Appendix B: Equations of the model in level and differential form
Contents - Previous
The model considered in the main text is repeated here for convenience in level form. Exogenous variables are represented with an overbar, while parameters are denoted with Greek letters.
Non-agricultural labour demand:
Demand for imports:
Level of non-agricultural profits:
Commodity balances and surplus:
The above equations constitute a system of 13 equations in 14 variables, namely Xa, Xn, La, Ln, P , M, w, E, S, T, F, e, pm and pa.
The exogenous variables are the tax rates ta and tm and the international terms of trade . Depending on the way the external sector is closed either F or e can be made exogenous. If both F and e are fixed, as under regime Ar, then the exchange rate utilized for the determination of the domestic prices in (B.12)-(B.13) is the fixed official one, while a new variable is introduced the "rationed" equivalent tariff rate , which is used in the price equation (B.12) to derive the import price that would make the rationed demand for imports equal to the actual demand for imports. The tax revenue in this case is still computed via (B. 10).
The above system is logarithmically differentiated to investigate departures from equilibrium
where the following parameters are defined in the initial equilibrium
share of agricultural labour force in total labour force.
share of agricultural production that is exported.
share of non-agricultural output that is utilized for public consumption and gross domestic investment (public and private).
ratio of imports to GDP.
ratio of exports to GDP.
income elasticities of domestic private consumer demand for agricultural and non-agricultural products.
negative of the own price elasticity of consumer demand for the agricultural product (hence ).
cross-price elasticity of demand of the non-agricultural product with respect to the price of the agricultural product.
Note that the above parameters are not all independent. For instance consider the standard properties of the demand functions, namely that the sum of the income elasticities weighted by the budget shares equals 1 (Engel aggregation), and that the sum of the price elasticities of the demands for the goods with respect to a given price, weighted by the relevant budget shares, is equal to the negative of the budget share of the good, whose price is used in the differentiation. From these we can solve for and as functions of the other two elasticities and the agriculture budget share as follows
Similarly using (B.7) and (B.8) it can easily be shown that
Also can be expressed as follows
Apart then from the import tariff and tax rates there are only seven independent structural parameters in the model, namely , and . These are all both easy to visualize as well as to empirically specify.
Using the same logic that led to (B.35) we can find the ratio of imports to the country's Gross Domestic Product (GDP) Y and the ratio of exports to GDP. In the model specified the country's GDP at international prices is given by
Using (B.36) it is easy to derive the following expressions (remember we have normalized the initial exchange rate e0 to be equal to one)
These expressions prove quite helpful in the empirical specification of the model.
Using the above equations we can derive output supply elasticities for the agricultural and non-agricultural sectors. Combining (B.16), (B.20) and (B.19) we obtain an equation for wage determination
By substituting (B.39) in (B.20) we obtain an expression for . When we introduce this into (B.14) we obtain a supply equation for agriculture
where and are the respective (positive! multipliers. As can be easily seen both of these are positive.
By substituting the expression (B.39) for in (B.15) we find the supply equation for the non-agricultural sector
where are the respective multipliers.
Given the above multipliers, the reduced form multipliers of the surplus and the tax revenue can be derived. Using (B.22), (B.24), (B.39), and (B.43) we obtain
Since it is not clear whether is positive or negative, it is not clear whether is negative or positive. It will most likely be negative. Similarly will also most likely be negative.
Using (B.39) and (B.40) in (B.17) we obtain an expression for the change in imports
Both of the multipliers above are negative.
Using (B.23), (B.39), (B.14) and (B.20) we can also obtain an expression for the change in exports.
The second multiplier above is positive while the sign of the first one is ambiguous.
If we use (B.45) and (B.49) in (B.28) we obtain expressions for the multipliers of the tax revenue. Using the price equations (B.27), (B.28) we obtain
When there is an external financial constraint under flexible exchange rates then the exchange rate adjusts to clear the external constraint, when there is a change in the tax or tariff rates. Using equations (B.26), (B.27), (B.28), (B.48) and (B.49) we derive an equation for the proportional change in the exchange rate
Once this equation is solved for , the change in the exchange rate can be substituted in the expressions for and , in order to derive the elasticities of pa and pm with respect to the changes in the relevant tax rates. These elasticities can then be multiplied by the elasticities of the various other variables with respect to pa and pm.
Notice that if we denote by ea and em the elasticity of the nominal exchange rate with respect to ta and tm respectively, then from (B.51) we have
This relation implies that for every export tax there is an import tariff that has an equivalent impact on the exchange rate. Equivalently the impact on the exchange rate of an export tax can be neutralized by some import tariff.
Under regime Ar, the external financial constraint cannot be accommodated by an adjustment of the exchange rate. In this case the implicit tariff rate of imports must adjust. Using equations (B.26), (B.27), (B.28), (B.48) and (B.49) we can solve for the change in implicit rate of import tariff in response to a change in the rate export tax
Given the attendant changes in the domestic prices
Hence the various multipliers with respect to and can be used in order to predict changes in the various variables.
Available economic and social development papers (ESD) Policy studies group policy analysis division
A. Policy reform and the agricultural sector
No. 65 Agricultural stabilization and structural adjustment policies in developing countries by Alexander H. Sarris (Rome 1987).
No. 66 Agricultural issues in structural adjustment programs by Roger D. Norton (Rome 1987).
No. 84 Measures of protection: methodology, economic interpretation and policy relevance by Pasquale L. Scandizzo (Rome 1989).
No. 90 The impact of stabilization and structural adjustment policies on the rural sector - case studies of Côte d'lvoire, Senegal, Liberia, Zambia and Morocco by Pascal Salin and Emil-Maria Claassen (Rome 1991).
No. 95 Guidelines for monitoring the impact of structure/ adjustment programmes on the agricultural sector by Alexander H.Sarris (Rome 1990).
No. 96 The effects of trade and exchange rate policies on production in agriculture by C. Kirkpatrick and D.Diakosavvas (Rome 1990).
No. 98 Institutional changes in agricultural product and input markets and their impact on agricultural performance by Ann Thomson (Rome 1991).
No. 99 Agricultural labour markets and structural adjustment in Sub Saharan Africa by Lawrence D. Smith (Rome 19911.
No. 100 Structural adjustment and household welfare in rural areas -a micro-economic perspective by Raghav Gaiha (Rome1991 ).
No. 103 The impact of structural adjustment on smallholders by J.M. Boussard (Rome 1992).
No. 104 Structural adjustment policy sequencing in Sub-Saharan Africa by L.D. Smith and Neil Spooner, Glasgow University (Rome 1991).
No. 105 The role of public and private agents in the agricultural sector of developing countries by L.D. Smith and A.Thomson (Rome 1991).
No. 115 Design of poverty alleviation strategy in rural areas by R. Gaiha (Rome, Jan. 1993). B. Environment and sustainable development studies
No.107 Land reform and structural adjustment in Sub-Saharan Africa: controversies and guidelines by J.-Ph. Platteau (Rome 1992). French version "Réforme agraire et ajustement structurel en Afrique subsaharienne: controverses et orientations".
No.110 Agricultural sustainability: definition and implications for agricultural and trade policy by T. Young (Rome 1992).
No.121 Policies for sustainable development: four essays by A.
Markandya (Rome, 1994).
To acquire ESD papers please write to:
Forthcoming ESD papers
Working papers policy studies group policy analysis division
To acquire working papers please write to:
Contents - Previous