Properties of the Demand Function
Besides the adding up condition that can conveniently be solved, the homogeneity and symmetry conditions were also tested. The homogeneity condition is also known as the ―absence of money illusion‖ since the units in which prices and
outlay are expressed have no effect on purchases (Deaton and Meulbauer, 1980).Basically, the homogeneity condition implies that if all prices and income are multiplied by a positive constant, say θ, the quantity demanded must remain
unchanged. The symmetry condition restricts cross price derivatives of the demand functions to be identical. The Wald test was employed to test whether the homogeneity and symmetry conditions hold. The test results show that the
homogeneity condition holds at 5% level of significance for all three main equations.The fourth equation (Others) represents the market share of coffee imported in Japan from the countries other than the three main countries of interest. The result from estimating this equation is not paid much attention since the data are aggregated from more than 19 countries, and, therefore, it gives less applicable interpretation. In addition, the null hypothesis of whether the symmetry restriction holds was not rejected for two of the three main equations (Table 12)