Can someone please explain the difference between these, and how they apply to someone that has monotonic preferences? I have read in the book but they all seem to be running together and am so confused! Thank you.
Symmetry
Convexity
Local Non-satiation
Transitivity
Completeness
Sure! I'd be happy to explain the differences between these concepts and how they apply to someone with monotonic preferences. Let's go through each one individually:
1. Symmetry: Symmetry is a property that states that if two options or bundles are identical to each other, then they should be equally desirable. In other words, if someone has monotonic preferences, it means that they have a set of preferences that do not change as long as the options being compared are the same. For example, if you have two identical apples, you should have the same level of preference for each of them. This implies that any preference orderings should respect this symmetry condition.
2. Convexity: Convexity refers to the idea that if two options are mixed in any proportion, then the resulting mixed option should be at least as desirable as the original options. In other words, if someone has monotonic preferences, it means that they have consistent preferences for combinations of goods. For example, if you like apples and oranges individually, then you should also like a mix of apples and oranges (like a fruit salad) to some degree. This implies that any preference orderings should satisfy the convexity condition.
3. Local Non-satiation: Local non-satiation states that if someone has monotonic preferences, they always prefer more of a good to less of it. This means that if you have a positive preference for something, then you would always want more of it if given the option. For example, if you like ice cream, you would always prefer to have more scoops rather than fewer. This implies that any preference orderings should follow the local non-satiation condition.
4. Transitivity: Transitivity is a property that states that if you prefer option A to option B, and you prefer option B to option C, then you must also prefer option A to option C. In other words, if someone has monotonic preferences, it means that their preferences are consistent and logical. For example, if you prefer vanilla ice cream over chocolate ice cream, and you also prefer chocolate ice cream over strawberry ice cream, then you must prefer vanilla ice cream over strawberry ice cream. This implies that any preference orderings should adhere to the transitivity condition.
5. Completeness: Completeness is the property that states that for any two options or bundles, it should be possible to compare them and determine a preference order. In other words, if someone has monotonic preferences, it means that they have clear and unambiguous preferences for every pair of options. For example, if you are given two choices, like going to the movies or staying at home, you should be able to clearly indicate which option you prefer. This implies that any preference orderings should satisfy the completeness condition.
So, to summarize, symmetry, convexity, local non-satiation, transitivity, and completeness are all important concepts in economics that help us understand how individuals make choices based on their preferences. If someone has monotonic preferences, it means that their preferences are consistent and follow these properties.