The study employs the basic theoretical foundation of TASM and makes modification on it by incorporating the multiple energy crop possibilities, potential feedstock-energy conversion rates, multiple alternative bioenergy technologies, and associated environmental effects such as GHG emissions offset. The model accommodates more than 110 agricultural commodities, distribution of set-aside land, labor supply and annual crop mixes in Taiwan’s four major production and processing regions. Since the market share of Taiwan’s agricultural commodity is relatively small to the rest of the world, the modified TASM assumes the individual producers and consumers are price takers (that is, the change in Taiwan’s agricultural production does not affect the world commodity prices). Market operations are assumed to be perfect competition with incorporation of input supply and price dependent demand curves. The values of commodities accommodated in the model account for more than 85 percent of Taiwan’s agriculture. Production activities of each commodity, crop and livestock mixes and their constraints are specified at the sub-regional level while the inputs markets such as crop land, forest land and labor are specified at the regional level. The algebraic illustration of the model used in this study is shown briefly as following:

Subject to

where

${Q}_{i}^{G}$ is the government purchase quantity for price supported product

i,

${Q}_{i}^{M}$ is the import quantity of product

i,

Q_{e} is bioenergy technologies,

Qi is quantity of commodity

i,

TRQ_{i} is the import quantity exceeding the quota for TRQ product

i, ${Q}_{i}^{x}$ is export quantity of product

i,

$ED\left({Q}_{i}^{M}\right)$ is the inverse excess import demand curve,

$ES\left({Q}_{i}^{X}\right)$ is the inverse excess export supply curve,

$EXED\left(TR{Q}_{i}\right)$ is the inverse excess demand curve of commodities which import quantity is exceeding quota,

tax_{i} is import tariff for product

i,

outtax_{i} is the out of quota tariff of product

i, P^{L} is the set-aside subsidy,

SUB_{j} is the subsidy on energy crop

j,

AL_{k} is the set-aside acreage in region

k,

EC_{jk} is the planted acreage of energy crop

j in region

k,

${\alpha}_{k}\left({L}_{k}\right)$ is the land inverse supply in region

k,

${\beta}_{k}\left({R}_{k}\right)$ is the labor inverse supply in region

k,

${P}_{i}^{G}$ is the government purchase price of commodity

i, CR

_{ik} is cost of input

i in region

k,

X_{ik} is the production activity of commodity

i in region

k,

Q_{ghg} is quantity of GHG emissions,

Y_{ik} is the total production of commodity

i in region

k,

P_{carbon} is the carbon-equivalent price, and

GHG_{g} is net emission of greenhouse gas

g.

Equation (9) is the objective function that incorporates Taiwan’s agricultural activities with various domestic and trade policies. Government subsidies on rice purchase, set-aside land and energy crops plantation that are influencing the social welfare in terms of quantity supply and demand are incorporated. These terms represent the social welfare in a closed market. All GHG emissions from various sources will be converted into carbon equivalent and the international carbon trading price is the basis of GHG payment. The relationship between social welfare and net GHG emissions is negative.

Equation (10) balances commodities, showing that the demand of commodity plus import should be less than or equal to its supply plus export. Equations (11) and (12) represent the resource endowment constraints by balancing the land and other resources usage. Equation (13) balances greenhouse gas components by constraining the net emissions from agricultural sector such that they cannot be greater than Taiwan’s total emissions. Because it is difficult to test the robustness of a mathematical model, as any change in policies, production data, output ratio and resource constraints may considerably influence the results, we compare the simulation results to actual statistics [

3,

8]. The total production and prices, and the cop yields are adjusted to calibrate TASM. The model validation result shows that most of the discrepancies between model results and actual agricultural data are within 6% range, indicating that the model should be suitable for simulation.