## Elasticities (30 minute read)

##### Learning Outcome:

At the end of this lesson, you will be able to define the elasticities used in a CGE model and describe how their values determine consumer and producer behavior.

##### The Elasticity Database

Elasticities describe the flexibility of producers and consumers to adjust the quantities they produce or buy in response to changes in prices and income. Together with the SAM, elasticities are part of the CGE model database.

Elasticities are “parameters” in CGE models. That means that their values remain fixed at their initial level, before and after a model experiment. The values are defined by the modeler using the best available estimates of supply and demand elasticities for the country under study. Elasticities are often packaged as part of CGE model databases, such as the GTAP global CGE database. The modeler can change these default elasticity values if they find better or updated sources of information on the parameters, or if they want to change elasticity values to test the sensitivity of experiment results to different values.

##### Elasticities in the UNI-CGE Model

There are five elasticity parameters in the UNI-CGE model (Table 1). In addition, the Frisch parameter is required by the Linear Expenditure System (LES), which describes household consumer demand.

The first column of Table 1 reports the name of the parameter. Elasticities whose names start with “ESUB” are Elasticities of SUBstitution that are used in Constant Elasticity of Substitution (CES) functions. Elasticities whose names starts with “ETRA” are Elasticities of TRAnsformation that are used in Constant Elasticity of Transformation (CET) functions. CES and CET functions are called "constant" because their elasticity parameter values remain the same for any combination of goods and at any level of consumption or output. (You can learn more about these functions in the Reference Material on CES and CET functions.)

Each parameter has a “dimension,” which is the set(s) over which the elasticity is defined. For example, the factor substitution elasticity, ESUBVA, is defined over set A, which is the set of production activities. If your model has two production activities – such as agriculture and manufacturing - then you will have two factor substitution elasticities, one for each activity. The values of the elasticity parameters for the elements within a set can vary. For example, agriculture may have a low factor substitution elasticity while manufacturing may have a high factor substitution elasticity.

**Table 1. Elasticity Parameters in the UNI-CGE Model**

View large type version of table HERE.

*ESUBVA - the factor substitution elasticity *

The first elasticity in Table 1, parameter ESUBVAa, is used in the CES value-added function. One elasticity is defined for each production activity A. ESUBVA describes the flexibility of producers to substitute among factor inputs when relative factor prices change. The ESUBVA parameter value ranges between zero and infinity.

- When the parameter value is low, producers cannot easily switch between labor, capital and other factors, even if there are large changes in their relative costs.

- When the parameter value is high, producers can easily substitute factors even when factor price changes are small. For example, companies will readily automate their jobs if wages rise.

*ESUBQ - the domestic-import "Armington" elasticity*

Parameter ESUBQ is called the "Armington" elasticity. One elasticity is defined for each commodity C. ESUBQ is used in the CES import aggregation function. It describes the willingness of consumers to substitute between domestic and imported varieties of the same good when their relative prices change. The ESUBQ parameter value ranges between zero and infinity.

- When the parameter value is low, consumers have strong preferences and are reluctant to shift between the domestic and imported varieties, even if there are large changes in their relative prices.
- When the parameter value is high, consumers are relatively indifferent about sourcing, and will readily shift between domestic and imported varieties in response to even small changes in their relative prices.

*ETRAX - the export supply elasticity*

Parameter ETRAX is used in the CET export supply function. One elasticity is defined for each commodity C. Like the ESUBVA parameter, it describes the flexibility of production technologies. It governs how easy it is for producers to switch their sales of a commodity between the domestic and export markets. ETRAX has a negative value ranging between zero and negative infinity. 1/ - When the absolute value of the parameter low, it is costly for producers to shift their sales between the domestic and export markets. Perhaps the two markets have different labeling requirements or product standards. Producers will make minimal shifts of their products between the two markets even if there are large changes in the relative sales prices.

- When the absolute value of the parameter is high, the cost to shift products between the two market is minimal. Producers will readily shift their production lines between domestic and exported varieties in response to even small changes in their relative prices.

*ELES - the income elasticity of demand*

The income elasticity of demand, ELES_{c,h}, is used in the LES demand system to describe household consumers' demand behavior. One elasticity is defined for each commodity and each household type in the model. ELES defines the percent change in the quantity of each commodity demanded by each household type given a percentage change in their income. Income elasticities have positive values in the UNI-CGE model, ensuring that all goods are normal (as income grows, so does demand for every commodity). The parameter value can range from zero to infinity.

- When the ELES parameter has a value of less than one, the percentage change in the quantity demanded will be less than the percentage change in income.
- When the ELES parameter is equal to one, the quantity demanded will change by the same proportion as income.
- When the ELES parameter has a value greater than one, the commodity is a luxury good. The quantity demanded will change by more than the percentage change in income.

*EDE - foreign export demand*

Single-country CGE models like the UNI-CGE model describe foreign demand for a country's exports using a simple, linear export demand function. The foreign demand elasticity, EDEc, describes the quantities of foreign demand as a function of the home country's world export price. The parameter has a negative value between zero and minus infinity. 1/

- When the absolute value of the parameter is low, export demand is inelastic. A low EDE value describes the exporting country as large in world markets, because even a large change in its export price will have minimal effects on the quantity demanded by foreign markets. That is, foreign countries have little choice but to accept the exporter's price.

- When the absolute value of the parameter is high, export demand is very elastic. A high EDE value describes the exporting country as small in world markets because even small changes in its export price will lead to large changes in export quantities. Foreign countries can easily shift to or from alternate suppliers if the exporter's price changes.

*Frisch parameter*

The Frisch parameter is not an elasticity, but it is part of the UNI-CGE elasticity data base. The parameter is used in the LES household consumer demand equation to describe the share of subsistence requirements in household spending. One parameter is defined for each household type. It has a negative value, and as its absolute value becomes larger, the share of spending on subsistence goods rises and the share of discretionary spending falls. Frisch parameter values are typically defined to be between - 1 (no subsistence requirements) for higher income countries and -4 for lower-income countries.

Transforming Elasticities into Exponents (Rho)The elasticities used in the CES and CET equations in the UNI-CGE model are not used directly in model equations. They are transformed into rho (ρ) terms that are used in the nonlinear equations that describe producers' CES decision on the ratio of factors to use in their production process, and their CET decision on the shares of domestic and export sales in their output. A rho exponent is also used to describe the CES consumer decision on the shares of imported and domestic varieties in consumption.

As
an example, the equation for the cost-minimizing quantity shares of imported (QM) and domestic (QD) varieties in the consumption of a commodity is:

where δ is the share of the domestic variety in total consumption, (1- δ) is the share of imports in consumption, PD is the price of the domestic variety, PM is the price of the imported variety, and exponent rhoq is the transformation of elasticity
ESUBQ.

The fourth column in Table 1 presents calculations that describe how the CES and CET elasticities in the UNI-CGE model are transformed into rho exponents used in model equations.

1/ Elasticity parameters in the country data files are all expressed as positive numbers. The model equations transform them into negative values when appropriate.

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How Elasticity Values Influence Model Results

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