Fragility of value is used correctly only to make very different points from what you are stating here, that must result from how different the preference orderings you obtain are from the original preference orderings if you make changes to the complex computation that the values are. Consumer preferences in general equilibrium theory are a real-valued function whose domain is the consumption set, a subset of a full commodity space. This function can be used to define an order relation that represents the consumer’s preferences, each represented by any of an infinity of functions since you can compose them with any strictly increasing function. Consumer preferences are not the same thing as agents’ preferences or values, which are not at all related to commodity bundles, and don’t have a consumption space as domain, even though they too can be used to define order relations. You cannot make this argument confusing goods and values. The values that are fragile are not the consumer preferences. As far as the actual preferences determine consumer preferences over commodity bundles, they determine the customer’s demand function according to prices and consumer endowments or wealth and translate into buying and selling decisions, and that is relevant to perfect competition. The rest of the preferences is entirely orthogonal to perfect competition—if it wasn’t, then it would, contradicting our assumption, have contributed to determining consumer preferences.
Fragility of value is used correctly only to make very different points from what you are stating here, that must result from how different the preference orderings you obtain are from the original preference orderings if you make changes to the complex computation that the values are. Consumer preferences in general equilibrium theory are a real-valued function whose domain is the consumption set, a subset of a full commodity space. This function can be used to define an order relation that represents the consumer’s preferences, each represented by any of an infinity of functions since you can compose them with any strictly increasing function. Consumer preferences are not the same thing as agents’ preferences or values, which are not at all related to commodity bundles, and don’t have a consumption space as domain, even though they too can be used to define order relations. You cannot make this argument confusing goods and values. The values that are fragile are not the consumer preferences. As far as the actual preferences determine consumer preferences over commodity bundles, they determine the customer’s demand function according to prices and consumer endowments or wealth and translate into buying and selling decisions, and that is relevant to perfect competition. The rest of the preferences is entirely orthogonal to perfect competition—if it wasn’t, then it would, contradicting our assumption, have contributed to determining consumer preferences.