In general, uncompensated cross-price effects are not equal. That is, \\[\frac{\partial x_{i}}{\partial p_{j}} \neq \frac{\partial x_{j}}{\partial p_{i}}.\\] regardless of relative prices. (This is a generalization of Problem \(6.1 .)\)

Let's consider the demand functions for two goods, \(x_i\) and \(x_j\). These demand functions represent the quantity demanded of goods \(i\) and \(j\) respectively, and depend on their respective prices \(p_i\) and \(p_j\). The demand functions can be written as: $$ x_i = x_i(p_i, p_j) $$ $$ x_j = x_j(p_i, p_j) $$

Next, we need to find the cross-price effects by calculating the partial derivatives of the demand functions with respect to the other good's price. This will give us: $$ \frac{\partial x_i}{\partial p_j} = \frac{\partial x_i(p_i, p_j)}{\partial p_j} $$ and $$ \frac{\partial x_j}{\partial p_i} = \frac{\partial x_j(p_i, p_j)}{\partial p_i} $$

Now we need to compare the cross-price effects by examining if the inequality holds true: $$ \frac{\partial x_i}{\partial p_j} \neq \frac{\partial x_j}{\partial p_i} $$ We can't determine if the inequality holds true for every possible pair of demand functions, as it depends on the specific functional forms and the price changes involved. However, typically in economics, it is reasonable to assume that this inequality holds true in general, since the cross-price effects depend on the responsiveness of one good's demand to the price change of another good and this responsiveness may vary between goods. In conclusion, the given assertion is generally correct for most cases, but it may not hold true in every specific situation. It is important for students to understand the concept of cross-price effects and consider the specific context when analyzing these relationships.