If the utility function (1) is linear homogenous, rather than only homothetic, the welfare implications of liberalization in this case are especially easy to analyze. As noted in Shoven and Whalley (1992), with linear homogenous preferences the Hicksian compensating variation measure of welfare change between equilibria is
where UhN and Uq refer to the old and new utility levels for household h, and IhN is the income of household h in the new (post change) equilibrium.
Because price and quantities do not change between equilibria, and because the term ST is multiplicative in utility from goods and own services, each household’s compensating variation can be written as
where the Я terms cancel, and STN and ST° denote the aggregate service consumption values relevant for household h in the new and base period (original) equilibria. 1% is household h new period equilibrium income.
If preferences are identical across the households in each country, the total welfare impact in the two countries, TCV1 and TCV2, can be written as
where ST® and ST” refer to the base case aggregate service consumption in countries 1 and 2, Wj and W2 are economy wide incomes in country 1 and 2 from (2), and again the Л terms cancel.
The ratio of the welfare gains in the two countries from liberalization is given