Cobb-Douglas Utility with Nonlinear Engel Curves in a Conspicuous Consumption Model

We solve Ireland's (1994) conspicuous consumption model (where social-status concerns are introduced into the utility function) for Cobb-Douglas (CD) utility. In the resulting generalized CD consumer model, Engel curves are no longer limited to linearity. In the homothetic CD case, total expenditure elasticities are therefore no longer limited to unity. Furthermore, whether a commodity is a luxury or a necessity is determined by whether it is visible or non-visible to society. Cross-commodity variation in the shape of Engel curves is thus derived from a measurable property of commodities. This reopens the possibility of explaining empirically observed consumption patterns with a CD utility model