A Single Espresso, Please! Rationalizing Espresso Price Dispersion Across Italian Cities

This paper aims at providing an explanation of the observed espresso price dispersion across major Italian cities. The empirical evidence suggests a positive relationships between the average espresso price in a city and the number of coffee shops (normalized for the adult population) operating in that city. This finding is shown to be robust after controlling for GDP per capita and consumers.price index. We provide an interpretation of the empirical findings relying on a model of price competition delivering a continuum of Nash equilibria, where firms adjust the mark-up to offset the negative effect of any increase in their number.


Introduction
For the average Italian adult, drinking an espresso is not only a ritual, but it is most often a repeated ritual during the day. According to anecdotical evidence, espresso is the second most drunk beverage in Italy (water being …rst), dozens million cups being consumed daily.
A discerning consumer travelling from Northern to Southern Italian cities would probably notice a non-negligible fall in espresso prices. Actually, in major Italian cities espresso cups are priced in bars very similarly within cities and very di¤erently across cities. 1  Since the standard espresso drunk at the bar is a fairly homogeneous good, except for location, broad price di¤erences look surprising. Moreover, descriptives suggest a large variance in the average number of consumers per bar across cities. In particular, it turns out that higher prices are associated to lower number of clients (proxied by adult inhabitants) per bar. These facts give rise to interesting questions: why prices are so high in some cities and not in others? do consumers per bar play a role in explaining these large 1 In what follows we refer to "bar"to indicate a plethora of establishments selling co¤ee (co¤ee shops, cafeterias, pubs. . . ), excluding restaurants. More details are provided in Appendix A.1 describing the dataset. 2 Table 1.

Empirical results
Observing the raw data we detect the presence of a negative relationship between the price of the espresso and the average number of clients per bar.
The scatter plot of clients per bar and espresso prices displays a downward pattern that approaches the average price of 1 euro when clients per bar are less than 400. The relationship is con…rmed by the correlation coe¢ cient of 0:6292. 4 The total adult population is o¢ cially de…ned by ISTAT as residents of 15 years of age or above. Given the panel structure of our dataset, we estimate a Linear Probability Model with Fixed E¤ects using the following speci…cation: where t indicates the year, i the city and it represents the city …xed e¤ects.
For ease of interpretation of the following results, the variable Clients is measured in hundred clients per bar and GDPpc in thousands of euros.    shows that increasing the average number of clients per bar has a signi…cant and negative e¤ect on the price of espresso. In particular, an extra hundred clients per each bar is estimated to lead to an average decrease of 6.2 cents in 6 We included both GDP per capita and consumers'price levels among the regressors as they are not highly collinear.
the price of espresso. 7 The latter …nding is rather counterintuitive. There are two ways of thinking about it: either increasing demand per bar yields a fall in espresso prices or increasing the number of sellers for a given population of consumers increases espresso prices. This …nding calls for a theoretical investigation.

A suggested interpretation
To rationalize our empirical …ndings, we rely upon Dastidar (1995). His The market is supplied by a population of n 1 identical …rms. The product is homogeneous and its demand function is p = a Q; where Q = n i=1 q i is aggregate output p is price and a is a positive parameter proxying the size of the market. All …rms produce with the same technology, to which a cost function C i = bq i +cq 2 i =2 is associated, where c is a positive parameter, and b 2 [0; a). The pro…t function of …rm i is then The non-cooperative one-shot game takes place under complete, symmetric and imperfect information. The solution concept is the Nash equilibrium, which here involves all …rms setting the same price p 2 [p avc ; p u ] : At the 7 Appendix A.2 provides a robustness check of our conclusions. lower bound p avc ; equilibrium price equals average variable costs, so that …rms are indi¤erent between producing or not. At the upper bound p u ; the equilibrium price is such that …rms would be indi¤erent between playing p u or marginally undercutting it in order to capture the entire market demand.
The continuum of price equilibria is 8 where BN stands for Bertrand-Nash, and is a parameter whose range is Taking the partial derivatives of (3) w.r.t. n (treated as a continuous variable) and , we get The partial derivative (4) tells that, in the Bertrand-Nash equilibrium, an increase in the number of …rms unambiguously decrease market price. Partial derivative (5) reveals that the equilibrium price increases with at the same rate with which price decreases w.r.t. the number of …rms. Therefore, the isoprice curve in the space (n; ) is a straight line increasing at 45 . This amounts to saying that the price-setting …rms may compensate the negative e¤ect of an increase in their number by increasing : If the latter increases more than proportionately w.r.t. n, the equilibrium price increases.

Bridging evidence and theory
In our context, the assumption of cost convexity appears a sound one. In other words, the data-generation process relies upon the conjecture that the number of bars were not subject to any technological, demand or supply shock in the ten years time span considered: given the characteristics of the sector (very homogeneous product, very low technology, very customary clients) our conjecture and the resulting constant rate appears justi…ed.   (1) and (2) respectively. Column (1) shows that our results are extremely robust to the …rst of our new, reduced speci…cations.  The signs and signi…cance are comparable and even the magnitude of the e¤ects is almost una¤ected. The results are less encouraging when focusing on Column (2). In that speci…cation, covering years 2005 and 2009, the number of clients per bar has a positive e¤ect on espresso prices. The e¤ect, however, has a very small magnitude and it is not statistically signi…cant (p-value' 0:81). GDP per capita is also not signi…cant and all the e¤ects seem to be captured by the consumers'price level, that is highly signi…cant.
A look at the descriptives for years 2005 and 2009, however, seems to con-…rm the evidence provided in the main text. Figure 2 shows a weaker but negative relationship between the price of espresso and the clients per bar.
On top of that the correlation coe¢ cient between these two variables is still 0:6262. The regression results in (2), instead, might be a¤ected by the reduced number of observations when focusing only on two years.