Dear Professor Pfeifer,

I want to measure the welfare variation using consumption equivalent. I know how to do this when there is only one type of household. While in the model with heterogenous household as patient and impatient, I am confused on how to deal with the consumption compensation parameter \lambda.

e.g. The two untility function of households with compensation parameters are:

{{E}_{t}}\sum\limits_{k=0}^{\infty }{\beta _{P}^{k}\left[ \log \left( 1+{{\lambda }^{P}} \right)c_{t+k}^{P}-\frac{1}{1+{{\phi }^{P}}}{{\left( n_{t+k}^{P} \right)}^{1+{{\phi }^{P}}}} \right]}

{{E}_{t}}\sum\limits_{k=0}^{\infty }{\beta _{I}^{k}\left[ \log \left( 1+{{\lambda }^{I}} \right)c_{t+k}^{I}-\frac{1}{1+{{\phi }^{I}}}{{\left( n_{t+k}^{I} \right)}^{1+{{\phi }^{I}}}} \right]}

There are two compensation parameters(\lambda^{P} and \lambda^{I}) now. I can calculate them respectively, while how should I get an aggregate compensation parameter? \lambda^{P}+\lambda^{I} seems not make any sense?

Thank your for your time.