c) In case of convex consumer preferences, any point that satisfies the tangency condition must be an optimal point. Is this statement true or false? Explain
False.
In the case of convex consumer preferences, any point that satisfies the tangency condition may be an optimal point, but it is not necessarily true for all cases. Convex preferences imply that the consumer prefers a diverse set of goods, and in some situations, there may be multiple points that satisfy the tangency condition. In these cases, the optimal point may not be unique and could be one of the tangency points.
Additionally, other factors such as the budget constraint, the prices of goods, and the consumers' individual preferences can also influence the optimal point. Therefore, while the tangency condition is an important criterion in determining optimality, it is not the sole determinant, and further analysis may be required to identify the optimal point.