Model Structure

The model used for this study is a SPE model. It covers 104 regions of production and 90 regions of consumption. The regional coverage is shown in tables 4-1 and 4-2. The model is a one product model with sugar as the sole product. Sugar is modeled in white sugar equivalents (WSE, = refined equivalents). All demand functions and the supply functions for sugar cane producing countries are isoelastic. The supply functions for beet sugar production in the EU-27 member states, Turkey, Switzerland, Japan and the USA employ a different functional form.⁵⁵ The supply functions do not disaggregate yield and area effects. Supply quantities in the model represent only processed sugar, raw and white. The production of sugar crops for other uses, chiefly ethanol, is ignored.⁵⁶. All demand and supply curves are functions of the own price solely and of effective producer and consumer subsidies. Income elasticities are not modeled explicitly. They are, however, implicitly accounted for in the annual shifters of demand growth over time. Since assumptions about GDP growth do not differ among the various scenarios, the effect is the same. Stocks and stock changes are not

55 The USA is the only country in the model with two supply functions, one for beet sugar and one for cane sugar.

modeled explicitly. All prices are expressed in real 2005 Euro. Effects of different inflation rates and changes in exchange rates are, thus, not accounted for.

Table 4-1: Regional Coverage of the Model – Production Regions

Region Code Region Code Region Code Region Code

Austria AT Benin BEN Barbados BAR Bangladesh BAN

Belgium & BE Burkina BUR Belize BEL China CHN

Luxemburg Faso Canada CAN India IND

Czech Rep. CZ Congo, D.R. CDR Costa Rica COR Indonesia INS

Denmark DK Congo, R. CON Cuba CUB Iran IRN

Spain ES Côte COT Dominican DOM Japan JAP

Finland FI d’Ivoire Rep. Malaysia MLY

France FR Egypt EGY El Salvador ELS Nepal NEP

Germany GE Ethiopia ETH Guatemala GUA Pakistan PAK

Greece GR Gabon GAB Honduras HON Papua New PNG

Hungary HU Guinea GUI Jamaica JAM Guinea

Ireland IE Kenya KEN Mexico MEX Philippines PHI

Italy IT Madagascar MAD Nicaragua NIC Thailand THA

Lithuania LT Malawi MAL Panama PAN Rest of Near RNE Latria LV Mauritius MAU St. Kitts & STK East

Netherlands NL Mali MLI Nevis Rest of RSA

Poland PL Morocco MOR USA-Beet UB South and Portugal PT Mozambique MOZ USA-Cane UC Central Asia Slovenia SI Nigeria NIG Trinidad & TRI Rest of East REA Slovak Rep. SK South Africa SAF Tobago Asia

Sweden SW Senegal SEN Rest of RCA Australia AUS

United UK Sierra Leone SRL Caribbean Fiji FIJ

Kingdom Sudan SUD Argentina ARG Rest of RSO

Bulgaria BUL Swaziland SWA Bolivia BOL South-East Romania ROM Tanzania TAN Brazil BRA Asia and

Turkey TUR Uganda UGA Chile CHL Oceania

Albania ALB Zambia ZAM Columbia COL

Russia RUS Zimbabwe ZIM Ecuador ECU

Serbia SER Rest of Sub RAF Guyana GUY

Switzerland SWI Sahara Paraguay PAR

Rest of REU Africa Peru PER

Europe Suriname SUR

Uruguay URU

Venezuela VEN

Source: Own compilation.

56 The effect of ethanol-based demand for sugar crops is implicitly accounted for by the calibration of technical progress shifters to meet FAPRI (2006) world market price projections.

Table 4-2: Regional Coverage of the Model – Consumption Regions

Region Code Region Code Region Code Region Code

EU-25 EUR Algeria ALG Barbados BAR Bangladesh BAN

Bulgaria BUL Benin BEN Belize BEL China CHN

Switzerland SWI Gabon GAB Honduras HON Guinea

Rest of REU Guinea GUI Jamaica JAM Philippines PHI

In this paragraph the approach of choosing non-isoelastic supply functions for some beet producing countries is briefly explained. It has first been applied for a better representa-tion of the sugar market in the ESIM model by Nolte and Grethe (2007).⁵⁷The most impor-tant reason for the decision not to apply isoelastic supply functions in some countries is that those functions do not allow production to cease at a positive price. Additionally, unless one chooses extremely high elasticity values production cannot even be simulated to decrease

57 For a more detailed explanation the reader may refer to that publication.

considerably, say by 80%, in the case of price changes in the order of size which is envis-aged by the 2006 CMO reform of sugar. To model the effects of large price changes on highly protected beet sugar markets another functional form is chosen. While an isoelastic function is shaped as follows,

β _iγ

i P

S = * (1)

with

i region

Si supply

pi price

β intercept parameter

γ elasticity

the functional form used here contains an (negative) additive intercept, α, on the quantity axis. This allows the function to fall to zero at a positive producer incentive price.

To prohibit the produced quantity to become negative the supply function is put as an argu-ment in a MAX function.⁵⁸

( )

{

^{α β} i^γ

}

i MAX P

S = 0, + * (2)

The shape of two examples of both functional forms is shown in figure 4.1. The quantities as well as the producer incentive prices are equal for both forms in the point of calibration, but decreasing the price leads to different supply responses. At about 60% of the initial price level the production is simulated to cease with the non-isoelastic supply curve in this example.

58 Note that in equation (2) γ is not an elasticity anymore.

Figure 4-1: Functional form of beet supply in the model compared to an isoelastic func-tion

Source: Own Graph.

The whole set of equations of the model looks as follows:

(

_{i i}

)

ⁱ

j

producersubsidyj producer subsidy

α, β, γ, δ parameters of demand and

supply functions ^a

Xsch,j,i trade flows

PSHj rental price for production

quota

PQsch,j,i rental price for TRQ

quotaj production quota

trqsch,j,i TRQ

exw_fasj transportation cost from

fac-tory to port

loadingj vessel loading cost

freightj,i ocean freight

tcsch transaction cost for

preferen-tial schemes

ex_subj,i export subsidy

tar_avsch,j,i ad valorem tariff

tar_spsch,j,i specific tariff

unloadingi vessel unloading cost

inld_transporti transportation cost from port

to place of consumption

a εi and δk are demand and supply elasticities in equations 3 and 4a.

The model is programmed in GAMS (General Algebraic Modeling System) as a MCP and solved with the PATH solver (Dirkse and Ferris, 1995). As described in chapter 4.1.1, the MCP formulation stems from the KT formulation of an underlying optimization problem. The KT conditions require complementary slackness of constraints and slack vari-ables. In the same manner the MCP formulation of a SPE requires each inequality constraint to be mapped with one variable of the same dimension, which is to vanish in case the ine-quality does not hold with strict eine-quality. For the model applied in this study the mapping looks as follows:

j

A lot of features which have been identified as useful for modeling the sugar market in section 2.2 are not implemented in the model used for this study. The most relevant of these are the distinction between raw and white sugar, the accommodation of substitutes in production and consumption of sugar crops and sugar, the separation of modeling of sugar crop production and the first stage of processing and the formulation as a dynamic model to account for time lags in production adjustment. The neglecting of these features is in general due to the limited scope of the study and the limited resources in terms of manpower and data availability. In the last chapter, however, the potential usefulness of a possible future implementation of each of those features will be discussed again in the light of the results obtained in this study.

Im Dokument The future of the world sugar market (Seite 66-72)