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Article Excerpt
When designing price contracts, one of the major questions confronting managers is how many blocks there should be in the contract. We investigate this question in the setting of a manufacturer-retailer dyad facing a linear deterministic consumer demand. Theoretical marketing models predict that the manufacturer's profits rise dramatically when the number of blocks in the contract is increased from one to two because both channel efficiency and its share of channel profits increase. However, increasing the number of blocks to three yields no incremental profits.
We test these predictions experimentally and find that increasing the number of blocks from one to two raises channel efficiency but not the manufacturer's share of profits. Surprisingly, having three blocks in the contract increases channel efficiency even further and also gives the manufacturer a slightly higher share of profits. We show that these results can be explained by a quantal response equilibrium model in which the manufacturer accounts for noisy best response due to nonpecuniary payoff components in the retailer's utility. We also show that the retailer is sensitive to the counterfactual profits it could have earned if it were charged a lower marginal price for earlier blocks in the multiple-block contract.
Key words: quantity discounts; price contracts; quantal response equilibrium; experimental economics; behavioral economics
1. Introduction
One of the most challenging issues marketing managers face today is how to design price contracts: When should a firm adopt a simple linear price contract, and when should it use a more complex nonlinear contract? Furthermore, because there are many types of nonlinear price contracts available, which of these contracts should the firm choose? Specifically, what is the optimal number of blocks, or marginal prices, in a price contract? The "number of blocks" question is important because it is one of the key variables managers must consider when designing a price contract. A one-block price contract is simply the linear price contract. Contracts with multiple blocks and declining marginal prices are quantity discounts called multiblock tariffs. (1) Multiblock tariffs are also further differentiated by the number of blocks in the contract: If there are two blocks, the contract is known as a two-block tariff; if there are three blocks, it is called a three-block tariff; and so on. How does the number of blocks in a price contract affect the profits of a firm?
The answer to the above question depends on the environment under which the price contracts are used. In the environment of a manufacturer-retailer dyad facing a deterministic final demand, the number of blocks in a price contract affects the firm's profits in a specific way. Marketing models predict that the total profits appropriated by the channel increase when the number of blocks in a price contract increases from one to two (Jeuland and Shugan 1983, Weng 1995, Kolay et al. 2004), but would remain unchanged when the number of blocks increases from two to a higher number. Moreover, the manufacturer's share of the total profits is predicted to rise to 100% when the number of blocks increases from one to two, and remains unchanged as the number of blocks increases further. The above predictions carry over to an environment when the firm faces a homogeneous consumer segment: Both the total surplus (firm's profits and consumer surplus) and the firm's share of the total surplus increase as the number of blocks in the price contract changes from one to two, but remain constant thereafter even as the number of blocks increases. However, if there are many segments of consumers with different demand schedules, then theoretical models predict that the firm's profits increase with the number of blocks in a multiblock tariff, albeit in a declining fashion (Murphy 1977, Dolan 1987, Wilson 1993).
The above theoretical results are extremely valuable to managers because they dramatically simplify the decision complexity involved in designing a price contract. For instance, these results imply that managers need not "think beyond two blocks" when designing quantity discounts to coordinate a channel. Nevertheless, the value of these theoretical predictions has not been empirically validated. The reasons for this are apparent: To construct a causal test of these predictions in the field, researchers would have to ensure that all of the structural assumptions underlying the theoretical models (be it the channel structure or the price-setting process in the channel) are satisfied, and field data that are relatively "clean" are difficult to come by. This suggests that controlled laboratory experiments where decision makers are induced to have values over outcomes and are motivated by monetary incentives, might be an appropriate tool for conducting such an empirical test. (See Amaldoss et al. 2000, Amaldoss and Jain 2002, Amaldoss and Rapoport 2005, Srivastava et al. 2000 for examples of such success in marketing.)
Another reason it is important to test these theoretical predictions is because they rest on certain assumptions that have been increasingly challenged in behavioral economics, a field that incorporates boundedly rational behavior into formal models in economics (Ho et al. 2006a, b). Specifically, a sharp feature of the optimal price contracts that drive the above predictions is that they are designed so that the firm's customers will always purchase an optimal quantity in the "correct" block. This type of customer behavior is guaranteed as long as the firm offers the customer a payoff level such that the optimal purchase quantity in the "correct" block is just higher than the payoffs earned by purchasing in other blocks. The two underlying behavioral assumptions in this case are that customers (1) care only about their pecuniary payoffs and (2) are best-responding to differences in pecuniary payoffs across different blocks in the contract. However, these assumptions might be unnecessarily restrictive because customers might have latent components of utility that are not reflected in their pecuniary payoffs (McKelvey and Palfrey 1995). One example of these nonpecuniary components might be counterfactual payoffs that they could have received (Camerer and Ho 1999, Camerer et al. 2002, Ho et al. 2007). For example, customers might dislike paying different marginal prices for the same product and compare their payoffs to a case in which they pay a lower marginal price for all units of the product. The main implication is that if any of these behavioral assumptions is relaxed, then the resultant optimal number of blocks in a price contract might differ from that which is prescribed by standard theoretical models.
This paper contributes to the marketing literature by using experimental economics methodology to examine empirically whether the number of blocks in a price contract matters to firms. As a first step, we test the theoretical predictions in the simplest possible setting--a manufacturer-retailer dyad facing a linear deterministic demand function. In our experimental treatments, we vary the number of blocks in the price contracts from one to three. The contracts we chose for the multiple-block treatments are the two-block and three-block tariffs because they belong to the format of nonlinear price contracts that have been studied most extensively (Wilson 1993). The theoretical predictions we test are (1) the total profits appropriated by the dyad increase when the number of blocks in a price contract increases from one to two; (2) channel profits remain unchanged when the number of blocks increases from two to three; (3) the manufacturer's share of the total profits increases when the number of blocks changes from one to two; and (4) the manufacturer's share of channel profits remains unchanged with a three-block contract.
The experimental results indicate that while increasing the number of blocks in a price contract from one to two does increase channel efficiency, increasing the number of blocks from two to three raises channel efficiency even further, contrary to theoretical predictions. Moreover, the manufacturer's share of profits does not rise significantly with the addition of more blocks in the contract. We show that this pattern of results can be better explained using a quantal response equilibrium (QRE) model (McKelvey and Palfrey 1995, Baye and Morgan 2004). The QRE model allows for noisy best response by the retailer so that it need not choose to buy in the block that yields the highest pecuniary payoffs all the time (i.e., the retailer "better," instead of "best," responds to its pecuniary payoffs). We also hypothesize that a component of these nonpecuniary payoffs in the retailer's utility is the retailer's sensitivity to the counterfactual payoffs it forgoes due to the difference in marginal prices across blocks. In such a setting, the retailer will prefer the three-block tariff because an additional block with an intermediate marginal price reduces this disutility. The manufacturer incorporates the retailer's behavior into its profit maximization problem and revises its equilibrium contract offer accordingly. The structural model that incorporates quantal response and the role of counterfactual payoffs yields two additional parameters and nests the standard model as a special case. We estimated these two behavioral parameters from the experimental data using maximum likelihood methods. The results strongly support the presence of latent payoffs in the retailer's utility and indicate that every counterfactual dollar is worth about one-fifth of an actual dollar.
This paper proceeds as follows: In [section] 2, we present the predictions of theoretical marketing models regarding how the number of blocks in a price contract can affect profit outcomes in a channel. The specific contracts we examine are the one-block linear price contract, the two-block tariff, and the three-block tariff. We then state the hypotheses to be tested. The experimental design and the results are discussed in [section] 3. In [section] 4, we present the QRE model and discuss the role of counterfactual profits in the multi-block tariff. We then present the results of the estimated model. Section 5 concludes the paper with a discussion of the research and managerial implications and some limitations of this paper.
2. Predictions of Standard Theoretical Models
There has been extensive work in marketing on how different types of price contracts can affect firms' profits in a channel. Jeuland and Shugan (1983) were the first to show that if firms in a manufacturer-retailer dyad facing a deterministic final demand adopt a one-block linear price contract, then the total profits of the firms are less than that achieved by a firm that is vertically integrated. However, they showed that if the channel members can adopt more complex price contracts such as a quantity discount, they can coordinate the channel and achieve the same level of total profits that can be appropriated by the merged firm. (2) The quantity discount schedule they derived was format free, that is, the number of blocks in the contract was not explicitly specified. Weng (1995) was the first paper that addressed the issue of the number of blocks in a price contract in a channel setting. His model is slightly different in that final demand is stochastic instead of deterministic. He demonstrated that the number of blocks in...
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