It has to be said up front that this book is not for the faint of heart. As is the case for a lot of Becker's research, it can be quite mathematical. However, if you are able to look beyond the maths, there are lots of interesting insights to be drawn. For instance, in Chapter 5 they look at the effects of neighbourhoods, where the quality of the neighbours matters. Home buyers are attracted by both the quality of local amenities, and the quality of neighbours. The implication of that model though, is that if local amenities improve in quality (or quantity), that will attract better quality neighbours. If we believe this model, then using hedonic demand models to estimate the value of local amenities must necessarily overestimate their value, because a change in house prices arising from a change in amenity will reflect both the value of the amenity plus the value of the change in the quality of neighbours. I don't believe that I have seen anyone engage with that implication within the hedonic demand literature.
They also demonstrate how a small difference in the quality of art or antiques can lead to a large difference in price. We might think of this as a 'superstar effect' in the art market. They also show how a fashion market with leaders and followers can lead to an upward sloping demand curve in some price ranges, where the price has fallen enough so that some followers can start to purchase the good, but because of its increasing popularity, many of the leaders stop purchasing.
Despite the mathematical foundations, Becker and Murphy write in a style that is reasonably easy to follow and for the most part they explain their reasoning well. The one exception I found is where they argue in Chapter 8 (written with Ivan Werning) that people with higher status have higher marginal utility of consumption (or income). Although this is an important assumption that drives the results in that chapter (and later, in the chapter on leaders and followers), it isn't strongly justified. They do offer this later in the chapter:
...complementarity is necessary to explain the observed positive relation between consumption and status among competing individuals. Without gambles, there would be a compensating differential for higher status, so that persons with higher status would have lower consumption and the same utility as others.
I can see the argument for consumption and status being complementary because it leads to the theoretical results, but I would have liked to have seen more explanation of the authors' reasoning underlying the assumption. This seems too much like working backwards from the conclusion to identify the necessary set of assumptions.
This book itself should be seen as complementary to George Akerlof and Rachel Kranton's excellent Identity Economics (which I reviewed here), which is less mathematical and admittedly doesn't cover quite the same ground. However, readers of one could not doubt enjoy greater insights by reading both books together. Nevertheless, for readers with a reasonable background in economics looking to understand some utility-based theory on how social relations might affect markets, by itself the book provides a good grounding.
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