Activity: Algebraic Verification of Convexity for Karim's Preferences

A student is indifferent between two consumption bundles for a weekend: Bundle X, consisting of 10 hours of video gaming and 2 hours of studying, and Bundle Y, consisting of 2 hours of video gaming and 10 hours of studying. A third option, Bundle Z, consists of an exact average of the first two: 6 hours of video gaming and 6 hours of studying. If this student's preferences exhibit the standard property of being convex, how would they rank Bundle Z relative to the other two?

Evaluating a Trade Proposal

Explaining Willingness to Trade

An individual's preferences for coffee and donuts are represented by a standard, downward-sloping indifference curve. Consider two bundles of goods on this same curve: Bundle A consists of 10 cups of coffee and 1 donut, while Bundle B consists of 2 cups of coffee and 5 donuts. Assuming this individual's preferences are convex, which statement accurately describes their willingness to trade?

The Interrelationship of Preference Characteristics

A consumer has many apples and very few oranges. As they acquire more and more oranges, they become willing to trade away an increasingly larger number of apples for each additional orange. This pattern of behavior indicates that the consumer has convex preferences.

An individual has convex preferences for two goods, Pizza (on the vertical axis) and Soda (on the horizontal axis), as represented by a single, downward-sloping indifference curve that is bowed towards the origin. Consider three points on this curve: Point A is located high on the curve (many Pizzas, few Sodas), Point B is in the middle, and Point C is located low on the curve (few Pizzas, many Sodas). Match each point to the statement that accurately describes the consumer's willingness to trade at that location.

The economic principle that explains why a consumer's indifference curve is typically 'bowed inwards' towards the origin, reflecting a decreasing willingness to trade away a good as it becomes scarcer, is known as a diminishing __________.

Identifying Convex Preferences from Indifference Curve Shapes

Evaluating a Marketing Strategy Based on Consumer Preferences