Quality Adjustment in Non-spanning Markets with Variety Aversion
© K. Nishimura; licensee Springer 2013
Received: 17 February 2013
Accepted: 20 June 2013
Published: 9 July 2013
This paper examines the dynamic process of quality adjustment in cases where the economy lacks a sufficient number of markets for coordinating the level of attributes that configure the qualities of products. It shows that an adjustment process through the development and selection of commodities with different qualities may succeed in achieving efficiency or at least, meet the necessary conditions for efficiency. This is true if the user can identify with the altered product and is unaffected by variety in the commodity. It also holds true when the consumer assesses product variety in a smooth (differentiable) function, but not necessarily so if the assessment is non-smooth regarding the homogeneous state. An unidentifiable case can also be subject to inefficiency as the effort of a small quality adjusting agent becomes attenuated.
JEL Classification:L15, H23, O33.
Many transactions in a product supply chain involve quality coordinations among vertically differentiated intermediate commodities. For example, manufacturers of turbine engines are selective about the performance of turbine blades, whereas producers of the blades focus on cost effectiveness that is better quality blades at lower costs. Similarly, the recycling industry will be affected by the recyclability of the secondary (recycled) inputs, which is controlled by the producers of primary products. The quality adjustment process described hereinafter is therefore somewhat in the same vein as the demand-driven technology evolution, as discussed in Adner and Levinthal ().
Based on the Lancasterian consumer theory (Lancaster ), quality is usually treated as the bundle of objective characteristics (attributes) of a commodity for which the consumer holds positive values.a This paper is concerned with commodities that are vertically differentiated by objective quality: In other words, better quality is preferred by all users (consumers) if the commodities are sold at the same price. For example, PCs with a fast processor and a relatively slow processor are vertically differentiated, whereas chocolate and vanilla ice cream are horizontally differentiated because they are equally priced.b
Quality can be subject to externalities when product attributes lack their individual markets. Attributes generally do not retain the excludability property that a normal commodity has in theory due to their bundledness, rendering the independent coordination of attributes impractical. While excludability being one of the characteristic of a public good, Leland () and Dreze and Hagen () indicate that for quality choices, individuals’ private assessment (i.e., the Lindahl price) of attributes are needed when the implicit market of attributes is incomplete. Conversely, these studies claim that if every attribute’s implicit price spans the explicit competitive prices of goods, the (first-order) conditions for efficiency are met.
This study focuses on cases in which the market of attributes forms an incomplete, non-spanning structure, and thus quality is partially or completely external to the economic coordination system. Given these circumstances, the study posits that producers follow a quality adjustment process based on trial-and-error, that is, they adjust the quality in accordance with demand in order to predominate the product market with improved quality. The idea is parallel to previous studies on dynamic search processes, such as Callander () under conditions of uncertainty and Sato () for public goods. Nevertheless, it was Jwa () who studied quality development in vertically differentiated products, assuming the price of quality being available.
Jwa () also pointed out the reduction in variety by the nature of competitive equilibrium, resulting in a single homogeneous quality across products. Similar issues have been addressed in Nishimura () about the quality of secondary materials in the recycling industry. More recently, from a slightly different perspectives, Brun and Pero () analyzed a firm’s decision to reduce its variety of industrial products. Such a reduction in the vertically differentiated variety is essentially equivalent to being variety averse, discussed in a number of empirical studies (e.g., Levav et al. ; Kaiser ). The essential problem is that products need differentiation to enable the selection of a better quality product, while it is refused to diversify after one being selected.c
In this paper, a model of quality adjusting process under non-spanning structure of implicit markets over the attributes is presented. Change in quality is controlled by the assumption that a competitive producer not only maximizes profit by taking the price of product, but also alters the quality (or that of the attributes) with the speculation that a product with a different quality (and corresponding price) can lead the market. The benchmark model deals with cases in which the buyer of a product is indifferent to the heterogeneity in product quality. The buyer chooses the quality altered product if the product with marginally altered quality is more valuable to him or her relative to the marginal cost of altering the quality, which the seller adds to the price of the product.d The new product will then dominate the market, thereby improving the quality in the market.
The steady state of the benchmark process is shown to satisfy the necessary conditions of efficiency. However, this is not the case when heterogeneity in product quality matters to the buyer. For example, intermediate and recycling industries typically use bulky inputs for production, and thus consistent quality is often preferred. However, if the producer of an upper stream industry alternates the quality of its product, the lower stream industry would consequently face heterogeneous inputs. This study presents several cases of buyers’ preference for homogeneous/heterogeneous quality. It shows that even when products with varied quality are differently priced, the quality adjustment procedure may not function when the variety assessment of the buyer is non-smooth around the center. Cases where heterogeneous products are assessed with a flat price could lead to inefficiency because the smaller the producer, the more its effort become attenuated.
The rest of the paper is organized as follows. Section 2 briefly specifies the spanning property in the implicit markets for attributes, and by doing so, focus on the equilibrium state of a non-spanning economy where some attributes are external to the economy. Section 3 outlines the foundations of the quality adjustment process driven by one of producers (a speculator) seeking alternating price-quality combinations in a non-spanning environment. Subsequently, the case of a consumer without distastes upon heterogeneous products is discussed. In Sect. 4, we consider cases where the consumer is variety averse, that is, the consumer/user prefers consistent product quality. Section 5 is devoted to demonstrating the results with a simple model of a recycling economy. Section 6 concludes.
2 Market Structure
2.1 Spanning Economy
We begin with a simple general equilibrium model of a Lancasterian economy that incorporates the essential features needed for the subsequent discussions. We use the term “commodities” to designate goods and services subject to actual market transactions. There are N types of commodities, indexed and Z types of attributes indexed . The quantity of j commodity is represented by , while the whole set of commodities is represented by a vector . Similarly, the amount of i attributes within the whole economy is represented by and the set of attributes is represented by . denotes the amount of attributes i per unit of commodity j, hence by definition and A denotes the matrix with the typical entry being . Therefore, the quality of commodity j can be represented by a vector of the quantity of attributes .
and so forth to save space.
As it is evident from these equations, we need and a right inverse matrix to exist, to assure that the commodities market equilibrium will reach a state of efficiency; however, this would be possible only if and the matrix is non-singular. These conditions are otherwise called the spanning property (Leland ) of the implicit market for attributes.
2.2 Model of Non-spanning
These terms are however insufficient with respect to the first-order conditions for economic efficiency. Non-spanning is indeed the case when the economy fails to coordinate multiple items with a single price.
3 Quality Adjustment Process
Assumption (Base model)
There is a producer called speculator in the member of the industry who challenges the commodity market by altering the quality of the commodity being produced.
The speculator will challenge the commodity market, not only with the quality, but also with the price that equals the marginal cost of the quality altered commodity.f
The consumers observe the quality and price of the speculator’s commodity and decide if it is advantageous for them, and whether to alter their consumption by purchasing the quality altered commodity.
The consumers are variety neutral, that is, their assessment is only of the speculator’s commodity and unaffected by other commodities.
If the new quality altered commodity is accepted, all the other firms will follow the speculator, and the market will again have homogeneous quality and price. If not, quality and price will remain unchanged.
Under the above assumptions, it is possible to infer the marginal price-quality assessments between supply and demand by observing the consequences of the consumer’s accept or refuse decision without knowing the actual curvatures of ϕ and ω, which cannot be observed.
4 Variety Averseness
In this regard, we take on the supply side for granted, with a speculator being one of many producing firms with identical technology. We therefore stay with ω to denote the marginal cost of producing commodities, and consequently perceive that ; however, the willingness to pay ϕ is not same.
The variety assessment function V measures the variety of the commodities in terms of the entries, namely, the speculator’s commodity σ, the quantity share of the speculator ξ, the quality of the remaining commodity , and the quantity share of the remaining commodity . Notice that by definition. The consistence preference is accounted for by η where a negative value designates variety averseness. The consumer’s evaluation of the speculator’s commodity therefore accounts for the quality of the corresponding commodity as well as the variety effect, as shown above.
4.1 Smooth Variety Assessment Function
This is a smooth (quadratic) function, that is, the function is differentiable with respect to all variables including σ.
4.2 Nonsmooth Variety Assessment Function
according to (21) and (22).
4.3 Unidentifiable Case
Notice that designates the fraction of the speculator’s market share.
5 Example: Recycling Economy
5.1 Brief Description of the Model
5.2 Speculator and Variety Averseness
Note that this process is essentially identical to the previous function (15).
Parameters in simulation cases
Figure 7 illustrates case 2 when the recycler is variety averse (), while the recycler’s variety assessment is with a smooth function (). As illustrated, the descent direction of the ceteris paribus net price is the same as that of the mutatis mutandis net price π which is destined to , in the neighborhood of . It can also be noted that this is true for any , provided the variety assessment function is smooth (). The non-smooth case, , is illustrated in Fig. 8. The descent direction of the ceteris paribus net price in this case is oriented not toward but toward , indicating that the recyclability adjusting process will fail to achieve the socially preferred state.
6 Concluding Remarks
The Japanese saying “the pile that sticks out gets hammered down,” essentially means that a person who stands out too much is subject to reprisal (or assimilation). In our model, we found that a producer seeking the opportunity to ameliorate its product can face reprisal due to the non-smooth variety aversion of the consumer. At the same time, we also found that this is not the case if the variety assessment is with a smooth function and the speculator’s strategy will lead to a state of efficiency.
The quality adjustment of producers based on trial and error discussed in this paper can be relevant when the economy lacks a sufficient number of commodity markets for all the attributes (and therefore quality) to be coordinated indirectly. Such a non-spanning structure can be typical in the markets of intermediate commodities with many inseparable attributes. Contrasted with final products purchased by end consumers with different tastes and a preference for variety, the market for intermediate commodities tends to contract as inputs of different quality are often perfect substitutes in production.
Producers, perhaps through research and development, change the quality of their product in pursuit of prosperity on the basis of trial and error. A consumer’s implicit valuation of the attributes are learned by the speculator and, eventually, by all providers through the consistent quality-price movement of the commodity. The implicit value of attributes, although not quite as efficient as the Lindahl price, is the necessary information for achieving economic efficiency. A quality adjusting producer and a variety averse consumer are perhaps the ones that are hammering out the technological structures of the economy.
where the last identity holds because of (32). Finally, (34), (13), and (9) gives the wanted result (14).
1 A characteristics approach has been extensively applied in the marketing and innovation metrics literature, using methods ranging from hedonic functions (i.e., Rosen ) to discrete choice models (i.e., McFadden ).
2 Horizontal product differentiation and the related models based on Hotelling () have been widely discussed in industrial organizations literature (e.g., Economides ; Shaked and Sutton , etc.).
4 It is assumed that a producer may not observe the buyer’s reservation price of quality, but may know its relativity with the asked price by observing the buyer’s decision.
5 The earned profits will be transferred to the representative consumer’s budget B, and thus we have the closed system.
6 The speculator is not a monopolist with the market power to dictate the price over the marginal cost; it is rather a marginal producer under competition as regards Assumption 5.
7 In this regard, we are implicitly assuming that a consumer evaluates quality differentiated commodities within the mixture of the commodities. For example, a firm’s evaluation of an English peaking worker, with respect to the firm’s productivity, will likely depend on the remaining workers’ speaking language. Similar features can also be found in the bulky transactions of intermediate commodities.
The author would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.
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