A set of linear expenditure functions for k commodity groups comprising all consumers' expenditure is constructed which contains 2k + 1 regression coefficients, one of them common to all k equations. The regression coefficientsare obtained by the least squares method, and their economic meaning is discussed. The method is applied to expenditure per head on 11 commodity groups in the United Kingdom, 1948-57. Estimates for income elasticities of demand and for shifts in demand are obtained, and their reliability is examined.