To derive the Marshallian demand curve for an inferior good in a two-commodity framework (say, goods X and Y), we use the concepts of substitution effect (SE) and income effect (IE). Assume good X is inferior.

When the price of X falls, two forces act:

1. Substitution Effect (SE):
   This effect isolates the impact of the relative price change, keeping real income constant. Since X becomes cheaper relative to Y, the consumer substitutes X for Y, increasing the quantity demanded of X. Importantly, the substitution effect is always positive for a price fall—demand for the cheaper good rises. Graphically, this movement occurs along the original indifference curve.
    
2. Income Effect (IE):
   The fall in X’s price raises the consumer’s real income (purchasing power). With the same money income, more of both goods can be purchased. For an inferior good, higher real income leads to lower demand, as consumers shift to superior substitutes. Thus, the income effect is negative for X.
    

The Total Price Effect (TPE) is the sum of these two effects:

TPE=SE+IETPE = SE + IETPE=SE+IE

• If |SE| > |IE|, the substitution effect dominates. Demand for X still rises when its price falls. In this case, the Marshallian demand curve for the inferior good remains negatively sloped, which is the usual situation.
   
• If |IE| > |SE|, the negative income effect outweighs the substitution effect. A fall in X’s price then causes demand for X to fall. This rare case produces a positively sloped demand curve. Such a commodity is termed a Giffen good.
   

Thus, while all Giffen goods are inferior, not all inferior goods are Giffen. In most practical cases, the substitution effect dominates, giving the inferior good a downward-sloping demand curve. Only in exceptional cases, when the income effect is overwhelmingly strong, does the curve slope upward.