True, false, or undetermined? **Text Transcription:**A household with strictly convex preferences may consume only one of two goods.---**Explanation for Educational Context:**This statement addresses consumer behavior, particularly focusing on the concept of "strictly convex preferences," a term often used in microeconomics. In economic theory, strictly convex preferences imply that consumers prefer a mix of different goods rather than consuming only one type of good. However, this scenario highlights a situation where, despite these preferences, a household may end up consuming only one of the available goods. This could be due to budget constraints, price changes, or other external factors affecting their choices.**Note:**There are no graphs or diagrams accompanying the text.

Strict convexity of preferences may be a stronger property than simply plain convexity. Preferences are strictly convex if: for any consumption bundle x, if x1 is prefered over x and x2 is prefered over x with x1≠x2 then for any 0<t<1 tx1+(1-t)x2≻x So, in two dimensions, with strictly monotonic preferences, strict convexity says that if two consumption bundles are each on the identical indifference curve as x, then any point on a line connecting these two points (except for the points themselves) are going to be on a better indifference curve than x. In two dimensions, if indifference curves arestraight lines, then preferences are convex, but not strictly convex.Hence the above statement is False