Suppose we consider four different demand curves for four goods, identical except their degree of inferiority. D1 is a good with fairly elastic demand, a normal good. D2 is slightly less so probably still a normal good but with a smaller income effect. D3 is the demand curve for an inferior good, the income effect works against the substitution effect but demand is still downward sloping but quite inelastic. However, D4 is the demand curve for a Giffen good.
Inferiority for this good is so great that the income effect overwhelms the substitution effect causing the slope of the demand curve to be positive.
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