یک مدل پویا از تبعیض قیمتی و مدیریت موجودی در بازار ماهی فالتون

We estimate a dynamic profit-maximization model of a fish wholesaler who can observe consumer characteristics, set individual prices, and thus engage in third-degree price discrimination. Simulated prices and quantities from the model exhibit the key features observed in a set of high quality transaction-level data on fish sales collected at the Fulton Fish Market. The model's predictions are then compared to the case in which the wholesaler must post a single price to all retailers. We find the added revenue the wholesaler receives from price discriminating to be small.

What are the benefits to a wholesaler of price discrimination resulting from privately negotiated prices versus posting a single price? At first glance, one might expect a fish wholesale market to be highly competitive. However, the Fulton Fish Market, with its storied history of mafia involvement, has substantial barriers to entry. These barriers to entry have caused an imperfectly competitive environment characterized by negotiated prices. Our aim in this paper is to measure the magnitude of the increase in profits resulting from price discrimination versus posting a single price. We solve and estimate a dynamic profit-maximization model of a fish wholesaler. Stocks of fish arrive every morning, and the fish must be sold within a relatively short period of time. Throughout the day, retailers arrive sequentially and randomly, but when a retailer shows up, the wholesaler observes his type and thus knows his price elasticity. Therefore the wholesaler can price discriminate across different types of retailers. The fish wholesaler is solving two problems simultaneously: (1) how to optimally price his stock of fish which is falling in value over time and is replenished only once a day; and (2) how to optimally price discriminate across customers with differing price elasticities. Our model is able to successfully match several key features of the Fulton Fish Market. In particular the model predicts, as we see in the data, that Asian retailers pay about 5 cents per pound less for fish than white retailers. More generally the model matches the mean and variance of prices with large differences in prices across different days as well as considerable intra-day price volatility. Overall, we conclude that the model is a reasonable approximation of the behavior of a Fulton Fish Market wholesaler. We then impose the restriction that the fish wholesaler must post a uniform price to all retailers, and is therefore unable to price discriminate. In this case, white retailers with inelastic demand pay lower prices and purchase larger quantities of fish. The more price-elastic Asian retailers pay higher prices and purchase less fish. From both types, the wholesaler earns less revenue. However the magnitudes are small. We find that posting a single price only generates about 6 dollars per day less revenue (about 15/100 of 1 percent of total revenue) compared to price discriminating. While our model is intended to provide an accurate representation of the behavior of a particular fish wholesaler, the problem of determining the optimal price of a stock of depreciating assets is a classic problem in economics and operations research. In operations research the study of dynamically pricing an inventory stock falls under the headings revenue management or yield management. 2 In the economics literature, work by Reagan (1982), Aguirregabiria (1999), Zettelmeyer et al. (2003), Chan et al. (2004), Sweeting (2008), and Copeland et al. (forthcoming) study the interaction between inventory management and pricing. Our model differs from these others in that the timing of new procurements of inventories is fixed though the quantity is stochastic. While these other papers focus on durable goods, such as automobiles and steel, or goods that expire at a pre-determined date, such as baseball tickets, hotel rooms and airline seats, our paper focuses on fish – a good that depreciates steadily but quickly. This paper proceeds as follows. In the next section we discuss the importance of price discrimination and previous papers that have highlighted discriminatory settings. In Section 3, we discuss the details of the Fulton Fish Market, the market on which our structural model is based. In Section 4 we develop our model, and in Section 5, we present our estimation strategy. We report our findings in Section 6 and conclude our analysis in Section 7.

We conclude that our model is a realistic approximation to the observed fish wholesaler's problem; however, like all models, it is a stark simplification of reality. It is possible that these simplifications non-trivially bias downward our computed cost of eliminating price discrimination. In the model, both prices and quantities are continuous variables, while at the Fulton Fish Market, prices tended to be quoted in 5 cent increments and fish were generally sold in 60 pound boxes. This endogenous discreteness may create kinks and non-convexities that create wedges between the prices it is optimal to charge Asians and whites. Since there is no physical reason for prices to be quoted in such coarse increments, this norm may provide a simple mechanism to limit bargaining and competition thus providing a greater opportunity to price discriminate. More importantly, the model assumes that the price elasticity for both races is constant across the entire demand curve. It may be that these elasticities are constant only along a portion of the demand curves. It may be that as quantity demanded gets closer to the minimum purchase size (i.e. 60 pounds), demand becomes more inelastic. If this is the case, our analysis underestimates the reservation prices, underestimating the value to the wholesaler of price discriminating. While the result that price discrimination yields very little additional revenue may be due to shortcomings of our model, it is also possible that wholesalers offer lower prices to their Asian customers because they worry that their Asian customers may exit the market completely and purchase all of their fish elsewhere. It is also possible that wholesalers continue to price discriminate despite the lack of evidence that it results in significantly increased revenue. Many of the wholesalers at the market have been operating for years. Indeed, the grandfather of the wholesaler from which the data were collected started his business in the 1920s. The way of transacting at the market is well-established and negotiated prices are the norm, based on history, despite any analytical evidence that these actually provide the highest revenue. Other fish markets, including the largest market, Skidjee in Japan, conduct business through an auction process. It is possible that negotiated prices resulting in price discrimination may not be the optimal way to sell fish, but that this method simply exists because of inertia.