Three essays in demand analysis
In this study, flexible representation of consumer demand systems is investigated within the framework afforded by duality in consumer theory. The first essay examines the market situation where supplies are inelastic and prices must adjust to clear the market, a situation that arises for most agricultural commodities, particularly for perishable commodities. A price dependent or inverse demand system can reflect such a market situation. Two flexible inverse demand systems are proposed. The first of these is a linear inverse demand system (LIDS) derived from a flexible specification of a distance function, and presents a particularly convenient system of linear equations. A simulation exercise reveals that the LIDS performs as well and in fact slightly better than the older inverse Translog system. However, in order to specify market demands, aggregation conditions need to hold. A new system of inverse share dependent equations belonging to the class of quasi-homothetic preferences is also proposed;Between the two polar cases of direct and inverse demands lies the class of 'mixed' demands where the prices of some goods and the quantities (demanded) of others adjust to clear the market. However, the existing theoretical framework for mixed demands does not allow a convenient transition to an empirical model. The concept of 'shadow' price is used in developing a theoretical framework that does allow the specification of an empirical mixed demand system. The Slutsky equations are derived, the elasticity forms of which are implemented in a differential approximation of the mixed demand system. The empirical context is provided by the Canadian market for meats where free trade with the U.S. in beef and pork makes Canada a price taker for these commodities, while for poultry, domestic marketing boards restrict the supply, and prices must adjust to clear the markets;The notion of separability is frequently invoked in applied demand analysis. In general, separability is a strong maintained hypothesis and should ideally be tested before it is maintained. However, while the alternative of imposing local separability on a Flexible Functional Form (FFF) exists, imposing global separability parametrically on most of the commonly used FFFs renders them inflexible. In the third essay, the ability of a recently proposed globally separable FFF, as well as that of the locally separable model, in providing correct inferences about separability is examined in a Monte Carlo study.