This brief section, "Of the Effect of Utility upon the Sentiment of Approbation", serves to address the influence which utility exerts on aesthetics and morality. This discussion is short because Smith's only real goal here is to refute the belief, held by some, that morality is derived from the utility of an action in relation to society and the individual.
First, Smith assesses the way in which utility impacts the beauty which people perceive in objects and systems. He argues that objects which appear to make their users' lives easier are made more valuable by virtue of people sympathizing with the owners of these objects; for example, someone might value a palace because of the imagined relaxation and satisfaction that such a palace would give its owner. Smith uses this logic to explain why people collect useless trinkets, enamored with their utility even though these items are never actually used (e.g. pocket watch collections).
Smith also says that this notion of utility is part of the reason why people aspire to be wealthy. Smith offers here an argument which is famous on account of its later presentation in The Wealth of Nations: people mistakenly value wealth because they think it can make them far happier than it actually can. This explains where the industrious spirit of lower-class people comes from, and also where the inclination of the wealthy to increase and tend to their wealth comes from. Yet people only have limited appetites, regardless of class, and so the surplus resources and wealth which the wealthy require their servants and dependents to generate ends up being distributed among those lower-class people who helped to produce such wealth. So, as Smith says, people pursuing their own interests in this case ends up producing the distribution of wealth and security which is most comfortable for everyone, as though an "invisible hand" were guiding the economy (182).
Additionally, Smith says, many patriots act out of love of the beauty perceived in the utility and efficiency of the political systems of their countries. Because of this, people of public spirit and people of humanity often do not understand each other, because the former care about efficiency and utility whereas the latter sympathize purely with the sentiments of individual constituents. For the utilitarian to understand the humanitarian, Smith suggests making utilitarians more aware of the efficiency to be gained when systems and people conduct themselves in accordance with propriety. For the humanitarian to understand the utilitarian, he suggests describing to humanitarians the ways in which governmental functions and systems are conducive to the happiness of society, when they run efficiently.
Smith does not believe that it is reasonable to conclude from all this that utility is the foundation of moral approbation and disapprobation. He believes that there are two particular reasons why such an argument cannot hold: namely, that morality is something fundamentally different from aesthetics, and that utility is usually an afterthought in moral decisions, not the driving force behind them.
The first point harkens back to Smith's argument that moral sentiments are endowed by God: such sentiments are different from aesthetic responses because aesthetic objects are the products of human design, whereas God designed our sentiments for the purpose of the harmonious goodness of society. Though our sentiments may, because of God's design, end up serving the utility of society, this does not mean that we act morally because of that utility. That is the precise error in attribution of cause which Smith discussed in Part II, in regard to God's design of our adherence to the principles of justice.
Smith's second point reinforces this. If we were to act primarily out of utility, all reason would provoke us to act out of self-interest. Yet we see people act upon the virtues of generosity, humanity, and self-control, sometimes even sacrificing their lives for others or for the glory of a nation. These observations all suggest that we act out of sympathy with society, seeing ourselves as society does rather than from the perspective of automatic self-preservation. We are compelled to act in response to the duties placed upon us by conscience.
This is the moment in the treatise which most clearly foreshadows the economic theory of free trade laid out in The Wealth of Nations, as evidenced by Smith's use of the invisible hand analogy. Though Smith obviously values virtue as expressed through duty and wisdom, it is clear that he has immense respect for the principle of utility. Indeed, economic ambition is largely built upon the illusion of how useful wealth is to a person, whose needs of security and good health can in fact be met without the sort of enormous wealth desired.
There is much to be said about the economic ramifications of the invisible hand idea, most of which is outside the scope of Smith's moral treatise. Suffice it to say, the "trickle-down" economic theory which this idea suggests (i.e. that the wealth created by the rich getting richer enables everyone to get richer) is predicated upon a quality of moral decency in the rich. If the rich are corrupt, they will gladly horde all the wealth which they generate, and will mistreat those who help them to produce it. What's more, as Smith himself says (particularly in the next part of this treatise), the rich and those of status are in a unique position: they have the public's favor by virtue of their class, and can therefore bend the rules of society more often and more easily than an average citizen can. Smith's invisible hand, while reasonable in theory, seems to put a grand amount of faith in human nature.
One ought to consider, in response to Smith's views on utility and approbation, that there is another school of thought, which maintains that people can act in society's interest but still be motivated by self-preservation or self-advancement. This occurs on a level which is purely evolutionary and is not accessible to the conscious mind. This would also be a perspective which an updated Smith would probably have to find a way to refute.
Nonetheless, Smith raises a good point about moral choices. When you are put in an immediate moral dilemma -- say, someone you love is in danger -- and you are required to act quickly, are you genuinely capable of calculating the utility of your actions? Note that this is an entirely different matter from whether or not utility is a good way of resolving moral dilemmas: Smith is only asking where our moral sentiments originate. After all, he believes that all that we need to do in order to be moral is to follow our naturally moral instincts and avoid corruption. Thus, the matter of utilitarian moral calculus is of little concern to him here.