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What are tastes referring to?

I have always considered them to be the instantaneous part of dynamic utility function:

$$U = u_1(x_1) + u_2(x_2) + \dots u_t(x_t)$$

Where $u_s$ denotes tastes in the following (instantaneous) sense:

"Beer tastes me more than wine" or "bread will taste me more than baguette"

However, when reading Becker's Accounting for tastes, I get the feeling that tastes describe rather those overall feelings of a person, hence, the whole (overall) utility function.

Therefore, when speaking about "changing tastes", are economists usually speaking about $u_1 \neq u_2$ or about general shifts in $U$?

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The most common view in economics of what changing tastes are is in terms of Strotz-Pollak-type multiple-selves models. There, the overall evaluation of future consumption streams changes. The way you've written down the problem doesn't really allow one to formulate this.

Here is a setting that illustrates the basic structure: There is a space of instantaneous consumptions $X$ and for each period $T$ a utility function $U^T:X^{T-1}\times X^\infty\to\mathbb{R}$. Consumption streams are infinite to save on notation. The interpretation is that $U^T$ gives in period $T$, depending on past consumption in $X^{T-1}$, preferences over future consumption streams in $X^\infty$. If tastes never change, we would have for two consumption streams $(x_1,\ldots,x_{T-1},x_T,x_{T+1},\ldots)$ and $(x_1,\ldots,x_{T-1},y_T,y_{T+1}\ldots)$ that have the same consumption in the first $T-1$ periods that $$U^1(x_1,\ldots,x_{T-1},x_T,x_{T+1},\ldots)\geq U^1(x_1,\ldots,x_{T-1},y_T,y_{T+1}\ldots)$$ holds if and only if $$U^T\big((x_1,\ldots,x_{T-1}),(x_T,x_{T+1},\ldots)\big)\geq U^T\big((x_1,\ldots,x_{T-1}),(y_T,y_{T+1},\ldots)\big).$$ If this is not the case, tastes change. Since people have different preferences at different periods, there are many ways to model the resulting actual behavior between the various "selves."

In this formulation, preferences need not be additively separable, and no instantaneous utility function needs to exist. However, we may assume such a representation. Then, there are for any two periods $T$ and $t$ a function $u_t^T$ such that $$U^T\big((x_1,\ldots,x_{T-1}),(x_T,x_{T+1},\ldots)\big)=u_1^T(x_1)+\ldots+u^T_{T_1}+\sum_{h=0}^\infty u^T_{T+h}(x_{T+h}).$$ In such a setting, past consumption is irrelevant.

The approach of Becker and Stigler is one in which tastes never change, but preferences over future consumption can depend on past consumption via some aggregates they view as capital. They argue that this can account for most situations in which tastes seemingly change. Becker's book elaborates on the point. But from the perspective of most economists working on changing tastes, Becker is arguing that preferences are not or, at least, that they are best interpreted as not changing.

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