# GCAM v5.4 Documentation: Supply of Food, Feed, and Forestry

Documentation for GCAM
The Global Change Analysis Model

View the Project on GitHub JGCRI/gcam-doc

# Supply of Food, Feed, and Forestry

## Inputs to the Module

Table 1: Inputs required by the supply module 1

Name Resolution Unit Source
Land use and land cover By GLU, land type, and year thousand $$km^2$$ Land Allocator
Historical harvested area (used to calculate historical yield) By GLU, crop, management practice, and year thousand $$km^2$$ Exogenous
Historical production (used to calculate historical yield) By GLU, crop, management practice, and year thousand $$km^2$$ Exogenous
Agriculture productivity growth (used to calculate future yield) By GLU, crop, management practice, year % per year Exogenous
Non-fertilizer, non-water, non-land variable cost of production By GLU, crop, management practice, and year 1975$/kg Exogenous Fertilizer coefficients By GLU, crop, management practice, and year 1975$/kg Exogenous
Water coefficients By GLU, crop, management practice, and year 1975$/kg Exogenous Commodity prices By region, commodity, and year 1975$/kg Marketplace
Fertilizer prices By region, commodity, and year 1975$/kg Marketplace Water prices By basin and year 1975$/m3 Marketplace

1: Note that this table differs from the one provided on the Supply Inputs Page in that it lists all inputs to the land supply module, including information passed from other modules. Additionally, the units listed are the units GCAM requires, rather than the units the raw input data uses.

## Description

### Variable Costs

Variable costs are defined here as the non-land costs of crop production, per-unit of crop. We model the cost of fertilizer and water explicitly, including input-output coefficients and prices of each. Other components of variable cost are derived from USDA cost data.

Variable costs set hard price floors in the model: production goes to zero when price is less than or equal to the variable costs. As a result, these costs should be interpreted as pure minimum or shut-down costs. They should be just the cost of materials and hired labor for producing a crop or product with a given technology in a subregion.

Value-added categories are not included in the variable costs. In addition, variable costs do not include land costs, as the model is based on allocating land on per unit profits. They should also not include cost categories that represent return to capital or profits. We can assume these costs are captured in the distribution of profit rates behind the logit. Otherwise, consider that if these costs are put into our variable costs, ultimately all marginal profit rates (from economic theory) would be zero and provide no value to our modeling. In addition, accounting costs such as depreciation should not be part of variable costs.

Data on labor costs can be difficult to use, since some farm wage categories are income that the farmer either earns or expects to be paid and thus, some labor costs are really profit to the land-owner (i.e., farmer). Therefore, we have restricted our variable cost data to include what is labeled as “hired labor”.

Note that introducing variable costs that differ by region can result in unintended consequences. Different variable costs create different price floors, which can result in a region ceasing production of a particular product if technical change lowers the global product price significantly (i.e., to a point where the variable cost is less than the price received).

The main points can be summarized as:

• Variable costs create price floors
• Variable costs should be based on technology data. They should not be used as calibration parameters to adjust profits.
• Variable costs should not include land costs, value-added categories of land, return to capital, and owner-wages.

## Equations

### Profit rate

Profit rate for all agricultural production technologies is calculated as:

$profitRate = 1e9*( price + subsidy - varCost - inputCosts + secondaryValue ) * yield + impliedSubsidy$

where $$price$$ is the commodity price, $$subsidy$$ is any exogenously-specified subsidy, $$varCost$$ is the non-land variable cost, $$inputCosts$$ are the costs of inputs (e.g., fertilizer, water), $$yield$$ is the yield for the technology, and $$impliedSubsidy$$ is an implicit subsidy calculated in the calibration periods to ensure profits are above a specified threshold. Note that the subsidy is multiplied by $$1e9$$, as the land allocator expects profit rates in 1975\$/billion m2.

See calcProfitRate in ag_production_technology.cpp.

### Supply

Agricultural supply is calculated as:

$supply = yield * land$

where $$yield$$ is the yield for the technology and $$land$$ is the land allocation (retrieved from the land allocation module).

See calcSupply in ag_production_technology.cpp.

### Yield

For technologies that have production in the historical period, yield for the historical period is calculated as:

$yield = supply / land$

For all technologies, future yield is calculated as:

$yield_{t} = yield_{t-1} * (1 + APG)^{timestep}$

where $$yield_{t}$$ is the yield in time $$t$$, $$APG$$ is the agricultural productivity growth rate and $$timestep$$ is the number of years between $$t$$ and $$t-1$$.

See initCalc in ag_production_technology.cpp.

## Livestock production

GCAM uses one of two different logit formulations to calculate the shares for each technology or subsector. For livestock, subsectors represent different production systems, where technologies represent different feed sources.

The first option, also known as the relative-cost-logit, is:

$s_i = \frac{\alpha_i c_i^\gamma}{\sum_{j=1}^{N} \alpha_j c_j^\gamma}$

where $$s_i$$ is the share of technology or subsector $$i$$, $$alpha_i$$ is the share weight, $$c_i$$ is the cost of technology or subsector $$i$$, and $$beta$$ is the logit exponent.

The second option, also known as the absolute-cost-logit, is:

$s_i = \frac{\alpha_i \exp(\beta c_i)}{\sum_{j=1}^{N} \alpha_j \exp(\beta c_j)}.$

where $$s_i$$ is the share of technology or subsector $$i$$, $$alpha_i$$ is the share weight, $$c_i$$ is the cost of technology or subsector $$i$$, and $$beta$$ is the logit exponent.

To be completed…

To be completed…

## IAMC Reference Card

Agricultural commodities

• Wheat
• Rice
• Other coarse grains
• Oilseeds
• Sugar crops
• Ruminant meat
• Non-ruminant meat and eggs
• Dairy products