Cultivation of Taste, Catastrophe Theory, and the Demand for Works of Art

In the process of cultivation of taste, tastes are changed by the experience of consumption. To model this we might assume that cultivation of taste for a particular good involves a change in only one parameter of the utility function, and that the other parameters, that is, the "underlying" utility function, remains unchanged. For example, assume that there are just two goods, x and z, of which x is subject to cultivation of taste, and z is not. Then