**Appendix A**

Here we present a formal model that led us to the Proposition in Section 2.1, that utility is higher when a durable good is possessed longer, all else being equal. In the basic model, let *C*1*t*, *C*2*t*,*C*1*t*+1, and *C*2*t*+<sup>1</sup> denote Goods 1 and 2 bought at *t* and *t* + 1, respectively. As described in the main text, to fix ideas, imagine that Good 1 is a mix of general consumer material good, whereas Good 2 is a relatively durable, but still material consumer good. The prices of both goods are constant and certain, expressed by *p*1 and *p*2, respectively. Because this is an intertemporal problem, we wrote δ > 0 for the utility discount rate and *r* > 0 as the interest rate. For analytical ease, the (instantaneous) utility function is further specified as additive: *<sup>U</sup>*(*<sup>C</sup>*1*t*, *<sup>C</sup>*2*t*) = *C*21*t* + *<sup>C</sup>*22*t*. Other typical specifications such as Cobb–Douglas or the constant elasticity of substitution (CES) utility functions do not alter our basic insights. Finally, the consumer earns income

*w* only in *t*, part of which is saved for the period *t* + 1. Formally, our problem is

$$\max\_{\mathbf{C}\_{1t}, \mathbf{C}\_{2t}, \mathbf{C}\_{1t+1}, \mathbf{C}\_{2t+1}} \mathcal{U}(\mathbf{C}\_{1t}, \mathbf{C}\_{2t}) + \frac{1}{1+\delta} \mathcal{U}(\mathbf{C}\_{1t+1}, \mathbf{C}\_{2t+1})$$

subject to

$$p\_1\mathcal{C}\_{1t} + p\_2\mathcal{C}\_{2t} + \frac{1}{1+r}(p\_1\mathcal{C}\_{1t+1} + p\_2\mathcal{C}\_{2t+1}) = w\_t$$

A regular optimization exercise enabled us to solve for the consumption of two goods in both periods and to write indirect utility as a function of wage, prices, discount rate, and interest rate.

In the extended model, where Good 2 continues to be possessed, our problem changes slightly to the following:

$$\max\_{\mathbf{C}\_{1t}, \mathbf{C}\_{2t}, \mathbf{C}\_{1t+1}} \mathcal{U}(\mathbf{C}\_{1t}, \mathbf{C}\_{2t}) + \frac{1}{1+\delta} \mathcal{U}(\mathbf{C}\_{1t+1}, \mathbf{C}\_{2t+1})$$

subject to

$$p\_1\mathcal{C}\_{1t} + p\_2\mathcal{C}\_{2t} + \frac{1}{1+r} \, p\_1\mathcal{C}\_{1t+1} = w$$

and

$$
\mathbb{C}\_{2t} = \mathbb{C}\_{2t+1}.
$$

Observe that the first constraint lacks Good 2 in the second period, as it does not have to be purchased. In addition, the second constraint states that the quantity of Good 2 consumed in the next period remains the same. It is commonplace to assume that investment goods are subject to depreciation; this assumption can be applied to our example. On the other hand, we have already seen that some behavioral literature suggests a positive endowment effect can also be attained from durable goods, in which case the value of the good being studied actually appreciates for that person. In any case, we bypassed the endowment effect here, as it is contained in M in the current formulation. Thus, temporal changes in the value of Good 2 to the consumer may be either positive or negative. We relegated more general cases to our future research, and simply assumed the second constraint in the current study.
