Consider the following (non-standard) utility maximisation problem : \begin{eqnarray*} \max_{x, y} \ & x^{p^2}y \\ \text{s.t.} \ & px+y\leq M\end{eqnarray*} Here, $p > 0$ is the price of commodity $X$. In this situation, we can think of $X$ as a Veblen good. Solving this problem, we get the demand for $X$ as: $x^d(p, M)=\left(\frac{p}{1+p^2}\right)M$ which is an increasing function of both price $p$ and income $M$. So, it is not a giffen good, but still has a demand that is increasing in price.

Related Answer: https://qr.ae/pveKFJ

Consider the following (non-standard) utility maximisation problem : \begin{eqnarray*} \max_{x, y} \ & x^{p^2}y \\ \text{s.t.} \ & px+y\leq M\end{eqnarray*} Here, $0 < p < 1$ is the price of commodity $X$. In this situation, we can think of $X$ as a Veblen good. Solving this problem, we get the demand for $X$ as: $x^d(p, M)=\left(\frac{p}{1+p^2}\right)M$ which is an increasing function of both price $p \in (0, 1)$ and income $M$. So, it is not a giffen good, but still has a demand that is increasing in price.

Related Answer: https://qr.ae/pveKFJ