In the paper we consider some commutator-type and power-type matrix equations in the group UT(∞,K) of infinite dimensional unitriangular matrices over a fieldK. We introduce a notion of a power outer commutator ω1k k (x1, ..., xk) and a power Engel commutator e1k k (x, y) as outer (respectively Engel) commutators modified by allowing powers of letters instead of letters alone. For a given infin...

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In this paper we estimate quadratic food Engel curves with measurement error using the 1994 Ethiopian Urban Household Budget Survey. In sharp contrast to the findings from developed countries, food share is found to increase with expenditure, and only starts to decline after some threshold level of expenditure. We establish the robustness of this inverted-U relationship by estimating a more fle...