If the partial derivative of the ordinary demand for a good is −1 (i.e. ∂x∗/∂px = −1), the good is
(a) Giffen and Inferior (b) Giffen and Normal
(c) Ordinary and Inferior (d) Ordinary and Normal
(e) Else / Insufficient information to answer
The answer is (b) Giffen and Normal.
A Giffen good is a type of inferior good for which an increase in price leads to an increase in quantity demanded. This goes against the typical economic intuition that an increase in price leads to a decrease in quantity demanded. Therefore, in order for a good to be Giffen, the partial derivative of the demand with respect to price (∂x*/∂px) must be positive.
In this case, the partial derivative of the demand with respect to price (∂x*/∂px) is -1. Since it is negative, it indicates a normal good, not an inferior good. Therefore, the good cannot be Giffen and must be normal.