Private household (GTAP)

Definition

The private expenditure UP is allocated to the demand by sectors qp with CDE function to capture the constrained optimizing behavior of private consumption

Linearized form

First of all, we can write the linearized form of commodity demand with the generic demand equation, from total derivation of utility maximization function of indirect utility function:

where i and j are TRAD_COMM

Note: at this stage, the generic demand equation does not depend on certain functional form of the utility function

Specific functional form

In order to obtain the parameter of EP and EY, we need to assign a specific functional form of the uitlity function.

There are multiple choices of household utility function, each has their features, advantage and disadvantage:

• Cobb-Douglas
  • fixed budget share
  • not parameters to estimate
• Linear expenditure system
  • fixed marginal budget shares
  • N parameters to estimate (N is the number of sectors)
    • N-1 marginal shares
    • share of luxury in total expenditure
• CES function
  • 1 parameter to estimate
• Constant difference of elasticity (CDE) function
  • Based on duality
  • Make use to 2N elasticities
    • N own price elasticities
    • N income elasticities

We use CDE function to represent non-homothetic utility. Recall that the homothetic utility has the following features:

• homogeneous at degree of 1.
• When wealth increases, ratio between consumption of goods do not change, or increase of wealth changes the quantity of consumption. but not the pattern of consumption
• In other words, taste do not change with time

The homothetic utility function is easy to use, but may not satisfy real world cases. That's why we would like to represent non-homothetic utility

Parameters EP and EY are functions of the expenditure share and the preference parameters in the CDE function

Note

Example