The parameter r can be interpreted as the experienced quality of the relational good, since it measures the benefit per time unit provided by the relational good for the individual’s utility. The quality of the relational goods experienced by an individual during one of the two periods of his/her life can be explained by means of the following function:

(15) r = f (D)

where D is a vector of n elements (Di) representing the personal dispositions of a number of people who experience close relationships with the reference individual. The number n, which is assumed equal and constant for each individual, is a subset of the population, and it includes the individual him/herself.

Let us assume for simplicity that the personal disposition of adults assumes only two values: a minimum level, D^m, and a maximum one, D^M. By contrast, youths assume only one value, i.e. D^M.

The function f is positive and concave in all the elements, and it exhibits constant returns to scale. For simplicity sake we ignore the fact that the market good may determine r. However, marginal R is generally affected by the marginal amount of economic goods consumed by the individual through the complementarity/substitutability link between the two types of goods in the utility function. Therefore, r can assume any value within a minimum level, which occurs when the dispositions of all the n individuals are at the minimum (D^m), and a maximum level when all the n individuals are at the maximum (D^M). Let us assume that f normalises r, so that its extreme values are in the neighbourhood of 0, and equal to 1 respectively, i.e.:

Disappointment, and the reactions of three groups of people

Let us distinguish between the experienced quality (r) from the expected quality of the relational good r^e. The analogous distinction is less relevant for the market good, since in this case the quality is objectively the same for everyone, and it is thus more easily evaluated through both own consumption and consumption by others. Relational goods reflect the creative aspect of people within relationships, which makes them special goods, and difficult to predict, as discussed in Section 3.

Over re the individual takes the decision on her/his time allocation, expecting a level of utility U^e. However, r^e may turn out to be different from r, and hence U^e is different from U, for the same individual in the same period. Since youths are driven from infancy by the need for relatedness and have no previous experience to draw upon, then e r^e_y =1. During youth, r_y is experienced within ]0,1], so that either a disappointment ( r^e_y>r_y) or a confirmation ( r^e_y=r_y) may occur. Let us also assume that different degrees of disappointment stimulate three different reactions by individuals, so that they can be collected in three groups.

Table 2 ranks the degrees of disappointment of three groups of individuals (I)-(III) who become adult according to two intermediate thresholds (s and S), and it accounts for four characterisations (i)-(iv) of their reaction which may remain outside consciousness. The reaction is characterised by the individual’s (i) expectation r^e_a , (ii) feeling for and understanding of others (mindsight), (iii) consideration of others, insofar as this is captured by the parameter measuring the substitutability of relational goods with market goods sa, and (iv) disposition to others (Do,a). The Table follows the arguments and justifications of Section 3, where the 'attachment' approach was discussed.

The individual of group I, who reflects ‘secure’ attachment, experiences relationships during his youth with little disappointment, which s/he interprets as negligible, thus confirming his expectations. S/he thus reacts by maintaining his/her original (i) expectation, (ii) feeling and understanding, (iii) consideration, and (iv) disposition to others. During adulthood, this individual will be in equilibrium. In fact, since s/he is able to foresee others’ dispositions, s/he closely relates to people with D^M_a , so that his/her expectations are confirmed, given that r^e_a =r_a =1 [26]. S/he regards the market good as complementary to the relational good, so that the greater consumption of market goods made possible by technical progress appears instrumental to better relationships.

Table 2. The three groups and their reactions to disappointment in relational goods

The individual of group II, who reflects ‘preoccupied’ attachment, experiences medium disappointment, which he interprets as confusing. S/he thus (i) downwardly adjusts his/her expectation ( r^e_a) towards the past experience of relational goods (ry), (ii) becomes unable to feel human relationships accurately, (iii) cautiously reduces the consideration of relationships, fearing further disappointment, and (iv) experiences a reduction in his/her disposition to others. During adulthood, this individual experiences further disappointment because s/he is involved in relationships only with those people who have experienced medium or severe disappointment during youth (group II, and, as will be seen, group III), and who exhibit D^m_a , thus yielding

If the model allowed more periods for the adults, the individuals of group II would adjust r^e_a asymptotically.[27] The rise in σa may approach the case where market and relational goods are independent goods. Finally, the individual of group III, who reflects ‘avoidant’ attachment, experiences severe disappointment, which s/he interprets as plainly contradicting her/his expectations. S/he thus (i) minimises her/his original expectation, (ii) becomes unable to feel human relationships, (iii) reduces the consideration of relationships even dramatically, and (iv) experiences a reduction in her/his disposition to others. During adulthood, this individual experiences confirmation of her/his adjusted expectations, although this is regarded as unimportant. In fact, like the individuals of group II, s/he is involved in relationships only with those people who have experienced medium or severe disappointment during youth (groups II and III). Therefore, s/he experiences which is what s/he has expected. Since s/he regards the market good as substituting well for the relational good, the greater consumption of market goods made possible by technical progress no longer appears instrumental to better relationships, but rather as an end in itself.

The experiences and reactions of individuals are thus captured by the level and the change of r and σ, which determine the level and the change of U and L. Table 3 collects all the results, drawing especially on Table 1 in Section 4.1, and on the Appendix.[28] The first row refers to youth, the second row to adult, the third row to the passage from youth to adulthood. Obviously, the superscripts I, II, III attach the symbols to the different groups.

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The main results are that:

- group I yields the highest level of utility in both periods of the life cycle, and the smallest amount of working time;

- group II yields the lowest level of utility in adulthood, whereas group III yields the greatest amount of working time;

- on passing from youth to adulthood, group II exhibits a reduction of utility, whereas group III exhibits an increase of utility.[29]

Therefore, in the aggregate, within the span of one generation, technical progress allows production and consumption of market goods to increase, while utility (or well-being) may increase or decrease. Market goods and relational goods may be largely independent, so that labour input may not change greatly. The model is thus able to explain the well-being paradox within a generation of people, depending on the values of the parameter σa, and on the relative size of three groups.

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26 This result can also be obtained by assuming that little disappointment during youth allows the individual to develop such vitality as to interpret even greater disappointments during adulthood as negligible.

27 If column (ii) and the underlying arguments were dropped, the conclusion would be the same on considering a sufficiently negative (and partially unaware) influence of reduced disposition on r.

28 When the change of ra is negative, and the change of σa is positive, the resulting change of U is ambiguous. Numerical simulations are employed in the Appendix to show the results.

29 The change of utility from youth to adulthood is equally burdened for all groups by the additional labour required for youth’s consumption in the household. This might account for the negative effect of children on wellbeing (see section 3.3).

By Prof. Maurizio Pugno

Next: Aggregate dynamics through generations

Summary: Index