Derive Marshallian demand curve for an inferior good in a two-commodity framework by using income and substitution effects. Is this demand curve always negatively sloped ? Explain.
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:
The Total Price Effect (TPE) is the sum of these two effects:
TPE=SE+IETPE = SE + IETPE=SE+IE
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.
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