{\mathrm{C}}^{\mathrm{A}}\mathrm{\right)}}^{\mathrm{2}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\mathrm{}{\mathrm{Y}}_{\mathrm{C}}^{\mathrm{B}}\mathrm{}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\mathrm{\left[}{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}^{\mathrm{B}}\mathrm{-}\mathrm{\left(}\mathrm{1}\mathrm{-}{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}^{\mathrm{A}}\mathrm{\right)}\mathrm{\right]}\hfill & & \\ & & \begin{array}{cccc}& \mathrm{+}{\mathrm{Y}}_{\mathrm{C}}{\mathrm{A}}_{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}\mathrm{C}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{+}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{B}}\mathrm{\right)}& & \end{array}\hfill & \begin{array}{cc}\mathrm{>}& \\ \mathrm{<}& \mathrm{0}\end{array}& \\ \begin{array}{c}\begin{array}{c}{\mathrm{b}}_{\mathrm{0}}\end{array}\\ {\mathrm{b}}_{\mathrm{1}}\end{array}& \begin{array}{c}\begin{array}{c}\mathrm{=}\end{array}\\ \mathrm{=}\end{array}& \begin{array}{c}\mathrm{\left(}\begin{array}{c}\begin{array}{c}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{+}{{\mathrm{RY}}_{\mathrm{C}}}^{\mathrm{B}}\end{array}\end{array}\mathrm{\right)}{\mathrm{D}}_{\mathrm{1}\mathrm{R}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}^{\mathrm{A}}\mathrm{\right)}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}\mathrm{\right)}\mathrm{2}\mathrm{+}{{\mathrm{D}}_{\mathrm{1}\mathrm{Y}}}^{\mathrm{B}}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{B}}\mathrm{>}\mathrm{0}\\ \mathrm{\left(}\mathrm{1}\mathrm{-}{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}^{\mathrm{A}}\mathrm{\right)}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{B}}\mathrm{-}{{\mathrm{D}}_{\mathrm{1}\mathrm{y}}}^{\mathrm{B}}{{\mathrm{RY}}_{\mathrm{C}}}^{\mathrm{B}}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{A}}\mathrm{-}{\mathrm{D}}_{\mathrm{1}\mathrm{Y}}{\mathrm{C}}^{\mathrm{A}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\begin{array}{cc}\mathrm{>}& \\ \mathrm{<}& \mathrm{0}\end{array}\hfill \end{array}\hfill & & \end{array}$

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

ϕ0 = 0

ϕ1 = α < 0

ϕ3 = 0

ϕ4 = 0

For the competitive solution:

${\mathrm{\phi }}_{\mathrm{2}}\mathrm{=}\frac{\sigma \mathrm{\left\{}{\mathrm{L}}^{\mathrm{C}\mathrm{\prime }}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{L}}}^{\mathrm{C}}\mathrm{\right)}}^{\mathrm{2}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}{\mathrm{R}}^{\mathrm{-}\mathrm{\sigma }}\mathrm{\left[}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{B}}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\sigma }\mathrm{\right)}\mathrm{\sigma }\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{{\mathrm{RY}}_{\mathrm{CC}}}^{\mathrm{A}}\mathrm{\right]}\mathrm{\right\}}}{{\mathrm{b}}_{\mathrm{2}}\mathrm{+}{\mathrm{L}}^{\mathrm{C}\mathrm{\prime }}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{L}}}^{\mathrm{C}}\mathrm{\right)}}^{\mathrm{2}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\mathrm{\left\{}{{\mathrm{RY}}_{\mathrm{CC}}}^{\mathrm{A}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{B}}{\mathrm{b}}_{\mathrm{0}}\mathrm{+}{{\mathrm{Y}}_{\mathrm{C}}}^{\mathrm{A}}{\mathrm{b}}_{\mathrm{1}}\mathrm{\left[}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{B}}\mathrm{\left(}\mathrm{1}\mathrm{-}\sigma \mathrm{\right)}\sigma {{\mathrm{RY}}_{\mathrm{CC}}}^{\mathrm{A}}\mathrm{\right]}\mathrm{\right\}}}$

where,

${\mathrm{b}}_{\mathrm{2}}\mathrm{=}\mathrm{\left(}{{\mathrm{Y}}_{\mathrm{CC}}}^{\mathrm{B}}\mathrm{+}{{\mathrm{RY}}_{\mathrm{CC}}}^{\mathrm{A}}\mathrm{\right)}\mathrm{\left(}{\mathrm{L}}^{\mathrm{C}\mathrm{\prime }}\mathrm{Y}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\begin{array}{c}\mathrm{A}\\ \mathrm{C}\end{array}{\mathrm{R}}^{\mathrm{1}\mathrm{-}\sigma }\mathrm{Y}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\begin{array}{c}\\ \mathrm{LL}\end{array}\mathrm{-}\mathrm{1}\mathrm{\right)}$

ϕ2 < 0 for σ > 1/2

ϕ2 = 0 for σ1/2

ϕ2 > 0 for σ < 1/2

## References

• Cagan, P.,Imported Inflation 1973-74 and the Accommodation Issue,” Journal of Money Credit and Banking, Vol. 12, No. 1 (February 1980), pp. 116.

• Crossref
• Export Citation
• Dornbursh, R.,Flexible Exchange Rates and Interdependence,” IMF Staff Papers. Vol. 30, No. 1 (March 1983), pp. 338.

• Dornbursh, R.,Policy and Performance Links Between IDC Debtors and Industrial Nations,” Brookings Papers on Economic Activity. No. 2, (Washington, 1985), pp. 303356.

• Crossref
• Export Citation
• Findlay, R. and C. Rodriguez,Intermediate Imports and Macroeconomic Policy Under Flexible Exchange Rates,” Canadian Journal of Economics. 10 (May 1977), pp. 208217.

• Crossref
• Export Citation
• Findlay, R.,Oil Supplies and Employment Levels: A Simple Macro Model,” in Flexible Exchange Rates and the Balance of Payments. J. Chipman and C. Kindleberger (eds.), Studies in International Economics, Vol. 7 (1980), pp. 313320.

• Export Citation
• Frankel, J.A.,Ambiguous Macroeconomic Policy Multipliers in Theory and in Twelve Econometric Models,” forthcoming in Empirical Macroeconomics for Interdependent Economies. R. Bryant and D. Henderson (eds.), (Washington: Brookings Institute, 1986a).

• Export Citation
• Frankel, J.A.,The Implications of Conflicting Models for Coordination Between Monetary and Fiscal Policy-Makers,” forthcoming in Empirical Macroeconomics for Interdependent Economies. R. Bryant and D. Henderson (eds.), (Washington: Brookings Institute, 1986b).

• Export Citation
• Frenkel, J.A. and Razin, A.,The International Transmission and Effects of Fiscal Policies,” Working Paper No. 1799, National Bureau of Economic Research (January, 1986).

• Export Citation
• Guavazzi, F. and A. Giovannini,Asymmetries in Europe, the Dollar and the European Monetary System,” in Thema: Europe and the Dollar, edited by San Paolo Bank (1985), pp. 7792.

• Export Citation
• Giovannini, A.,The Real Exchange Rate, the Capital Stock and Fiscal Policy,” European Economic Review (February, 1987).

• Goldstein, M. and M.S. Khan,Effects of a Slowdown in Industrial Countires on Growth in Non-Oil Developing Countries,” IMF Occasional Paper 12. (Washington: International Monetary Fund, August 1982).

• Export Citation
• Khan, M.S., and P.J. Montiel,Real Exchange Rate Dynamics in a Small Primary-Exporting Country,” IMF Staff Papers. Vol. 34, No. 4 (Washington: International Monetary Fund, December 1987).

• Export Citation
• Krugman, P.,Oil and the Dollar,” in Economic Interdepenence and Flexible Exchange Rates. J.S. Bhandari and B. Putnam (eds.), National Bureau of Economic Research (1983), pp. 179190.

• Export Citation
• Krugman, P.,Oil Shocks and Exchange Rate Dynamics,” in Exchange Rates and International Macroeconomics. J. Frenkel (ed.), National Bureau of Economic Research (1983), pp. 259284.

• Export Citation
• Metzler, L.A.,Tariffs, the Terms of Trade, and the Distribution of National Income,” Journal of Political Economy. Vol. LVIII, No. 1 (February 1949), pp. 129.

• Crossref
• Export Citation
• Mundell, R.A.,Capital Mobility and Stabilization Policy Under Fixed and Flexible Exchange Rates,” International Economics. (1968), Chap. 18, pp. 250271.

• Export Citation
• Mussa, M.,A Model of Exchange Rate Dynamics,” Journal of Political Economy. Vol. 90, No. 1 (February 1982), pp. 74104.

• Mussa, M.,Economically Sensible Solutions for Linear Rational Expectations Models with Forward and Backward Looking Dynamic Processes,” Working Paper No. 1398, National Bureau of Economic Research (1984).

• Export Citation
• Obstfeld, M.,Intermediate Imports, the Terms of Trade, and the Dynamics of the Exchange Rate and Current Account,” Journal of International Economics. Vol. 10, No. 4 (November 1980), pp. 461480.

• Crossref