This paper proves the Hatta (1977) coefficient is the shadow value of government revenue - it is a scaling coefficient that converts efficiency effects from marginal policy changes into dollar changes in utility. The decomposition is generalised to economies with heterogenous consumers and variable producer prices to show (a) the Foster and Sonnenschein (1970) effect, where extra income reduces consumer utility, makes the shadow value of government revenue negative; and (b) when Bruce and Harris (1982) and Diewert (1983) isolate Pareto improvements they choose patterns of revenue transfers to make the shadow value of government revenue positive for every consumer. We use the decomposition to extend the welfare test in Bruce-Harris by allowing revenue transfers with distorting taxes, and generalise the welfare decomposition of tax inefficiency in Diamond and Mirrlees (1971) by allowing variable producer prices
